A separable programming approach for resource optimisation in controlling epidemics

Optimal resource allocation in controlling epidemics is a topic of importance, in particular to health-planners in developing countries. Commonly practised resource allocation criteria depend on some trivial statistics, hence critical factors such as human mobility are often ignored in making health decisions. In this work we propose to incorporate inter-regional mobility factor into the decision-making process. Starting from the well-known compartment models for epidemic transmission, we formulate a nonlinear optimisation problem for the regional allocation of resources, aimed at minimising the total number of infectious persons in the country. Computational challenges in finding the global optimum to this problem are overcome by restating it in the form of a separable program, which is eventually reduced down into an efficiently solvable mixed-integer linear program. We derive numerical results by applying our solution techniques to relevant data on dengue transmission in Sri Lanka. Finally, we interpret the results and show that resource allocations are inadequate unless the mobility factor is taken into account.