Transmission Dynamics of a Novel Fractional Model for the Marburg Virus and Recommended Actions

Abstract

Marburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana-Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R-0 < 1, Castillo's method and the next-generation matrix are used to demonstrate the disease-free equilibrium's asymptotic global stability. When R-0 > 1, the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model's basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution's existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model's numerical simulations.