Mathematical model of respiratory diseases spread with Discrete Time Markov Chain (DTMC) and deterministic approach for constant total population size are analyzed and compared in this article. Intervention of medical treatment and use of medical mask included in to the model as a constant parameter to controlling influenza spreads. Equilibrium points and basic reproductive ratio as the endemic criteria and it level set depend on some variable are given analytically and numerically as a results from deterministic model analysis. Assuming total of human population is constant from deterministic model, number of infected people also analyzed with Discrete Time Markov Chain (DTMC) model. Since Δt → 0, we could assume that total number of infected people might change only from i to i + 1, i − 1, or i. Approximation probability of an outbreak with gambler’s ruin problem will be presented. We find that no matter value of basic reproductive ℛ0, either its larger than one or smaller than one, number of infection will always tends to 0 for t → ∞. Some numerical simulation to compare between deterministic and DTMC approach is given to give a better interpretation and a better understanding about the models results.
Skip Nav Destination
Article navigation
6 April 2016
SYMPOSIUM ON BIOMATHEMATICS (SYMOMATH 2015)
4–6 November 2015
Bandung, Indonesia
Research Article|
April 06 2016
Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model
F. Novkaniza;
F. Novkaniza
Department of Mathematics,
Universitas Indonesia
, Depok 16424, Indonesia
Search for other works by this author on:
Ivana;
Ivana
Department of Mathematics,
Universitas Indonesia
, Depok 16424, Indonesia
Search for other works by this author on:
a)
Corresponding author: [email protected]
AIP Conf. Proc. 1723, 030015 (2016)
Citation
F. Novkaniza, Ivana, D. Aldila; Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model. AIP Conf. Proc. 6 April 2016; 1723 (1): 030015. https://doi.org/10.1063/1.4945073
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Inkjet- and flextrail-printing of silicon polymer-based inks for local passivating contacts
Zohreh Kiaee, Andreas Lösel, et al.
Effect of coupling agent type on the self-cleaning and anti-reflective behaviour of advance nanocoating for PV panels application
Taha Tareq Mohammed, Hadia Kadhim Judran, et al.
Design of a 100 MW solar power plant on wetland in Bangladesh
Apu Kowsar, Sumon Chandra Debnath, et al.
Related Content
Construction of a stochastic SVIS model for prevention of influenza spread with vaccines
AIP Conf. Proc. (October 2018)
Optimal dimensionality reduction of Markov chains using graph transformation
J. Chem. Phys. (December 2020)
Analysis of protein-protein interaction to obtain significant protein in influenza virus type A/H9N2
AIP Conference Proceedings (August 2022)
Optimal control problem in correlation between smoking and epidemic of respiratory diseases
AIP Conference Proceedings (February 2014)