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

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 (con-tacts between individuals) and indirect transmission (through the environment). For the time-periodic model, the basic reproduction number R is defined as the spectral radius of the next generation oper-ator. Then, we show the virus is uniformly persistent when R > 1 while tends to die out if R < 1. When there is no seasonality, that is, all coefficients are constants, we obtain the explicit expression for the basic reproduction number R, such that if R < 1, then the virus-free equilibrium is glob-ally asymptotically stable, but if R > 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 R is performed.