Threshold dynamics of a time-delayed hantavirus infection model in periodic environments

Abstract

We formulate and study a mathematical model for the propagation of hantavirus infection in the mouse population. This model includes seasonality, incubation period, direct transmission (contacts between individuals) and indirect transmission (through the environment). For the time-periodic model, the basic reproduction number R0 is defined as the spectral radius of the next generation operator. Then, we show the virus is uniformly persistent when R0 > 1 while tends to die out if R0 < 1. When there is no seasonality, that is, all coefficients are constants, we obtain the explicit expression for the basic reproduction number R0, such that if R0 < 1, then the virus-free equilibrium is globally asymptotically stable, but if R0 > 1, the endemic equilibrium is globally attractive. Numerical simulations indicate that prolonging the incubation period may be helpful in the virus control. Some sensitivity analysis of R0 is performed.