Approximate Solution of the Fractional Order Sterile Insect Technology Model via the Laplace–Adomian Decomposition Method for the Spread of Zika Virus Disease

Abstract

Sterile insect technology (SIT) is an environmental-friendly method which depends on the release of sterile male mosquitoes that compete with the wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring and as such reduces the population of Zika virus vector population over time, thereby eliminating the spread of Zika virus in a population. The fractional order sterile insect technology (SIT) model to reduce the spread of Zika virus disease is considered in this present work. We employed the use Laplace–Adomian decomposition method (LADM) to determine an analytical (approximate) solution of the model. The Laplace–Adomian decomposition method (LADM) produced a solution in form of an infinite series that further converges to the exact value. We compared solutions of the fractional model with the classical case using our plots and discovered that the fractional order has more degree of freedom and as such the system can be varied to get many preferred responses of the different classes of the model as the fraction (β) could be varied to the desired rate, say 0.7, 0.4, etc. We have been able to show that LADM can be used to solve an SIT model which has never been done before in literature.

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

“…The PHI-four equation has been studied in earlier research to provide the analytical and numerical solutions by using Adomian decomposition method [4], Sumudu transform method and Homotopy perturbation method [5][6][7], asymptotic iteration method [8], fourth order compact and conservative scheme [9], orthogonal spectral collocation scheme [10] based on Jacobi envelopes, Soliton of solitary wave using Anstaz technique [11], first integral method [12], modified extended direct algebraic method [13], natural decomposition method [14], bifurcation analysis and Anstaz method [15], variational iteration method [16], He's method [17] and others. For instances, recently LADT has been successfully implemented in a variety of differential model like; SDIQR model of Covid-19 [18], Lane emden differential equation [19], model of lassa diseases [20], numerical solution of large deflection beam [21], simulation of unsteady MHD flow in incompressible fluid [22], approximation of time fractional advection dispersion equation [23], approximate solution of fractional order sterile insect technology model [24] etc. Similarly various integral transforms [25,26] are implemented to solve higher order partial differential equations.…”

Approximate Solution of the Fractional Order Mathematical Model on the Transmission Dynamics on The Co-Infection of COVID-19 and Monkeypox Using the Laplace-Adomian Decomposition Method

“…al. [8] introduced a fractional order sterile insect technology (SIT) model to combat Zika virus transmission, employing the Laplace-Adomian decomposition method (LADM) to derive an analytical solution. They demonstrated that the fractional model offers greater flexibility, allowing for varied responses by adjusting the fractional order.…”

“…Substituting equation (9),(10) into equation(8) we obtained:Online ISSN: 2053-2210 (Online) Website: https://www.eajournals.org/ Publication of the European Centre for Research Training and Development -UK…”