Controlling Influenza Disease : Comparison Between Discrete Time Markov Chain and Deterministic Model

摘要

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 ?t →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 R_0. either its larger than one or smaller than one. number of infection will always tends to 0 for t → oo. 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.