Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle

Rift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number ℛ0 is computed and used in analysing the stability of disease when an outbreak occurs. Numerical simulations are performed in order to the variation of each population at order α=1,0.75,0.5, and 0.25. Results from simulations show that there is an increase in susceptible and exposed population in both human and mosquitoes as the value of α decreases. The infected population decreases with a decrease in the value of α. However, a rapid increase in susceptible mosquitoes is observed just after the first 30 days and a rapid decrease in infected human and mosquitoes after the first 30 days for α=1. Hence, fractional-order derivative also plays a significant role in providing insight on disease transmission and dynamics.