Existence of two periodic solutions for a non-autonomous SIR epidemic model

Existence of multiple periodic solutions for an SIR model with seasonality

“…The treatment function T (I) describes the fact that treatment increases linearly with I until the maximum treatment capacity is reached, and treatment remains constant after the capacity. Evidently, this treatment function proposed by Wang [13] improves the constant treatment in [16], and makes the model more realistic. We split the total population (denoted by N) into three distinct compartments: the susceptible S, the infected I, and the recovered R. The model with seasonal transmission and staged treatment has the following form:…”

“…Many studies exploring the role of treatment functions in their dynamic epidemic models presented interesting mathematical phenomena, such as bistability and periodicity [12][13][14][15]. Recently, by taking into account seasonality of the disease, Bai and Zhou [16] investigated a periodic SIR model with a constant treatment, and ✩ This research was supported by NSFC (Grant #10971163 and #11001215), and by IDRC of Canada (Grant #104519-010). they established a set of sufficient conditions for the existence of two periodic solutions.…”

Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

“…Therefore, the existence of periodic solutions of some nonautonomous epidemic models was explored [35][36][37]. Recently, many scholars focused on nonautonomous stochastic periodic systems.…”

Periodic solution of a stochastic SIRS epidemic model with seasonal variation

“…This is because many childhood diseases such as measles, chickenpox, and mumps, have been found to be endemic and to exhibit regular oscillatory levels of incidence in large populations [1,3,4,10].…”