Global stability and a comparison of SVEIP and delayed SVIP epidemic models with indirect transmission
This paper studies global stability of SVEIP and delayed SVIP epidemic models with indirect transmission. The system considered is described as \(\dot{S}=A-S(f(I)+g(P))-\mu S-\nu S+\delta V\), \(\dot{V}=\nu S-\varepsilon V(f(I)+g(P))-\mu V-\delta V\), \(\dot{E}=(S+\varepsilon V)(f(I)+g(P))-(\mu+\sigma)E\), \(\dot{I}=\sigma E-\varphi(I)\) and \(\dot{P}=h(I)-\omega(P)\), where \(S\) is the susceptible compartment, \(V\) is the vaccinated compartment, \(E\) is the exposed compartment, \(I\) is the infectious compartment, and \(P\) is the pathogens in the environment. An infectious animal generates infection with both direct and indirect modes of transmission. The corresponding model with constant time delay has also been considered. Under the assumptions that \(f\), \(g\), \(\varepsilon\), \(h\) and \(\omega\) are sufficiently smooth and some other conditions, the global stability of equilibria are determined by the basic reproduction numbers. If the basic reproduction number is greater than one, it is shown that there exists a unique endemic equilibrium for the systems and it is globally asymptotically stable. Some numerical simulations are presented to illustrate the theoretical results.
scientific article; zbMATH DE number 7257302