A viral co-infection model with general infection rate in deterministic and stochastic environments

In this paper, we present a model of infection in which a virus can simultaneously infect two types of target cells. The model has a general form of infection rates in deterministic and stochastic settings, incorporating bilinear infection rates, saturated incidences and half-saturated incidences. In the deterministic case, we investigate the existence and local asymptotic stability of disease-free and positive equilibrium points, respectively. Considering that the infection rate coefficient is affected by random noise, we built the corresponding stochastic model using the Ornstein-Uhlenbeck process. In the stochastic case, by constructing suitable Lyapunov functions, we established sufficient conditions for the ergodic stationary distribution and extinction of the model, respectively. In addition, the covariance matrix in the probability density function of the model near the positive equilibrium point is determined.