Mathematical modelling of human African trypanosomiasis using control measures
type: Item
instance of: scholarly article
title: Mathematical modelling of human African trypanosomiasis using control measures
zbMATH Open document ID: 1431.92135
DOI: 10.1155/2018/5293568
author: Hamenyimana Emanuel Gervas
author: Nicholas Kwasi-Do Ohene Opoku
author: Shamsuddeen Ibrahim
published in: Computational \& Mathematical Methods in Medicine
publication date: 2019-02-26T00:00:00Z
review text: Summary: Human African trypanosomiasis (HAT), commonly known as sleeping sickness, is a neglected tropical vector-borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper, we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments, while in the human population, the HAT is modelled by four compartments. The next-generation matrix approach is used to derive the basic reproduction number, \(R_0\), and it is also proved that if \(R_0 \leq 1\), the disease-free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persists in the population if the value of \(R_0 > 1\). Furthermore, the optimal control model is determined by using the Pontryagin's maximum principle, with control measures such as education, treatment, and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures is very efficient and effective to eliminate HAT in Africa.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 92C60
zbMATH DE Number: 7029768
zbMATH Keywords: human African trypanosomiasis
zbMATH Keywords: transmission dynamics
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: optimal control
Wikidata QID: Q60313337
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5293568
OpenAlex ID: W2898349498
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description: scientific article; zbMATH DE number 7029768