A Human-Vector Susceptible–Infected–Susceptible Model for Analyzing and Controlling the Spread of Vector-Borne Diseases

We propose an epidemic model for the spread of vector-borne diseases. The model, which is built extending the classical susceptible–infected–susceptible model, accounts for two populations —humans and vectors— and for cross-contagion between the two species, whereby humans become infected upon interaction with carrier vectors, and vectors become carriers after interaction with infected humans. We formulate the model as a system of ordinary differential equations and leverage monotone systems theory to rigorously characterize the epidemic dynamics. Specifically, we characterize the global asymptotic behavior of the disease, determining conditions for quick eradication of the disease (i.e., for which all trajectories converge to a disease-free equilibrium), or convergence to a (unique) endemic equilibrium. Then, we incorporate two control actions: namely, vector control and incentives to adopt protection measures. Using the derived mathematical tools, we assess the impact of these two control actions and determine the optimal control policy.