Three Dimensional Epidemic Model with Non-monotonic Incidence and Saturated Treatment: A Case Study of SARS Infection of Hong Kong 2003 Scenario

Abstract In this paper, we have proposed a mathematical compartmental model with non-monotonic incidence and saturated treatment and we have validated the model with SARS infection in Hong Kong, 2003. We have analysed the stability of disease free and endemic equilibria as well as different bifurcations. We have shown that the epidemic disappears if the cure rate of treatment crosses a threshold value. We have obtained a necessary and sufficient condition for backward bifurcation, which shows the basic reproduction number less than unity is not sufficient to eradicate the disease completely. Saddle-node and Hopf bifurcation with respect to awareness factor have been investigated, which shows that the awareness factor is effective to change the disease dynamics. The model has been fitted to SARS cases in Hong Kong. The most effective parameters for controlling infections have been identified through sensitivity analysis. Moreover, we have investigated how the number of infected cases reduces if there was some vaccination polices in SARS infection. Finally, the model has been also used as an optimal control problem as vaccination and treatment controls are time dependent functions.