APPROXIMATE SOLUTION OF FRACTIONAL ORDER MATHEMATICAL MODEL ON THE CO-TRANSMISSION OF ZIKA AND CHIKUNGUNYA VIRUS USING LAPLACE ADOMIAN DECOMPOSITION METHOD

Gaining insight into the transmission dynamics of the Zika and Chikungunya viruses, as well as their co-infection, is essential for implementing efficient public health interventions. This paper presents a comprehensive fractional order mathematical model consisting of thirteen non-linear compartments to accurately represent the intricate interactions between humans and infected mosquito populations, as well as the challenges associated with their identification. In order to solve this model, we utilize the Laplace Adomians Decomposition Method (LADM), which is a very effective analytical technique for solving nonlinear differential equations. By utilizing LADM, we obtained infinite series solutions for the previously given model that ultimately converged to its precise solutions. The numerical simulations of the model demonstrate the transmission patterns of Zika virus, Chikungunya virus, and their co-infections for different values of . We utilized the fmicon algorithm, a MATLAB optimization tool, to accurately fit into the model, real-life data from Espirito Santos State in Brazil, where two viruses are concurrently spreading. The simulation deduce that, reducing mosquito biting rates and promoting compliance with treated bed net usage can substantially mitigate Zika-Chikungunya co-infection dynamics

Modeling the Control of Zika Virus Vector Population Using the Sterile Insect Technology

This work is aimed at formulating a mathematical model for the control of mosquito population using sterile insect technology (SIT). SIT is an environmental friendly method, which depends on the release of sterile male mosquitoes that compete with wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring. The basic offspring number of the mosquitoes’ population was computed, after which we investigated the existence of two equilibrium points of the model. When the basic offspring number of the model M0, is less than or equal to 1, a mosquito extinction equilibrium point E2, which is often biologically unattainable, was shown to exits. On the other hand, if M0>1, we have the nonnegative equilibrium point E1 which is shown to be both locally and globally asymptotically stable whenever M0>1. Local sensitivity analysis was then performed to know the parameters that should be targeted by control intervention strategies and result shows that female mating probability to be with the sterile male mosquitoes ρS, mating rate of the sterile mosquito β2, and natural death rates of both aquatic and female mosquitoesμA+μF have greater impacts on the reduction and elimination of mosquitoes from a population. Simulation of the model shows that enough release of sterile male mosquitoes into the population of the wild mosquitoes controls the mosquito population and as such can reduce the spread of mosquito borne disease such as Zika