A Stochastic Model for General Multi-Host Epidemic Models based on mean and variance

Pathogenic factors can affect several groups of an epidemic. In this paper, by using the Brownian motion, an Ito stochastic differential equation is presented to express the stochastic behavior of an infected disease based on mean and variance. The model includes different species of population with the presence of suspected, exposed, infected and immune types. The model covers all the previous models including SI, SIS, SIR, SEIR, and SIRS. Also, the incubation, an important period in the epidemic, is considered. Finally, a few numerical examples of this model's behavior are presented.