Abstract

This paper explores optimal treatment of an SIS (Susceptible-Infected-Susceptible) disease that has two strains with different infectivities. When we assume that neither eradication nor full infection are possible, it is shown that there are two categories of equilibria. First, there are two continua of interior equilibria characterised by a fixed, positive total level of infection, where both strands of the disease prevail. Second, there are two sets of equilibria where one strand of the disease is eradicated asymptotically. The feasibility of equilibria depends on parameter assumptions; a combination of low natural rate of recovery and large difference between infectivities leaves only a small proportion of equilibria as feasible. Simulations exploring the relationship between cost and optimal policy are carried out. There exists a parameter range such that, counter-intuitively, it is optimal to allow the high-infectivity strain of the disease to prevail, while asymptotically eradicating the low-infectivity strain. Within this parameter range, fixed and variable optimal policy lead us to different steady states. There is added benefit from policy flexibility.