An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions and , respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number .
Mingming Li. Xianning Liu. "An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate." Abstr. Appl. Anal. 2014 (SI01) 1 - 7, 2014. https://doi.org/10.1155/2014/131257