Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Citations (Scopus)


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 0, 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.

Original languageEnglish
Title of host publicationSymposium on Biomathematics, SYMOMATH 2015
EditorsMochamad Apri, Yasuhiro Takeuchi
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413702
Publication statusPublished - 6 Apr 2016
EventSymposium on Biomathematics, SYMOMATH 2015 - Bandung, Indonesia
Duration: 4 Nov 20156 Nov 2015

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


ConferenceSymposium on Biomathematics, SYMOMATH 2015


Dive into the research topics of 'Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model'. Together they form a unique fingerprint.

Cite this