A new mathematical model for Zika virus transmission

Shahram Rezapour,Hakimeh Mohammadi,Amin Jajarmi

doi:10.1186/s13662-020-03044-7

Abstract

We present a new mathematical model for the transmission of Zika virus between humans as well as between humans and mosquitoes. In this way, we use the fractional-order Caputo derivative. The region of the feasibility of system and equilibrium points are calculated, and the stability of equilibrium point is investigated. We prove the existence of a unique solution for the model by using the fixed point theory. By using the fractional Euler method, we get an approximate solution to the model. Numerical results are presented to investigate the effect of fractional derivative on the behavior of functions and also to compare the integer-order derivative and fractional-order derivative results.

Highlights

1 Introduction Zika virus was first detected in monkeys in 1947, and the first cases of Zika virus infection were reported in 1952 in Uganda and the Republic of Tanzania
It has spread to other countries around the world, so far Zika virus infection has been recorded in 86 countries
According to the report of World Health Organization (WHO), Zika virus infection during pregnancy can cause infants to be born with microcephaly and other congenital malformations, known as congenital Zika syndrome

Summary

Introduction

Zika virus was first detected in monkeys in 1947, and the first cases of Zika virus infection were reported in 1952 in Uganda and the Republic of Tanzania. The study of diseases dynamics is a dominating theme for many biologists and mathematicians (see, for example, [1–3]) It has been studied by many researchers that fractional extensions of mathematical models of integer order represent the natural fact in a very systematic way such as in the approach of Baleanu et al [4–17]. Fractional-order derivatives have expanded and have been widely used in modeling real-world phenomena and investigating the process of disease transmission and control (see, for example, [25–35]). 5. Definition 2.1 ([44]) For an integrable function g, the Caputo derivative of fractional order ν ∈ (0, 1) is given by CDνg(t) =. Definition 2.3 ([44]) The Laplace transform of Caputo fractional differential operator of order ν is given by m–1. According to the explanation presented, the transmission model of Zika virus for t ≥ 0 and ν ∈ (0, 1) is given as follows:.

Nonnegative solution

Conclusion