Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate

Abstract

In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number R 0 by employing the classical renewal process, which determines whether the disease persists or not. In the main part, we investigate the global stability of the equilibria by the approach of Lyanpunov functionals. Some numerical simulations are conducted to illustrate the theoretical results and to show the effect of the transmission rate and immunity waning rate on the disease prevalence.

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

“…Notice that we only discuss the bifurcation of parameters γ −h and b−h in this subsection. The bifurcation diagrams of other parameters and thresholds h can Proof To establish this Theorem 8, observe that systems (40)…”

“…Similarly, the basic reproduction number of system (41) is given by R 0 = βb α(α+γ) . From (40), we have if (40) is locally stable (L.S.) node point.…”

“…[9,12,21,25,28,34,41,45,46], H.C. [14,23,24] and I.C. [22,25,26,44] and the other control [1,3,10,18,40,42]. Nevertheless, in this manuscript, we design a SIR epidemic system to address the D.T.C.…”