Mathematical Biosciences and Engineering, 2019, 16(5): 4758-4776. doi: 10.3934/mbe.2019239

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

Junli Liu

School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, P.R. China

Received: , Accepted: , Published:

Special Issues: Transmission dynamics in infectious diseases

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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 R0 is defined as the spectral radius of the next generation oper-ator. 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 glob-ally 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.
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