Open AccessThreshold dynamics of a time-delayed hantavirus infection model in periodic environments
Author(s) -
Jun Li Liu
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019239
Subject(s) - basic reproduction number , hantavirus , transmission (telecommunications) , incubation period , population , epidemic model , equilibrium point , stability theory , mathematics , biology , incubation , virus , virology , physics , demography , mathematical analysis , computer science , telecommunications , biochemistry , nonlinear system , quantum mechanics , sociology , differential equation
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 0 is defined as the spectral radius of the next generation oper-ator. 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 R 0 , such that if R 0 < 1, then the virus-free equilibrium is glob-ally asymptotically stable, but if 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.