# A Simple Mathematical Model for Ebola in Africa

## Authors

• Gosekwang Marica Moremedi* University of South Africa
• Roselyn Kaondera-Shava University of Botswana
• Jean M-S Lubuma University of Pretoria
• Neil Morris University of Pretoria
• Berge Tsanou University of Pretoria

## Abstract

In 2014, an outbreak of Ebola virus (Ebola) decimated people in western Africa. With more than 16000 clinically confirmed cases, and approximately 70\% case mortality, it was, В out of the twentieth Ebola threats since 1976, the deadliest. In В almost all the outbreaks, the index case (first patient) became infected through contact with an infected animal (hunted for food), such as a fruit bat or primate (apes, monkeys).В The virus can be spread to others via direct contact (through broken skin or mucous membranes in, the eyes, nose, or mouth) with: (1) blood or body fluids (including but not limited to urine, saliva, sweat, feces, vomit, breast milk, and semen); (2) objects (needles, syringes) that have been contaminated with body fluids; (3) infected fruit bats or primates. As reported in [1], 10\% and 3\% of the {\it Ebola-Zaire} virus type, survived on glass and plastic surfaces, respectively, after 14 days at $4^{\circ}$C. Moreover, 0.1-1\% of Ebola virus particles remained viable for up to 50 days at $4^{\circ}$C [2].In this talk, we propose a deterministic dynamical moedel which focuses both on the direct (route 1) and environmental (routes 2, 3) transmission routes. It is a SIR model with an additional environmental compartment regarded as the pool of Ebola viruses. This latter class is motivated; firstly by the consumption of bush-meat and fruit bats; second by the poor living and sanitary conditions of people in Ebola outbreak areas in Africa. The full model has only a unique endemic equilibrium which is locally asymptotically stable (LAS), while the model without provision of viruses has two equilibria: the disease-free equilibrium В which globally asymptotically stable (GAS) and the endemic equilibrium which is LAS.

## Author Biography

### Berge Tsanou, University of Pretoria

Mathematics and Applied mathematics

2015-05-24

## Section

Conference Contributions (Pretoria)