Global dynamics of a network-based SIQS epidemic model with nonmonotone incidence rate. (December 2021) - Cheng, Xinxin; Wang, Yi; Huang, Gang
Highlights: A new network-based SIQS epidemic model with nonmonotone incidence rate is introduced. The epidemic threshold and equilibriums are obtained and analyzed. The stability of disease-free equilibrium and the permanence of the disease are proved. Global dynamics of the unique endemic equilibrium are obtained. Simulations indicate that quarantine strategy is an effective measure in preventing epidemic spreading. Abstract: The risk of propagation of infectious diseases such as avian influenza and COVID-19 is generally controlled or reduced by quarantine measures. Considering this situation, a network-based SIQS (susceptible-infected-quarantined-susceptible) infectious disease model with nonmonotone incidence rate is established and analyzed in this paper. The psychological impact of the transmission of certain diseases in heterogeneous networks at high levels of infection may be characterized by the related nonmonotone incidence rate. The expressions of the basic reproduction number and equilibria of the model are determined analytically. We demonstrate in detail the uniform persistence of system and the global asymptotic stability of the disease-free equilibrium. The global attractivity of the unique endemic equilibrium is discussed by using monotone iteration technique. We obtain that the endemic equilibrium is globally asymptotically stable under certain conditions by constructing appropriate Lyapunov function. In addition, numerical simulations are performed to indicate the theoretical results.