Modeling the Transmission Routes of Hepatitis E Virus as a Zoonotic Disease Using Fractional-Order Derivative

Abstract

Hepatitis E virus (HEV) is one of the emerging zoonotic diseases in Sub-Saharan Africa. Domestic pigs are considered to be the main reservoir for this infectious disease. A third of the world’s population is thought to have been exposed to the virus. The zoonotic transmission of the HEV raises serious zoonotic and food safety concerns for the general public. This is a major public health issue in both developed and developing countries. The World Health Organization (WHO) estimated that 44,000 people died in 2015 as a result of HEV infection. East and South Asia have the highest prevalence of this disease overall. In this study, we proposed, developed, and analyzed the transmission routes of the infection using a fractional-order derivative approach. The existence, stability, and uniqueness of solutions were established using the approach and concept in Banach space. Local and global stability was determined using the Hyers–Ulam (HU) stability approach. Numerical simulation was conducted using existing parameter values, and it was established that, as the susceptible human population declines, the number of infected human populations rises with a change in fractional order θ^. When the susceptible pig population increases, the number of infected pig populations rises with a change in θ^. It was observed that a few variations in the fractional derivative order did not alter the function’s overall behavior with the results of numerical simulations. Moreover, as the number of recovered human populations increases, there is a corresponding increase in the population of recovered pigs with a change in θ^. The exponential increase in the infected pig population can be controlled by treatment of the infected pigs and prevention of the susceptible pigs. The authors recommend policymakers, and stakeholders prioritize the fight against the virus by enforcing the prevention of humans and treatment of infected pigs. The model can be extended to optimal control and cost-effectiveness analysis to determine the most effective control strategy that comes with less cost in the combat of the disease.