An advanced version of a conformable mathematical model of Ebola virus disease in Africa

Abstract

An SIR-type (Susceptible-Infected-Recovered) model for the study of the spread of Ebola Virus Disease (EVD) is developed, by using conformable derivatives. Every possible way of transmission of the disease is incorporated (direct or indirect), such as funeral practices, consumption of contaminated bush meat and the environmental contamination etc. We have added an extremely important term to the model which have very high physical significance i.e., the possibility of the birth of an infected individual and the migration of an infected individual to the existing population. Well-posedness of the proposed problem has been shown by using a well-known theorem. The situations for the disease to be died out or sustain, have been discussed in the details. We found that the only disease-free situation is, the absence of flow of Ebola virus disease from the environment. We also have observed that by adopting a few strategies, such as isolation of infected individuals and careful burial of deceased bodies, the spread of EVD can be controlled. Memory effects for each case (disease-free and endemic states) are discovered (by using Khalil’s conformable transform) and plotted to make future predictions more accurately. Graphs are clearly elaborating that the problem is stable for both the equilibria states i.e., endemic state and disease-free state.

Keywords

• Initial value problem
• Ebola virus disease
• Nonlinear differential equations
• Conformable derivative
• Well-posedness