The stochastic SIS epidemic model with variable population size

Abstract

The infectious disease is very serious problem in many countries. There are many attempts for controlling the spread of infectious disease. The spread of disease can be considered as random event so it could be constructed as stochastic model. The stochastic SIS epidemic models describe the spread of the disease from which an individual could be infected more than once. This paper will dicuss the stochastic SIS epidemic model when the population size N is not constant according to population growth law. To formulate the model, some assumption must be made. The population growth is assumed logistic. The model solution is obtained by using the Ito's formula and the Kolmogorov forward differential equations. Then, we apply the model for an example by comparing constant population size and variable population size. The variable population size shows the fluctuation of N(t). It is more appropriate to represent the demographics condition.