E Mbah Godwin Christopher, Sunday Onah Ifeanyi, Ojoma Ahman Queeneth, C Collins Obiora, C Asogwa Christopher, Chukwudi Okoye
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.
Department of Mathematical Sciences, Confluence University of Science and Technology, Kogi State, Nigeria.
Afr J Infect Dis. 2022 Dec 22;17(1):10-26. doi: 10.21010/Ajidv17i1.2. eCollection 2023.
Ebola Virus causes disease both in human and non-human primates especially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date.
We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus in a population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease- endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle's Invariant principle.
The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.
Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.
埃博拉病毒在人类和非人类灵长类动物中均会引发疾病，尤其在发展中国家。2014年疫情爆发期间，它导致了大量死亡，特别是在西非的一些贫困地区，其影响至今仍有体现。
我们研究了埃博拉病毒的传播，并获得了一个由十八个方程组成的方程组，该方程组完整地描述了在纳入控制措施的人群中埃博拉病毒的传播情况，同时还纳入了接触该疾病的一个主要源头，即传统的尸体清洗行为。我们使用雅可比矩阵方法研究了无病平衡点的局部稳定性，并使用中心流形定理研究了疾病流行平衡点的稳定性。我们还使用拉萨尔不变原理研究了平衡点的全局稳定性。
结果表明，无病平衡点和流行平衡点在局部和全局都是稳定的，并且该系统呈现出前向分岔。
进行了数值模拟，我们的图表显示，对易感人群而言，使用疫苗和避孕套最为有效；对暴露人群而言，检疫最为有效；对感染人群而言，隔离最为有效；对患病死亡者进行妥善埋葬最有利于避免疾病在人群中进一步传播，并实现更快更好的康复。
