Dynamics of an epidemic model with quadratic treatment

This paper introduces a novel treatment function into an SIR model with bi-linear infection force. Treatment is assumed to increase at a decreasing rate as the sub-population of infected rises. But at some finite number of infected individuals, society’s ability to treat the infected reaches a peak and then begins to fall, perhaps due to diminishing supplies or efficiency of health care resources. The system is found to have as many as four equilibria, with possible bi-stability, backward bifurcations, and limit cycles. Particular attention is paid to the effect of variations in the key treatment parameter, rr. It is found that when rr is either low or high, small changes in rr do not affect the equilibrium outcome.