Stochastic dynamics of hepatitis B epidemics
Anwarud Din, Yongjin Li, Tahir Khan, Khurshaid Anwar, Gul Zaman
Abstract
Nowadays in the world, the biggest problem is how to control the transmittable disease. Mathematical biology is one of the useful areas to study and investigate the control of transmittable diseases. In the current study, we developed a mathematical model which reflects the dynamics of hepatitis B virus by using the tools of stochastic modeling and particularly considering the environmental noise. For a better understanding of the disease, we divide the whole population into four disjoint classes. The main focus of the study is to show the effect of stochasticity on the dynamics of the disease as well as to obtain the required threshold parameter. The stochastic Lyapunov function is formulated, whose analysis shows that there exists a positive solution to the model. The study was further enriched by investigating the sufficient conditions of hepatitis B extinction and stationary distribution. In order to support theoretical results, at the end of the study, we present sample simulations of the model by using the stochastic Runge-Kutta method.