Mathematical modeling on co-infection: transmission dynamics of Zika virus and Dengue fever

In this paper, a deterministic mathematical model for Dengue Fever (DF) and Zika virus (ZIKV) co-infection transmission dynamics is formulated and analyzed. Two sub-models, namely ZIKV-only and DF-only sub-models, are considered first of all. Rigorous qualitative analysis of the sub-models reveals that each of the diseases undergoes the phenomenon of backward bifurcation when the associated reproduction number of both ZIKV-only and DF-only sub-models (denoted by R0z+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0z}^{+}$$\end{document} and R0d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_{0d}$$\end{document} respectively) is less than unity. It is shown, using the centre manifold theory that the full ZIKV-DF co-infection model undergoes a backward bifurcation phenomenon. In addition, simulation of the full ZIKV-DF model shows the clear picturization of disease transmission and also we provide the solution of model numerically in detail.