Qualitative and Quantitative study of Zika virus epidemic model under Caputo’s fractional differential operator

Abstract

The Zika virus is considered to be one of the dangerous virus, which spread in the community through small insect so-called mosquitoes. Some of the other will known methods by which the consider virus may transform are: pregnant mother can pass it to her baby during the pregnancy or birth time, it can also spread through sexual intercourse. Therefore, the world health organization (WHO) declares the Zika infection with clusters of microcephaly and other neurological disorders constitutes a public health emergency of international concern. To understand the dynamics of Zika infectious virus, we investigate the fractional order mathematical model for the transference of Zika infectious disease. The proposed model is divided into seven compartments. Particularly, the author’s used the results of fixed point theory to discuss the existence and uniqueness of the solution and stability analysis for the proposed model. Furthermore, we have calculated the equilibrium points, basic reproduction number and stability of the basic reproduction number. In addition, for the numerical solution of the said model, the author’s used two steps fractional Adam’s Bashforth method (FABm). Finally, numerical simulation and discussion of the graphical representation of the solutions obtained via FABm are given.