An Stochastic Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

Abstract

In this paper, a stochastic epidemic model with two different types of infectious diseases that spread through both horizontal and vertical transmission is investigaed. By constructing suitable Lyapunov functions and applying Itˆ o’s formula as well as Chebyshev’s inequality, the sufficient conditions for stochastic ultimate boundedness and permanence are established. The reliability of theoretical results are further illustrated by numerical simulations.