Transmission dynamics and optimal control of malaria in Kenya
type: Item
instance of: scholarly article
title: Transmission dynamics and optimal control of malaria in Kenya
zbMATH Open document ID: 1376.92069
DOI: 10.1155/2016/8013574
author: Gabriel Otieno
author: Joseph K. Koske
author: John M. Mutiso
published in: Discrete Dynamics in Nature and Society
publication date: 2017-11-13T00:00:00Z
review text: Summary: This paper proposes and analyses a mathematical model for the transmission dynamics of malaria with four-time dependent control measures in Kenya: insecticide treated bed nets (ITNs), treatment, indoor residual spray (IRS), and intermittent preventive treatment of malaria in pregnancy (IPTp). We first considered constant control parameters and calculate the basic reproduction number and investigate existence and stability of equilibria as well as stability analysis. We proved that if \(R_0 \leq 1\), the disease-free equilibrium is globally asymptotically stable in \(D\). If \(R_0 > 1\), the unique endemic equilibrium exists and is globally asymptotically stable. The model also exhibits backward bifurcation at \(R_0 = 1\). If \(R_0 > 1\), the model admits a unique endemic equilibrium which is globally asymptotically stable in the interior of feasible region \(D\). The sensitivity results showed that the most sensitive parameters are mosquito death rate and mosquito biting rates. We then consider the time-dependent control case and use Pontryagin's Maximum Principle to derive the necessary conditions for the optimal control of the disease using the proposed model. The existence of optimal control problem is proved. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that the optimal control strategy for malaria control in endemic areas is the combined use of treatment and IRS; for epidemic prone areas is the use of treatment and IRS; for seasonal areas is the use of treatment; and for low risk areas is the use of ITNs and treatment. Control programs that follow these strategies can effectively reduce the spread of malaria disease in different malaria transmission settings in Kenya.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 49N90
zbMATH DE Number: 6806272
zbMATH Keywords: insecticide treated bed nets
zbMATH Keywords: indoor residual spray
zbMATH Keywords: Pontryagin's maximum principle
Wikidata QID: Q59123661
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/8013574
OpenAlex ID: W2516570614
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description: scientific article; zbMATH DE number 6806272