Numerical study of Zika model as a mosquito-borne virus with non-singular fractional derivative

Abstract

Zika virus infection, which is closely related to dengue, is becoming a global threat to human society. The transmission of the Zika virus from one human to another is spread by bites of Aedes mosquitoes. Recent studies also reveal the fact that the Zika virus can be transmitted by sexual interaction. In this paper, we use the fractional derivative with Mittag–Leffler non-singular kernel to study Zika virus transmission dynamics. This fractional is also known as the Atangana–Baleanu Caputo (ABC) derivative which is employed for the resulting system of ordinary differential equations. We investigate the proposed Zika virus model by using the Legendre spectral method. The model parameters are estimated and validated numerically by investigating the effect of fractional order exponent on various cases such as Susceptible human, infected human, asymptomatic carrier, exposed human, and recovered human. Numerical results obtained with the proposed method have been compared with exact solutions, showing in all parameters a very satisfactory agreement.