School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi 710048, P.R. China.
Math Biosci Eng. 2019 May 28;16(5):4758-4776. doi: 10.3934/mbe.2019239.
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.
我们构建并研究了一个描述汉坦病毒在鼠群中传播的数学模型。该模型考虑了季节性、潜伏期、直接传播（个体间接触）和间接传播（通过环境）。对于时变模型，基本繁殖数$R$定义为下一代算子的谱半径。然后，我们证明了当$R>1$时病毒是一致持续存在的，而当$R<1$时病毒趋于消亡。当没有季节性，即所有系数都是常数时，我们得到了基本繁殖数$R$的显式表达式，使得如果$R<1$，则无病毒平衡点是全局渐近稳定的，但如果$R>1$，则地方病平衡点是全局吸引的。数值模拟表明，延长潜伏期可能有助于控制病毒。我们还进行了对$R$的敏感性分析。
