Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Mathematical Modelling of Human African Trypanosomiasis Using Control Measures

Version 1 : Received: 23 October 2018 / Approved: 24 October 2018 / Online: 24 October 2018 (09:05:54 CEST)

A peer-reviewed article of this Preprint also exists.

Hamenyimana Emanuel Gervas, Nicholas Kwasi-Do Ohene Opoku, and Shamsuddeen Ibrahim, “Mathematical Modelling of Human African Trypanosomiasis Using Control Measures,” Computational and Mathematical Methods in Medicine, vol. 2018, Article ID 5293568, 13 pages, 2018. https://doi.org/10.1155/2018/5293568. Hamenyimana Emanuel Gervas, Nicholas Kwasi-Do Ohene Opoku, and Shamsuddeen Ibrahim, “Mathematical Modelling of Human African Trypanosomiasis Using Control Measures,” Computational and Mathematical Methods in Medicine, vol. 2018, Article ID 5293568, 13 pages, 2018. https://doi.org/10.1155/2018/5293568.

## Abstract

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, R0, and also it is proved that if R0 ≤ 1 the disease free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persist in the population if the value of R0 > 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 are very efficient and effective to eliminate HAT in Africa.

## Keywords

Human African Trypanosomiasis (HAT), Mathematical modelling, optimal control, Control measures

## Subject

Computer Science and Mathematics, Computational Mathematics

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Comment 1
Commenter: Ndajem Modester Mubat
The commenter has declared there is no conflict of interests.
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Commenter:
The commenter has declared there is no conflict of interests.
Comment: @ Ndajem Modester Mubat, Thank you for your comment. We are encouraged.

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