Optimal (control of) intervention strategies for malaria epidemic in Karonga district, Malawi
type: Item
instance of: scholarly article
title: Optimal (control of) intervention strategies for malaria epidemic in Karonga district, Malawi
zbMATH Open document ID: 1406.92601
DOI: 10.1155/2014/594256
author: J. Michel Tchuenche
author: Ansley Kasambara
author: Peter Mpasho Mwamtobe
author: Shirley Abelman
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Malaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660,000 people die, mostly (91\%) in the African Region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and parasitically transmitted by the bite of the female \textit{Anopheles} mosquito. A deterministic mathematical model with intervention strategies is developed in order to investigate the effectiveness and optimal control strategies of indoor residual spraying (IRS), insecticide treated nets (ITNs) and treatment on the transmission dynamics of malaria in Karonga District, Malawi. The effective reproduction number is analytically computed, and the existence and stability conditions of the equilibria are explored. The model does not exhibit backward bifurcation. Pontryagin's Maximum Principle which uses both the Lagrangian and Hamiltonian principles with respect to a time dependent constant is used to derive the necessary conditions for the optimal control of the disease. Numerical simulations indicate that the prevention strategies lead to the reduction of both the mosquito population and infected human individuals. Effective treatment consolidates the prevention strategies. Thus, malaria can be eradicated in Karonga District by concurrently applying vector control via ITNs and IRS complemented with timely treatment of infected people.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 49N90
zbMATH DE Number: 7022676
zbMATH Keywords: malaria epidemic
zbMATH Keywords: optimal control
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/594256
OpenAlex ID: W2081187491
Wikidata QID: Q59039744
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description: scientific article; zbMATH DE number 7022676