An SIRS epidemic model with a non-linear incidence rate and time delay is proposed. The positivity and boundedness are studied. The basic reproductive ratio R0 which is independent of the type of the nonlinear incidence rate is found. The local asymptotic stability of the disease-free equilibrium and positive equilibrium are analysed. The global stability for the disease free equilibrium is found. The condition for Hopf-bifurcation from the positive equilibrium are shown at critical latency. Numerical simulations are performed to support analytical results.
Volume 12 | Issue 2
Pages: 3502-3515
DOI: 10.5373/JARDCS/V12I2/S20201468