Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

DOI

10.2991/assehr.k.210508.105How to use a DOI?

Keywords

Schistosomiasis model, Stability analysis, Center manifold, Lyapunov function

Abstract

In this work, a deterministic mathematical model of schistosomiasis transmission dynamics is discussed. In rural areas, many people work as a cattle farmer. Cattle farmers in endemic areas are very susceptible to schistosoma worm infection. To study the dynamics of schistosomiasis spread in traditional cattle farmer communities, we develop a mathematical model by considering human, cattle, and snail population as well as parasite density in environment. The model is expressed as a system of first order differential equations. Firstly, we verify the non-negativity and boundedness of the solutions of the model. After determining the equilibrium points of the system, we determine the basic reproduction number. Linearization and Routh Hurwitz condition are used to analyze the local stability condition of the disease free equilibrium point. Center manifold theory is used to study the local stability condition of the endemic equilibrium point. We prove global stability condition of the disease free equilibrium point by formulating suitable Lyapunov function and using LaSalle invariance principle. Several numerical simulations are presented. Our results show that the farmer should keep the cattle, water, and food clean. In addition, the farmer should use molluscicide in their farm area and give schistosomiasis drug to the cattle, regularly.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Wahyudin Nur
AU  - Trisilowati
AU  - Agus Suryanto
AU  - Wuryansari Muharini Kusumawinahyu
PY  - 2021
DA  - 2021/05/11
TI  - Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities
BT  - Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020)
PB  - Atlantis Press
SP  - 462
EP  - 470
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.210508.105
DO  - 10.2991/assehr.k.210508.105
ID  - Nur2021
ER  -