Mitigating vector-borne diseases on networks: A feasible and stable nonlinear MPC approach

In this paper, we deal with the problem of controlling a vector-borne epidemic disease, evolving over a network. In particular, we consider a discrete-time implementation of a network epidemic model consisting of two interacting populations of humans and vectors in each node of the network. In our model, humans can travel and become infected upon interaction with carrier vectors, while vectors can become carriers if interacting with infected humans. We devise an optimal control strategy by incorporating two control actions, associated with (i) human mobility restriction across the network, and (ii) reduction of carrier population. The control problem is solved by leveraging a nonlinear model predictive control for which we guarantee both the closed-loop stability and the recursive feasibility through a suitable selection of the terminal ingredients. The latter are determined by solving, offline, a dual optimization problem. Finally, we demonstrate our approach on a case study calibrated on realistic data.