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

Junli Liu; Junli Liu

doi:10.3934/mbe.2019239

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 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: 23 February 2019 Accepted: 17 May 2019 Published: 27 May 2019

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 $R_0$ is defined as the spectral radius of the next generation operator. Then, we show the virus is uniformly persistent when $R_0>1$ while tends to die out if $R_0 < 1$. When there is no seasonality, that is, all coefficients are constants, we obtain the explicit expression for the basic reproduction number $\mathbf{{R}_0}$, such that if $\mathbf{{R}_0} < 1$, then the virus-free equilibrium is globally asymptotically stable, but if $\mathbf{{R}_0}>1$, 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 $R_0$ is performed.
- Hantavirus,
- seasonality,
- time delay,
- uniform persistence,
- basic reproduction number
Citation: Junli Liu. Threshold dynamics of a time-delayed hantavirus infection model in periodic environments[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4758-4776. doi: 10.3934/mbe.2019239

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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 $R_0$ is defined as the spectral radius of the next generation operator. Then, we show the virus is uniformly persistent when $R_0>1$ while tends to die out if $R_0 < 1$. When there is no seasonality, that is, all coefficients are constants, we obtain the explicit expression for the basic reproduction number $\mathbf{{R}_0}$, such that if $\mathbf{{R}_0} < 1$, then the virus-free equilibrium is globally asymptotically stable, but if $\mathbf{{R}_0}>1$, 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 $R_0$ is performed.

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