Stochastic Modeling of spreading infectious diseases

The spreading of infectious diseases has affected the populations throughout the history of human life. Mathematical models and computer simulations are important instrument in order to study and forecast the behavior of the infections in a population and for making a right decision to control and eliminate them via preventive measures or drug interventions. We investigate a mathematical model for spreading the disease that has been introduced by Parsamanesh and Erfanian ([1]), in which a preventive strategy has been included. Individuals in this model are partitioned into three classes: susceptible, infectious, and immune. The model includes natural and disease caused death as well as birth and immigrant. All transmissions in population are considered to be probabilistic. We identify these changes with their corresponding transition probabilities in a small time interval. By using a procedure developed in [2,3] we get a system of stochastic differential equations (SDE) for model. The existence and uniqueness of solutions are proved and solutions of the stochastic system are simulated. The extinction and persistence of the model are also compared with deterministic one. Some quantities such as probability distribution of extinction and expected duration of epidemic are calculated numerically.

کلیدواژه ها:

Modeling ، Infectious disease ، Immunity ، Stochastic differential equation.