@article{Guo2022, 
author = {Jinsheng Guo and Shuang-Ming Wang},
title = {Threshold dynamics of a time-periodic two-strain SIRS epidemic model with distributed delay},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {6331-6355},
keywords = {SIRS epidemic model, spatiotemporal heterogeneity, distributed delay, threshold dynamics},
url = {https://www.sciopen.com/article/10.3934/math.2022352},
doi = {10.3934/math.2022352},
abstract = {In this paper, a two-strain SIRS epidemic model with distributed delay and spatiotemporal heterogeneity is proposed and investigated. We first introduce the basic reproduction number        R    0    i   and the invasion number                      R        ^              0    i      (  i  =  1  ,  2  ) for each strain    i. Then the threshold dynamics of the model is established in terms of        R    0    i   and                      R        ^              0    i   by using the theory of chain transitive sets and persistence. It is shown that if                      R        ^              0    i    >  1    (  i  =  1  ,  2  ), then the disease in two strains is persist uniformly; if        R    0    i    >  1  ≥      R    0    j      (  i  ≠  j  ,  i  ,  j  =  1  ,  2  ), then the disease in    i-th strain is uniformly persist, but the disease in    j-th strain will disappear; if        R    0    i    <  1 or        R    0    i    =  1    (  i  =  1  ,  2  ) and        β    i    (  x  ,  t  )  >  0, then the disease in two strains will disappear.}
}