Journal of Dynamics and Differential Equations ( IF 1.473 ) Pub Date : 2020-06-29 , DOI: 10.1007/s10884-020-09862-3
Min Lu, Jicai Huang, Shigui Ruan, Pei Yu

A susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone incidence rate $$\frac{kIS}{1+\beta I+\alpha I^2}$$ ($$\beta >-2 \sqrt{\alpha }$$ such that $$1+\beta I+\alpha I^{2}>0$$ for all $$I\ge 0$$) is considered in this paper. It is shown that the basic reproduction number $$R_0$$ does not act as a threshold value for the disease spread anymore, and there exists a sub-threshold value $$R_*(<1)$$ such that: (i) if \(R_0

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