An optimal control problem and cost-effectiveness analysis of malaria disease with vertical transmission applied to San Andrés de Tumaco (Colombia)

Abstract

In this work, we studied malaria disease in San Andrés de Tumaco-Colombia (Tumaco) using mathematical modeling with the objective of contributing to the understanding its transmission dynamics and to the development of control strategies. To this end, we formulated a system of ordinary differential equations that describe the malaria disease transmission dynamics in Tumaco and considered both vectorial and vertical transmission of disease. We performed a sensitivity analysis of parameters that allowed us to define the following control variables: indoor residual spraying (IRS), bed nets (BN), intermittent prophylactic treatment in pregnancy (IPTp) and antimalarial treatment (AT). Using previously identified control variables, we formulated an optimal control problem with different control strategies. We analytically and numerically solved the optimal control problem and generated a cost-effectiveness analysis of these strategies using data from rural areas of Tumaco. The results suggested that simultaneous implementation of IRS, BN, IPTp and AT strategies are the best options.