FRACTIONAL TRANSMISSION MODEL FOR ZIKA VIRUS

Abstract

In this work, we studied the dynamics of a Zika virus model within the framework of the Caputo fractional derivative. Using a fixedpoint approach, we establish conditions for which the considered fractional model admits a unique system of solutions. The two-step Adams-Bashforth numerical scheme incorporating the fractional order parameter index σ is then used to furnish numerical
simulations demonstrating the behaviour of the model state variables with respect to distinct values of the fractional order parameter index.
As the value of σ increases from 0.7 to 1, there is decrease in the number of susceptible individuals and then a gradual increase after some time t, until it steadies at equilibrium. It was also observed that as the value of the fractional order parameter increases from 0.7 to 1 the number of exposed and infected individual decreases while the number of recovered individual increases after some time. Furthermore as the value of susceptible and exposed vector decreases, the number of infected
vector increases and then decreases after some time.