Stability analysis and optimal control intervention strategies of a malaria mathematical model

Abstract:

Nowadays, cases of death due to malaria have been substantially reduced. However, the incidence of malaria has been concentrated mainly in specific sectors both urban and rural. This suggests that the dynamics of transmission is changing, which generates a new public health alert. In this work we study the malaria disease applied to the municipality of Tumaco (Colombia) through a mathematical model with the objective of contribute to the understanding of the transmission dynamics and development of control intervention strategies. To this end, we formulate a system of ordinary differential equations that describe the malaria disease transmission dynamics for humans and mosquitoes population. We performed the stability analysis, analysis of bifurcations and sensitivity analysis of parameters to the mathematical model, which allowed us to define the following control strategies: indoor fumigation, bed nets, intermittent prophylactic treatment in pregnancy and antimalarial treatment. For these variables we formulated and analyze an optimal control problem in which control strategies are incorporated by treatment (antimalarial and prophylactic in pregnancy) and the combination of the four control variables. The results of the cost-effectiveness analysis suggest that in urban areas it is enough to consider control strategies for treatment, while in rural areas the simultaneous implementation of the four control variables is the most cost-effective strategy.

Año de publicación:

2019

Keywords:

• Bifurcations
• Optimal Control
• Sensitivity analysis of parameters
• MALARIA

Fuente:

scopus