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

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...

Full description

Saved in:
Bibliographic Details
Published inComputational & applied mathematics Vol. 38; no. 3
Main Authors Romero-Leiton, Jhoana P., Castellanos, Jairo Eloy, Ibargüen-Mondragón, Eduardo
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2019
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Cost analysis
Differential equations
Disease control
Malaria
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Optimal control
Ordinary differential equations
Parameter sensitivity
Rural areas
Sensitivity analysis
Spraying
Colombia
Cost-effectiveness analysis
Sensitivity analysis of parameters
Malaria
92B05
Optimal control
49J15
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-019-0909-2