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• W2895824254 abstract "• Propose and study an SIR model with a generalized incidence under preventive vaccination and treatment controls. • Treatment strategies are responsible for backward bifurcations and multiple endemic equilibria. • The infective population decreases with respect to the maximal capacity of treatment; and/or the preventive vaccination rate. • The infective population also decreases with respect to the psychological or inhibitory effects of infectives. In this paper, we propose and study an SIRS epidemic model that incorporates: a generalized incidence rate function describing mechanisms of the disease transmission; a preventive vaccination in the susceptible individuals ; and different treatment control strategies depending on the infective population. We provide rigorous mathematical results combined with numerical simulations of the proposed model including: treatment control strategies can determine whether there is an endemic outbreak or not and the number of endemic equilibrium during endemic outbreaks, in addition to the effects of the basic reproduction number; the large value of the preventive vaccination rate can reduce or control the spread of disease; and the large value of the psychological or inhibitory effects in the incidence rate function can decrease the infective population. Some of our interesting findings are that the treatment strategies incorporated in our SIRS model are responsible for backward or forward bifurcations and multiple endemic equilibria; and the infective population decreases with respect to the maximal capacity of treatment. Our results may provide us useful biological insights on population managements for disease that can be modeled through SIRS compartments." @default.
• W2895824254 created "2018-10-26" @default.
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• W2895824254 date "2019-03-01" @default.
• W2895824254 modified "2023-10-13" @default.
• W2895824254 title "Complicated endemics of an SIRS model with a generalized incidence under preventive vaccination and treatment controls" @default.
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• W2895824254 doi "https://doi.org/10.1016/j.apm.2018.10.016" @default.
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