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Mathematical Modelling of Human African Trypanosomiasis Using Control Measures

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 dyn...

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Autores principales: Gervas, Hamenyimana Emanuel, Opoku, Nicholas Kwasi-Do Ohene, Ibrahim, Shamsuddeen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6282183/
https://www.ncbi.nlm.nih.gov/pubmed/30595713
http://dx.doi.org/10.1155/2018/5293568
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author Gervas, Hamenyimana Emanuel
Opoku, Nicholas Kwasi-Do Ohene
Ibrahim, Shamsuddeen
author_facet Gervas, Hamenyimana Emanuel
Opoku, Nicholas Kwasi-Do Ohene
Ibrahim, Shamsuddeen
author_sort Gervas, Hamenyimana Emanuel
collection PubMed
description 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) ≤ 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.
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spelling pubmed-62821832018-12-30 Mathematical Modelling of Human African Trypanosomiasis Using Control Measures Gervas, Hamenyimana Emanuel Opoku, Nicholas Kwasi-Do Ohene Ibrahim, Shamsuddeen Comput Math Methods Med Research Article 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) ≤ 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. Hindawi 2018-11-22 /pmc/articles/PMC6282183/ /pubmed/30595713 http://dx.doi.org/10.1155/2018/5293568 Text en Copyright © 2018 Hamenyimana Emanuel Gervas et al. http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Gervas, Hamenyimana Emanuel
Opoku, Nicholas Kwasi-Do Ohene
Ibrahim, Shamsuddeen
Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
title Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
title_full Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
title_fullStr Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
title_full_unstemmed Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
title_short Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
title_sort mathematical modelling of human african trypanosomiasis using control measures
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6282183/
https://www.ncbi.nlm.nih.gov/pubmed/30595713
http://dx.doi.org/10.1155/2018/5293568
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