The propagation of online rumors is rapid, and its propagation mechanism has always been a research difficulty. In this paper, the network rumors are compared to the nuclear fission process, and a network rumors propagation model is constructed. First, the initial online rumors are compared to neutrons, uranium nuclei are compared to individual rumor receivers, and fission barriers are compared to individual active propagation thresholds. Second, the process of nuclear fission is analyzed and the degree of energy accumulation is used to compare the social impact of online rumors. Finally, the online rumor propagation model based on nuclear fission is constructed. Through experimental simulation, it has been shown that compared to classic infectious disease models, this model can better describe the propagation process of rumors in social networks. Through research and analysis, suggestions for suppressing rumors have been proposed, providing new ideas and references for future researchers.

## I. INTRODUCTION

Internet rumors are prevalent in people’s lives. What is a “rumor”? According to the statistics of research literature, most of the researchers call them untrue, fabricated by people with intent, and baseless information.^{1–5} However, some scholars believe that rumors are not just negative false news but are also unsubstantiated news or interpretations.^{6–9} Based on the above studies, this paper argues that rumors are superimposed messages of false news and true news based on events. After propagation, they will trigger public opinion and bring certain negative social impacts, which can disturb social harmony and stability, economic development, and even national security. Therefore, it is of great positive social significance to study the propagation of Internet rumors, discover their propagation laws, and provide theoretical and practical support for blocking their proliferation.

The infectious disease model is a widely used theoretical tool to study rumor propagation on the Internet. The infectious disease model simulates the process of rumor propagation through the state changes of three groups: susceptible, transmitter, and immune, and has been continuously improved to make it closer to the process of rumor propagation in the real network. However, the infectious disease model is not yet able to truly reflect the rumor propagation in the network. This is mainly due to the fact that infectious diseases do not propagate actively, while rumors propagate actively, and the model ignores the rationality and subjectivity of the rumor spreaders; second, the infectious disease model only takes into account the changes in the group size, but not the resulting social impact and potential risks.

In this paper, through the analysis of the process of rumor propagation and the nuclear fission process, it is found that the two have similarities. Therefore, the neutrons produced in the process of nuclear fission are analogous to the rumor information propagating in the network, the uranium nucleus is compared to the individual audience of the rumor, and the nuclear fission potential is regarded as the decision threshold of whether the individual propagates the rumor or not. Then, the rumor propagation model based on the nuclear fission is constructed, and finally, the reasonableness and validity of the model are verified through simulation experiments. The model better reflects the individual decision-making process, quantifies the social impact of rumor propagation, and provides a theoretical basis and practical support for the governance of online rumors.

## II. RELATED STUDIES

Most of the current studies on rumor propagation are based on the infectious disease model for theoretical analysis and empirical validation.^{10} The D–K model proposed by Daley and Kendall in 1964 analogizes the process of rumor propagation to the process of infectious disease propagation and divides the group within a certain range into three categories: susceptible (S: those who do not know the rumor), infective (I: those who propagate the rumor), and recovered (R: those who know the rumor but do not propagate the rumor). Numerous scholars have expanded on this foundation (some have added node types, such as potential and rumor refutation, while others have introduced communication mechanisms, such as suspicion and anti-rumor), proposing the SEIR model,^{11} SIRS model,^{12} SIDR model,^{13} SC1C2IR model,^{14} SIR-CO model,^{15} and a series of other kinetic propagation models.

There are also scholars who view the rumor-propagating process, whether individuals propagate rumors or not, as an ideological game of users.^{16} Scholars have also constructed a tripartite evolutionary game between rumor mongers, network operators, and government officials.^{17–19} Indu and Thampi^{20} combined the wildfire propagation model in forests with rumor propagation and proposed a new nature-inspired algorithm, which can calculate the probability of nodes sharing information based on the identified salient features and, at the same time, measure the rumor propagation speed, and verified the feasibility of the method using two real datasets. Srinivasan and Babu^{21} proposed a new defensive rumor control method by analyzing the immune strategy of swarming insects to control the process of rumor propagation by propagating counter-rumors and proved that counter-rumor propagation is, indeed, an effective method to control rumors. Tan *et al.*^{22} proposed a rumor propagation model based on elastic collision (ECR model), which analogizes the propagation dynamics between nodes in OSN to the dynamics of elastic collision of small balls, and verified the validity of the model through the analysis of collision parameters. Tan *et al.*^{23} proposed a new OSN rumor communication model (GRP model), which takes users as the center, models the relationship between users and the communication relationship between users, considers the personalized characteristics of users, and finally, verifies the validity of the model through the real data of a microblog. Han *et al.*^{24} introduced the rumor process and network topological characteristics, proposed a rumor propagation model based on physical theory, and used heat energy to measure the impact of rumors on the network. Yanhui *et al.*^{25} established the CFDR propagation model of network rumors by considering the diffusion concentration of drug in the blood and the drug diffusion principle in drug kinetics, and they also considered the authoritative media intervention factors and the influence of time delay. Zhang^{26} with the application of physics perspective of mechanical wave propagation principle to describe the propagation process of network rumors, rumor makers as a wave source, the OSN a large number of Internet users as propagation medium, and consider the influence of the Internet propagation state, at the same time using CA (Cellular Automata) for single source and multi-source propagation simulation verification. In addition, some scholars have conducted research from different disciplines, such as BK seismic model,^{27} heat transfer,^{28} fluid mechanics,^{29} explosion mechanics,^{30} combustion theory,^{31} and common habitat model.^{32}

## III. NUCLEAR FISSION AND THE PROPAGATION OF INTERNET RUMORS

### A. The process of Internet rumor propagation

In the process of rumor propagation, rumor propagation is the forwarding of news, and individuals propagating rumors can be roughly divided into two groups: one group of individuals will forward the rumor immediately after receiving the rumor; the other group of individuals will think and choose rationally after receiving the rumor, but will forward the rumor after receiving it several times within a short period of time and being affected by the rumor continuously and deepening. These two types of individuals are differentiated by their intrinsic characteristics: those who receive rumors and immediately forward them are considered blind and irrational; those who receive rumors several times and are eventually influenced by them and forward them are considered rational.

What is more, when an online individual receives a rumor message, his behavior (e.g., reading, liking, and commenting) will have a certain impact on the retweeting behavior of the following individuals, which may further trigger public opinion and cause a certain degree of negative social impact.

### B. Nuclear fission processes

In nuclear fission, there are two main types of uranium nuclei: one is ^{235}U and the other is ^{238}U. In an even–even nucleus (^{238}U, that is, the number of protons and neutrons in the nucleus is even), protons and neutrons in the nucleus have a tendency to exist in pairs and the fission potential barrier is high and relatively stable. In an odd A nucleus (^{235}U, that is, the number of protons is even, but the mass number is odd), the fission potential barrier is low and unstable. After absorbing only one neutron, the nucleus of ^{235}U becomes unstable, decays, and releases neutrons, which can go on to hit other uranium nuclei, triggering a chain reaction. The fission potential barrier of ^{238}U is relatively high, i.e., absorbing a neutron will not break through its fission potential barrier to fission, and only after absorbing more than one neutron will it gradually become unstable. When neutrons break through the fission potential barrier of the nucleus, the fission occurs. The fission of the two types of uranium nuclei releases neutrons and energy and then degenerates into other substances that are no longer fissile.

### C. Nuclear fission and the propagation of Internet rumors

Based on the analysis of the process of rumor propagation and the chain reaction of nuclear fission, the chain reaction is established as shown in Table I.

Nuclear fission . | Internet rumor mongering . |
---|---|

Neutrons | Rumors |

^{235}U | Individuals who directly forward rumors |

^{238}U | Individuals who receive rumors multiple times and forward them |

Surface energy | Impact of stopping the propagation of rumors, e.g., reputation |

Coulomb energy (chemistry) | Enhance the impact of rumor propagation, e.g., interest value |

Energy released | Social impact from reading, liking, commenting, and other behaviors |

Nuclear fission . | Internet rumor mongering . |
---|---|

Neutrons | Rumors |

^{235}U | Individuals who directly forward rumors |

^{238}U | Individuals who receive rumors multiple times and forward them |

Surface energy | Impact of stopping the propagation of rumors, e.g., reputation |

Coulomb energy (chemistry) | Enhance the impact of rumor propagation, e.g., interest value |

Energy released | Social impact from reading, liking, commenting, and other behaviors |

## IV. CONSTRUCTING A MODEL OF ONLINE RUMOR PROPAGATION BASED ON NUCLEAR FISSION

### A. Dissemination rules

#### 1. Definition of Internet user status

In a microblog, online rumor propagation mainly relies on individuals sharing the rumor directly or forwarding it to the homepage. In this process, individuals may exist in three states: a state in which they have never heard of the rumor information, defined as the stable state; a state in which they receive the rumor and forward it directly to other people, defined as excited state; and a state in which, after forwarding the rumor, their interest in it decreases and they are no longer interested in the rumor, defined as ground state. Rational Internet users also have a special state due to their own nature, i.e., when they receive rumor information, their interest value is not enough to cross the propagation threshold, defined as latent state. The comparison with the state of the nuclear fission process is described in Table II. In order to simply simulate the real state, in the initial social network, we only define an excited state of the netizens and observe the state changes of the netizens in the social network.

State of the object . | The state of Internet . | |
---|---|---|

in nuclear fission . | users during rumor propagation . | Individual state . |

Not hit by neutrons | Never heard that rumor | Stable state (S) |

Receiving impacts and emitting neutrons outward | Receiving the rumor and actively forwarding it to friends | Excited state (E) |

Received impacts but did not cross the fission barrier and did not exude neutrons | The rumor is received but does not reach the propagation threshold and is not propagated outward | Latent state (L) |

End of neutron emission, back to stable state | Gradual loss of interest in the rumor during retweeting and no longer interested in the rumor | Ground state (G) |

State of the object . | The state of Internet . | |
---|---|---|

in nuclear fission . | users during rumor propagation . | Individual state . |

Not hit by neutrons | Never heard that rumor | Stable state (S) |

Receiving impacts and emitting neutrons outward | Receiving the rumor and actively forwarding it to friends | Excited state (E) |

Received impacts but did not cross the fission barrier and did not exude neutrons | The rumor is received but does not reach the propagation threshold and is not propagated outward | Latent state (L) |

End of neutron emission, back to stable state | Gradual loss of interest in the rumor during retweeting and no longer interested in the rumor | Ground state (G) |

#### 2. Rules for propagating rumors on the Internet

As can be seen from Fig. 1, when a blind individual in the stable state (S) receives a rumor, the individual becomes interested in the information, changes to the excited state (E), and propagates the rumor to the outside world; however, a rational individual does not forward the rumor to the outside world the first time he/she receives the rumor, but is doubtful and changes to the latent state (L), and repeats the receipt of the rumor before he/she changes from the latent state to the excited state (E) and chooses to believe it for forwarding. However, along with the propagation of information, regardless of whether the individual is rational or not, the interest value of Internet users gradually decreases and eventually transforms into the ground state (G), and no longer receives the information of the rumor and undergoes a state change.

#### 3. Changes in the status of rumor spreaders

The state transition diagram of the online rumor propagation model based on nuclear fission is shown in Fig. 2, and the transition probabilities between individuals are denoted by *α*_{1}, *α*_{2}, *β*, and *γ*.

### B. Dissemination models

#### 1. Theoretical analysis

In the field of infectious disease dynamics, the basic regeneration number is a central concept that describes the number of infected individuals to which an infected person can transmit the disease during his or her average infectious period in the initial phase of the disease when all individuals are susceptible. This value is often viewed as a critical threshold for the extinction or non-extinction of the disease. In view of this, this section will delve into the basic regeneration number in the rumor propagation system, the stability of the equilibrium when rumors do not exist, and the stability of the equilibrium when rumors do exist, and analyze them from a theoretical point of view.

There are two types of propagators in the nuclear fission-based rumor propagation model proposed in this paper, namely *L*(*t*) and *E*(*t*).

*F*,

*V*based on X, Y, and

*F*(

*L*,

*E*) and

*V*(

*L*,

*E*), respectively,

Because there will be a stable state when the proportion of rational individuals is large, *α*1 < *α*2; rational individuals receive rumor information from potential individuals and need to be contacted many times before they can be changed into the excited state for propagation, but the excited state individuals will eventually be transformed into the stable state, so *β* < *γ*. Based on the above analysis, the eigenvalue of matrix (5) is $\alpha 2S\beta >\alpha 1S\gamma $.

Therefore, this rumor propagation model corresponds to the basic regeneration number $R0=\alpha 2\beta $.

Equilibrium in the absence of rumors.

The model considers stable group sizes with no additional input–output share, so the rumor-free equilibrium point is $P0=1,0,0,0$, and the Jacobi matrix for this point is$J0(P0)=\alpha 2S\u2212\beta 0\beta \alpha 1S\u2212\gamma (1,0,0,0)=\alpha 2\u2212\beta 0\beta \alpha 1\u2212\gamma .$The eigenvalue of the solution is $\lambda 1=\alpha 2\u2212\beta ,\lambda 2=\alpha 1\u2212\gamma .$

Since

*R*_{0}< 1, i.e.,*α*_{2}<*β*,*α*_{1}<*α*_{2}<*β*<*γ*, we obtain*λ*_{1},*λ*_{2}< 0. According to the Routh–Hurwitz criterion, the rumor-free equilibrium point $P0=1,0,0,0$ is locally asymptotically stable when*R*_{0}< 1; at*R*_{0}≥ 1,*P*_{0}is unstable.The equilibrium point when rumors propagation.

Next, we make the differential equation zero,$dS(t)dt=\u2212\alpha 1\u2217S(t)\u2217E(t)\u2212\alpha 2\u2217S(t)\u2217L(t)=0,dL(t)dt=\alpha 2\u2217S(t)\u2217L(t)\u2212\beta \u2217L(t)=0,dE(t)dt=\alpha 1\u2217S(t)\u2217E(t)\u2212\gamma \u2217E(t)+\beta \u2217L(t)=0,dG(t)dt=\gamma \u2217E(t)=0.$The rumor epidemic equilibrium can be found at $P1=(S\u2217,L*,E\u2217,G\u2217)=(\beta \alpha 2,I*,E*,0)$, where $I\u2217=\u2212\alpha 1\alpha 2E*$.

Then, the Jacobi matrix of the point is$J1(P1)=\u2212\alpha 1E\u2212\alpha 2L\u2212\alpha 2S\u2212\alpha 1S\alpha 2L\alpha 2S\u2212\beta 0\alpha 1E\beta \alpha 1S\u2212\gamma (S*,L*,E*,G*)=0\u2212\beta \u2212\alpha 1\alpha 2\beta \u2212\alpha 1E00\alpha 1E\beta \alpha 1\alpha 2\beta \u2212\gamma .$The eigenvalue relationship of the solution is$\lambda 1=\u2212\alpha 1E<0,\lambda 2+\lambda 3=\alpha 1\alpha 2\beta \u2212\beta \u2212\gamma <0,\lambda 2\lambda 3=\beta \gamma >0S.$

From the eigenvalue relations of the solution, all three eigenvalues are negative, following the third-order Routh–Hurwitz criterion, and therefore, the rumor prevalence equilibrium of the model *E*_{1} = (*S*^{∗}, *L*^{∗}, *E*^{∗}, *G*^{∗}) is stable at *R*_{0} ≥ 1.

#### 2. Differences in the nature of individual Internet users

Individual differences among Internet users are a reality. The knowledge level of most Internet users cannot help them identify whether the information they receive is true or false, but they will take into account factors such as the entertainment nature of the information, the closeness of the sharer, and the relevance of their own interest, or the fact that this group of Internet users is willing to share information, and will forward the rumor to others the first time they receive it. However, there are also a small number of netizens who have a high level of knowledge in the area of the rumor, or their own character is more cautious and will not easily believe in the rumor, so there is a great possibility that they will not forward the rumor when they receive it for the first time, but when they receive the rumor many times from different people around them, they may choose to believe in the rumor, which will lead them to believe it. However, if they receive the rumor several times from different people around them, they may choose to believe that the rumor is true and share it.

Based on the study of the type of uranium nucleus that undergoes fission, a further analogy can be made between the fission of uranium nucleus and the process of rumor propagation, and the netizens during the process of rumor propagation can be divided into two categories: one category is blind netizens, who are extremely interested in the information and believe that the information is correct and that it does not require any cost for forwarding and propagating. All of these netizens, who are not exposed to rumors, can actively forward the rumors when they receive them for the first time and continue to send the rumors to other users in the microblog network, thus making the phenomenon of large-scale rumor propagation occur. The other category is rational Internet users, which are not sufficiently influenced to propagate rumors outward because of the influence of the user’s own factors (personality, status, psychology, etc.). For example, if the receiver is a cautious person or a person with high status and strong influence, he or she will first confirm the authenticity of the rumor after receiving it. This group of people values their reputation and wants to avoid doing anything to damage it, so they are unlikely to share what they believe to be false information as a credible sender.^{33,34} Or perhaps the receiver himself or herself does not like to propagate information to the outside world.

Therefore, this paper carries out two simulation experiments in the subsequent experimental process: first, assuming that only blind netizens (^{235}U) exist in the social network to simulate the process of rumor propagation without interference under the ideal state; second, assuming that both blind netizens (^{235}U) and rational netizens (^{238}U) exist in the social network, and adjusting the proportion of the existence of the two to carry out the control, in order to strive to be similar to the real state of the process of the network rumor propagation.

#### 3. Individual communication strategies

Rumor propagation is not just about the propagation of information, but more importantly about individual choices. When a netizen receives rumor information, whether to propagate it and how to propagate it are the strategic choices that the netizen needs to make. This paper analyzes this process based on the nuclear fission process.

The process of uranium fission, simplified, involves an unstable heavy nucleus absorbing a neutron from the outside, gaining a certain amount of excitation energy. It then crosses the fission barrier, transforming the originally stable nuclear state into an excited state, splitting apart and releasing some neutrons and part of the energy. At the same time, the neutrons released from this process can strike other heavy nuclei at high speeds and be absorbed by unstable heavy nuclei, continuing to split and causing a series of chain reactions. Thus, this triggers a series of chain reactions. Based on the above description of the nuclear fission phenomenon, this paper draws an analogy between the process of rumor propagation and the nuclear fission process, in which the Coulomb energy *E*_{c} and the surface energy *E*_{s}, which determine the fission or not of the uranium nucleus, can be regarded as the influences of netizens to enhance the rumor propagation and to stop the rumor propagation after receiving a rumor, respectively. When netizens receive rumor information, the two influences interact with each other to form netizens’ communication decision threshold.

When not exposed to rumor information, the value of netizens’ interest in rumors is 0. At this time, *E*_{c} = 0 < *E*_{s}, the influencing factor of not wanting to propagate rumors *E*_{s} is dominant, and netizens are in a steady state; when netizens receive information about rumors, they will be interested in the information to a certain extent, and at this time, the influencing factor of netizens’ wanting to propagate rumors *E*_{c} will rise. When *E*_{c} > *E*_{s}, the influencing factor of wanting to propagate the rumor dominates and netizens choose to propagate the rumor. Blind Internet users have a relatively low value of *E*_{s}, so as soon as they come into contact with the rumor information, they will forward it to the outside world. However, rational Internet users are influenced by their own factors, and the value of *E*_{s} is relatively high, and only receiving a rumor once will not increase their decision threshold, and every time they receive it, the value *E*_{c} increases, until it is greater than *E*_{s}, and then, rational Internet users choose to propagate it as well.

Based on the above analysis, it is assumed that the rumor information propagates by rounds and the number of rounds is recorded as *l*. Considering the existence of a propagation threshold, a state value *a* (*a* is an integer) is set for each individual, and when an individual receives a rumor message once, its state value is reduced by 1, and when its state value becomes 0, the propagation starts. Therefore, the state of each individual is represented by the number of rounds *l* and the state value *a*. The state of the stable blind individual, *S*_{1}, is represented as $S1l,1$ at the *l* round. Record *r* as rumor information.

*a*= 1. He/she changes state and propagates as shown below,

*a*≥ 2. He/she changes state and propagates as shown below,

*η*is the number of received rumors. As the state value changes each time a rational user receives a rumor message, when the difference between the number of received messages and the state value becomes 0, the rational netizen in the latent state changes to the excited state and chooses to propagate the rumor outward.

*E*

_{c}inevitably decreases gradually. When it decreases to a point where it is not enough to outweigh the factors that inhibit the propagation of rumors, netizens stop the act of rumors propagation to other netizens and stop receiving these rumors. In previous studies, some scholars have suggested that rumors are very attractive to people when they are not confirmed at the beginning of their propagation,

^{14,15}but as people repeat the output over and over again in social interaction, the attractiveness of the rumor to them gradually decreases, a process similar to the annealing model in physics.

^{24}So, we refer to the annealing algorithm in physics and consider the interest of excited state individuals in rumors as a function of time and the number of propagations, using the following formula to define that:

*T*

_{0}denotes the initial interest value of the netizen in rumors, i.e., the larger the value, the greater the netizen’s interest in rumors;

*k*represents the number of times the individual propagates the rumor; and

*φ*denotes the effect of each propagation of the rumor by the individual on the interest. According to this expression, the netizen’s interest value decreases with the time step and the number of times the individual propagates the rumor.

### C. Scale of dissemination

After the previous description, it can be found that the uranium nucleus absorbs neutrons and undergoes fission, thus releasing more neutrons. In this paper, the number of neutrons in the fission of the uranium nucleus corresponds to the number of rumor propagations in the social network, and netizens propagate rumors to others around them after receiving the rumors in the social network, triggering the “chain reaction” of the rumor propagation. Equations (9)–(12) can be used to observe the change in the number of rumor propagation in the process of rumor propagation.

*l*, and the rumor spreading multiplication factor

*k*is introduced, which is the ratio of the number of rumors propagated in the previous round to the number of rumors propagated in that round and can also be regarded as the number of individuals that propagate, and the specific calculation formula is

*fans*is the number of followers of the propagating individual,

*promotion*is the promotion quantity,

*activists*is the number of daily active users of the microblog,

*α*is the reading rate, and

*n*is the number of nodes in the simulated network. After the above calculation, the average number of diffusion of different groups can be found. From this, the formula for calculating the number of rumor propagates can be derived and the specific calculation formula is

*l*rounds of propagation. Currently, there are studies that propose the average time of rumor propagating once, set the approximate ratio of the number of the proliferation of rumor propagation, and use Eq. (12). The trend of rumor growth in a certain social network without any control measures can be obtained, and the result can effectively serve as a warning to the government and the public.

### D. Social impact

The reason why there is a need to control rumors is that they can be extremely burdensome to society when they are propagating on a wide scale, and then, it becomes particularly important to measure the impact of these rumors on society.

*T*

_{n}is the energy carried by the rumor,

*m*

_{n}is the nature of the rumor message itself, $MZ,A$ is the nature of the netizens who are about to receive the rumor, $MZ,A+1$ is the nature of the netizens who receive the rumor, and the three kinds of energies can be found by using mass–energy equations. $[mn+MZ,A]c2$ is the sum of the energy of the rumor message and the netizens who are going to propagate the rumor, $MZ,A+1c2$ is the energy value of the netizens after receiving the rumor, and

*E** is the energy value of the netizen after receiving the rumor except for the netizen’s own energy, and the specific components are

## V. EXPERIMENTAL SIMULATION

Based on the above description of the model, this section designs simulation experiments to realistically simulate the propagation of rumors in social networks and, at the same time, evaluate the impact on the scale of rumor propagation and the impact of rumor propagation on the society, as well as the impacts of various types of parameters on the propagation of rumors under the model, as deduced in Sec. IV.

### A. Simulation experiments

In order to validate the nuclear fission-based rumor propagation model proposed in this paper, this paper first generates an online social network with 500 nodes. The initially excited state rumor spreader is set to be only one, and the rest of the nodes are in the steady state, with a time iteration of 40 rounds. The following discussion examines the evolution of the number of Internet users in the stable state, latent state, excited state, and ground state over time.

#### 1. There are only blind netizens in the network

In the graph, the horizontal coordinate is the time and the vertical coordinate is the number of people. From Fig. 3, it can be seen that the number of users in the base state shows a fast-rising trend at the beginning and then gradually tends to be stable, and the value is close to the number of all Internet users, while the number of users in the excited state also grows rapidly at the beginning, but after reaching the peak, it rapidly declines until it tends to zero; at the same time, the number of users in the stable state is also declining with the rise in the number of users in the base state and the excited state. Ideally, when a netizen propagates the rumor information to the surrounding, if the surrounding people are irrational netizens, that is to say, after receiving the rumor, they will be extremely interested in the rumor information and then propagate the information to the surrounding people, and with the outward propagation time and time again, the value of the interest in the information decreases, and no longer continue to forward the rumor. Figure 3 can be a good fit for the change of netizens’ state during rumor propagation without any control.

#### 2. The coexistence of blind and rational Internet users on the Internet

In real life, there will not only exist irrational Internet users but a few Internet users who have some knowledge accumulation. The first time they hear the rumor information, they will be suspicious and will not immediately propagate to the surrounding crowd. We call this the latent state. Taking into account the existence of this type of crowd, we carry out the simulation as shown in Fig. 4.

With the results of this experiment, it can be found that the trends of the number of users in the steady state and the base state are similar to those in the ideal state, but there is an additional curve of the number of users in the latent state. The latent state Internet users receive rumor information from people around them, but do not forward it to the outside world for the time being, that is to say, the interest value that the rumor brings to them does not exceed the influence value that they do not want to propagate the rumor. By combining Fig. 3 with Fig. 4, it can be found that the peak value of the number of motivated netizens in this experiment is lower than that in the ideal state due to the presence of latent state people, and the time to reach the peak value is higher due to the presence of latent state people, which consumes part of the rumors actively propagating in the social network, so even if only a small number of the rational netizens exist, it still has a greater impact on the number of motivated netizens. Therefore, the experimental simulation with the presence of a fraction of rational Internet users is more in line with the rumor propagation in the real situation.

### B. Scale of rumor diffusion without interference

The formula for the number of rumors generated over time in a social network can be obtained, and through the study of the related literature, London, Jr. *et al.*^{35} analyzed the statistics of a large amount of rumor data, concluded that most of the rumors stop after the second propagation, and pointed out that the average propagating time of rumors is 21.03 min. Bringing this research conclusion into the rumor propagation scale formula, the simulation results are as follows.

From Fig. 5, it can be concluded that rumors grow exponentially in the absence of external factors. It is often easier to propagate information with negative connotations, such as sadness and horror.^{35,36} However, the scale of such propagation is very scary, and it may only take a few short jumps to propagate to a very large group of people, which is also very consistent with the “small world theory” we know.

Figure 5 shows that the scale of propagation is actually very small in the first 15 times of propagation, and these 15 times of propagation take only 5.25 h, which also provides a certain warning that we have to take certain measures at the initial stage of rumor propagation. The government and the media have to carry out supervision, and once the first signs of rumors that may develop into rumors are found, timely verification and guidance have to be carried out so as to avoid false rumors from developing into misguided public opinions. Information that develops into a misguided public opinion in a single propagation can be controlled at a lower cost.

### C. Impact of rumor propagation on society

Through the analysis in this paper, using the nuclear fission-based rumor propagation model to simulate the propagation of rumors in a social network, it can be found that each time a user in the excited state propagates a rumor to the surrounding users, whether the user who receives the information chooses to continue to propagate the rumor or not, it will have an impact on the society, and we use the change of the energy value to measure the effect of propagating a rumor on the society. It is set so that a user can generate one unit of energy for each rumor propagation by other users.

The horizontal coordinate of Fig. 6 is the time, and the vertical coordinate is the energy value. Figure 6 depicts the energy value generated at each point in time, and it is also a good illustration of the propagation of rumors in social networks in the real state. Two obvious peaks can be found in Fig. 6. The first peak is mainly generated by irrational netizens in the network receiving rumors and forwarding them, as well as some rational netizens reading, commenting, and liking the rumors, which is a higher peak and has a larger impact, while the second peak is relatively small, which is the social impact of the rumor propagation brought by a very small number of rational individuals who have received rumor information many times and broken through the threshold of the propagation decision.

The total impact of rumor propagation in social networks is shown in Fig. 7. It can be seen that in the early stage of rumor propagation, the impact on the society is relatively small, but if the rumor is allowed to develop, it will have a great impact on the society. The government and related media should monitor the social network in real time and check the rumor information at the early stage of rumor development and make corresponding strategies.

### D. Adjustment parameters

In this paper, the proposed model of nuclear fission rumor propagation is parameterized to see the effect of important parameters on the number of people involved in rumor propagation, compared, and then linked to the actual situation to explain its practical significance.

#### 1. Proportion of rational Internet users

The proportion of rational individuals in the network is adjusted, and the comparison results are shown in Fig. 8. As shown in Fig. 8, the ratio of blue, green, and yellow curves is 0.05, 0.15, and 0.25, respectively, and it can be concluded that the larger the ratio of ideal individuals in the network, the larger the peak number of people in the latent state who received the rumor but did not propagate it outward, and the peak number of people in the excited state who propagate the rumor is significantly reduced, and the longer the time to reach the peak is.

When the proportion of rational Internet users is larger, the number of latent Internet users who receive rumors but do not propagate them outward becomes larger. They will take into account the impact of their personal communication decisions, and the overall probability of choosing to propagate rumors in the social network decreases, and in turn, the number of rumors circulating in the social network will decrease. Therefore, when the proportion of rational Internet users changes, the number of individuals in the excited state also changes significantly, which also affects the arrival time of its peak and equilibrium.

#### 2. Dissemination of decision thresholds

Rational individual propagation decision threshold parameter tuning is carried out, and the comparison results are shown in Fig. 9. As shown in Fig. 9, the three groups of green, yellow, and blue curves have the values of 3, 7, and 10, respectively, which leads us to conclude that the larger the propagation decision threshold is, the more rumor information can be accepted by the rational individuals in the latent state, the larger the peak value is, and the longer the time to arrive at the peak value is, while the peak value of the number of the inspired netizens in the stimulated state decreases with the increase in the propagation decision threshold. When rational Internet users indicate that they are more willing to propagate rumors to the outside world, i.e., the propagation decision threshold becomes lower, the number of individuals staying in the latent state will be less, and at the same moment, more people are willing to choose to propagate rumors and become Internet users in the excited state.

#### 3. Coefficient of proliferation of rumor propagating *k*

Based on the number of followers on Twitter, users can be categorized as small-scale users, medium-scale users, and big-V users. After the formula, their rumor propagation multiplication coefficients can be calculated, with *k* roughly taking the values of 2, 5, and 7, respectively. The experimental comparison results are shown in Fig. 10.

The rumor propagation multiplication coefficient parameter is adjusted, and the comparison results are shown in Fig. 10. As shown, the yellow, green, and blue curves take *k* values of 7, 5, and 2, respectively. It can be seen that as the value of rumor propagation proliferation coefficient *k* increases, the peak value of the number of individuals in the excited state and latent state will be larger, and the arrival time of their peak value will be shorter. When the rumor spreader’s propagating ability is stronger, the range of propagating individual diffusion is larger, so there will be more stable state individuals receiving the rumor information in a shorter period of time, and the users in the latent state also have more chances to repeat the contact with the rumor information to go into the excited state to continue propagating, which has a greater impact on the number of individuals in the excited state. In addition, after the analysis of the rumor propagating scale formula, it can be concluded that when the propagating proliferation coefficient *k* < 1, the information propagation will gradually stop.

### E. Comparison of models

In order to reflect the realism and test the validity of the model, the rumor propagation model based on nuclear fission proposed in this paper is compared with the classical SEIR model, and the simulation results are shown in Fig. 11.

In Fig. 11, the left image is the classical SEIR model and the right image is the nuclear fission-based rumor propagation model proposed in this study. From the results in Fig. 11, we can find that the size and trend of the change in the number of Internet users not exposed to the rumor and the number of Internet users who have finished propagating the rumor are almost the same in the two models, and the difference lies in the change in the number of spreaders and latent state individuals after being exposed to the rumor information. In both models, the existence of latent state individuals is taken into account, who receive rumor information from the social network but do not immediately choose to propagate it to the outside world, resulting in a significant decrease in the number of rumors active in the social network, which in turn has a greater impact on the number of Internet users propagating rumors in the network. However, the difference is also very significant. The SEIR model simulation shows that the number of exposer users is higher than the number of spreader users, while the results of the model in this paper show that the number of spreader users is significantly higher than the number of latent state individuals. The specific reasons for this are that the state of exposer (E) is considered for each individual in the SEIR model, and the state change between individuals is still based on probabilistic transformation, which does not fit well with the facts; this study proposes a rumor propagation model based on nuclear fission, which takes into account the fact that only a very small number of rational netizens will be transformed into the latent state when they are exposed to the information of a rumor, and it also takes into account the propagation decision threshold, the multiplication coefficient, etc., to better fit the real situation.

## VI. DISCUSSION AND EVALUATION

From the description of the experimental process and its results, it can be found that the change in the number of Internet users in each state during the rumor propagation process receives the influence of many factors. When netizens located in social networks receive rumor information, it will make netizens become interested in the rumor information and then further propagate the rumor information to their friends, so the rumor information begins to propagate widely in social networks. This study also finds that the extent of rumor propagation is closely related to the proportion of rational Internet users. This precisely reflects the importance of education. The higher the level of education, the easier it is to question rumors when receiving information that is difficult to distinguish between right and wrong, and at the same time, the higher the level of literacy, the awareness of law-abiding will be improved to a certain extent. When excessive cost is compared with insufficient interest, fewer people will choose to propagate rumors.

At the same time, we have also found that rumors propagate on a small scale at the initial stage, so official platforms need to carry out real-time monitoring. When the possibility of rumors is detected, the government or official media should check the content of the rumors and make corrections and guidance in a timely manner so that the majority of rational netizens who understand the truth of the matter in the social network can effectively inhibit the propagation of rumors, which will, in turn, create a wrong public opinion orientation in the society. Therefore, it is necessary to increase the strength of network supervision and make a good network public opinion supervision system to prevent rumors from propagating. The government and official media, as the most important link in rumor management, should pay attention to their role, face up to their position, strive to improve the rule of law system and related regulations, “enforce the law strictly and punish those who break the law,” raise the cost of crossing the line, deal with the problem in a timely manner, and solve it efficiently.

In this paper, we compare the nuclear fission theory with the rumor propagation process, describe the specific process of rumor propagation in social networks, and propose a rumor propagation model based on nuclear fission. First, through the understanding of nuclear fission theory, we analogize the nuclear fission process with the rumor propagation process and consider the factors affecting individual decision-making as well as the differences between individuals; second, we also list the formula of the rumor propagation scale and the formula of the impact of rumor propagation on the society; third, the node propagation rule of the rumor and the change of the state of the netizens in the process of propagation are also defined. Finally, we analyze the important factor parameters through simulation experiments, and at the same time, we also compare them with the classical infectious disease model, which also verifies the reasonableness and validity of the nuclear fission rumor propagation model.

The presentation of the model and conclusions in this paper are expected to serve as an inspiration for subsequent research scholars. In the future, more Internet users’ states and the factors affecting individual decision-making can be considered and researched, starting from the study of states and individual decision-making.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Wenrong Zheng**: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). **Fengming Liu**: Conceptualization (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). **Yingping Sun**: Methodology (supporting).

## DATA AVAILABILITY

The data that supports the findings of this study are available within the article.

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