Since the end of 2019, with the outbreak of the new virus COVID-19, the world changed entirely in many aspects, with the pandemia affecting the economies, healthcare systems and the global socium. As a result from this pandemic, scientists from many countries across the globe united in their efforts to study the virsus's behavior and are attempting to predict mathematically its infection model in order to limit its impact and developing new methods and models to achieve this goal. In this paper we explore a time-depended SEIR model, in which the dynamics of the infection in four groups from a selected target group (population), divided according to the infection, are modeled by a system of nonlinear ordinary differential equations. Several basic parameters are involved in the model: coefficients of infection rate, incubation rate, recovery rate. The coefficients are adaptable to each specific infection, for each individual country, and depend on the measures to limit the spread of the infection and the effectiveness of the methods of treatment of the infected people in the respective country. If such coefficients are known, solving the nonlinear system is possible to be able to make some hypotheses for the development of the epidemic. This is the reason for using Bulgarian COVID-19 data to first of all, solve the so-called ”inverse problem” and to find the parameters of the current situation. Reverse logic is initially used to determine the parameters of the model as a function of time, followed by computer solution of the problem. Namely, this means predicting the future behavior of these parameters, and finding (and as a consequence applying mass-scale measures, e.g., distancing, disinfection, limitation of public events), a suitable scenario for the change in the proportion of the numbers of the four studied groups in the future. In fact, based on these results we model the COVID-19 transmission dynamics in Bulgaria and make a two-week forecast for the numbers of new cases per day, active cases and recovered individuals. Such model, as we show, has been successful for prediction analysis in the Bulgarian situation. We also provide multiple examples of numerical experiments with visualization of the results.

1.
M.
Touma
,
COVID-19: molecular diagnostics overview
,
Journal of molecular medicine
,
98
,
947
954
(
2020
),
2.
F.
Zhou
,
T.
Yu
,
R.
Du
,
G.
Fan
,
Y.
Liu
,
Z.
Liu
, et al,
Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study
,
Lancet
,
395
(
10229
),
1054
1062
(
2020
),
3.
Y.
Wang
,
Y.
Wang
,
Y.
Chen
,
Q.
Qin
,
Unique epidemiological and clinical features of the emerging 2019 novel coronavirus pneumonia (COVID-19) implicate special control measures
,
Journal of medical virology
,
92
(
6
),
568
576
(
2020
),
5.
Gabriel Goh, Epidemic calculator
, http://gabgoh.github.io/COVID/|
6.
N.
Imai
,
I.
Dorigatti
,
A.
Cori
,
C.
Donnelly
,
S.
Riley
,
N.
Ferguson
,
Report 2: Estimating the potential total number of novel Coronavirus cases in Wuhan City, China
,
2020
Medical Research Council (MRC)
, http://hdl.handle.net/10044/1/77150|
7.
R. Verity at
al
.,
Estimates of the severity of coronavirus disease 2019: a model-based analysis
.
Lancet Infect Dis.
,
1
9
(
2020
),
8.
Y.
Fang
,
Y.
Nie
,
M.
Penny
,
Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: A data-driven analysis
,
J. Med. Virol.
,
1
15
(
2020
),
9.
M.
Liu
,
J.
Cao
,
J.
Liang
,
M.
Chen
, Epidemic-logistics Modeling: A New Perspective on Operations Research,
Springer
,
2020
,
10.
Pauline
van den Driessche
,
Reproduction numbers of infectious disease models
,
Infect Dis Model.
, Vol.
2
(
3
),
288
303
(
2017
), |
11.
J.
Carcione
,
J.
Santos
,
C.
Bagaini
,
J.
Ba
,
A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model
,
Frontiers in Public Health
, Vol.
8
(
230
),
1
13
(
2020
),
12.
W.
Kermack
,
A.
McKendrick
,
A contribution to the mathematical theory of pandemics
.
Proc R Soc Lond, Series A.
,
115
(
772
):
700
721
(
1927
).
13.
P.
White
, 5 - Mathematical Models in Infectious Disease Epidemiology,
Infectious Diseases
(Fourth Edition),
Elsevier
,
49
53
.e1 (
2017
),
14.
J.
Ponciano
,
M.
Capistran
,
First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics
,
PLOS Computational Biology
,
7
(
2
):
e1001079
(
2011
),
15.
Z.
Chladna
,
J.
Kopfova
,
D.
Rachinskii
,
S.
Rouf
,
Global dynamics of SIR model with switched transmission rate
,
J. Math. Biol.
,
80
,
1209
1233
(
2020
),
16.
X.
Liu
,
P.
Stechlinski
,
Infectious disease models with time-varying parameters and general nonlinear incidence rate
,
Applied Mathematical Modelling
,
36
(
5
),
1974
1994
(
2012
),
17.
D.
Brockmann
,
V.
David
,
A.M.
Gallardo
,
Human Mobility and Spatial Disease Dynamics
,
Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
,
11
(
2
),
1
27
(
2009
).
18.
Y.
Jiang
,
R.
Kassem
,
G.
York
,
M.
Junge
,
R.
Durrett
,
SIR epidemics on evolving graphs
, arXiv:1901.06568,
1
24
(
2019
), https://arxiv.org/abs/1901.06568|
19.
N.
Liu
,
J.
Fang
,
W.
Deng
,
J.
Sun
,
Stability analysis of a fractional-order SIS model on complex networks with linear treatment function
,
Advances in Difference Equations
327
,
1
10
(
2019
),
20.
B.
Takacs
,
R.
Horvath
,
I.
Farag
o,
Space dependent models for studying the spread of some diseases
,
Computers & Mathematics with Applications
,
80
(
2
),
395
404
(
2020
), |
21.
Institute for Health Metrics and Evaluation (IHME
), http://www.healthdata.org/|
22.
Y-C.
Chen
,
P-E
Lu
,
T-H
Liu
,
A Time-dependent SIR model for COVID-19 with Undetectable Infected Persons
, arXiv:2003.00122. 11 Apr 2020; 1–16 (
2020
), https://arxiv.org/abs/2003.00122|
23.
O.
Kounchev
,
G.
Simeonov
,
Z.
Kuncheva
,
The TVBG-SEIR spline model for analysis of COVID-19 spread, and a Tool for prediction scenarios
, arXiv:2004.11338 [math.NA]. \p1–21 (
2020
), https://arxiv.org/ftp/arxiv/papers/2004/2004.11338.pdf|
24.
J.
Ma
,
Estimating epidemic exponential growth rate and basic reproduction number
,
Infectious Disease Modelling
, Vol.
5
,
129
141
(
2020
),
25.
M.
Böhmer
 et al,
Investigation of a COVID-19 outbreak in Germany resulting from a single travel-associated primary case: a case series
,
TheLancet Infectious Diseases
,
1
9
(
2020
),
26.
This content is only available via PDF.
You do not currently have access to this content.