Optimal control strategies for a two-group epidemic model with vaccination-resource constraints

In a resource-limited environment, we propose and study an epidemic model consisting of two groups of hosts to reflect the different risk levels of becoming infected and transmitting infection. To further investigate vaccine implementation policies, we study the global dynamics of the model with group-dependent constant coverage rates by utilizing Lyapunov functions. We find that when the vaccination-dependent basic reproduction number is less than one (ℜ₀ < 1), the disease-free equilibrium is globally asymptotically stable. Otherwise, if ℜ₀ > 1, the endemic equilibrium is globally attractive. For the case when the disease is endemic, we apply the optimal control theory to the model under the assumption of a resource-constrained environment and we derive optimal coverage strategies. We also perform numerical simulations for the optimal control problem to verify and further support the theoretical results. In limited control resource cases with both constant and variable coverage rate strategies, we show that when the total control resources are rather scarce, the resources should be biased towards at the group with the high level of infection risk; and that the control resources should preferably be directed at the lower risk group if the total resources are relatively abundant.