Spread of Zika virus disease on complex network—A mathematical study

Abstract

Zika virus epidemic poses a major threat to public health globally. Initially, this disease was limited to Africa but now it is spreading throughout the World. It is well known that zika virus is transmitted to human by the bites of Aedes mosquitoes. Recently, there are reported cases of sexual transmission and transmission due to blood transfusion in many countries e.g., Argentina, France, New Zealand, USA etc. In this paper a mathematical model of Zika virus on complex network is formulated and analyzed keeping in mind both mosquito-borne and sexual transmission of this disease. The existence and global stability of disease-free equilibrium are discussed in detail. The basic reproduction number R0 of the model is computed and it is found that for R0<1, the disease-free equilibrium of the model is globally asymptotically stable under some condition. In addition to this the final size relation of the proposed model is also computed. The key parameters of the model are computed using curve fitting to the real data by least-square method. Sensitivity analysis and numerical simulation are also performed for our proposed model. Finally, this model is extended to optimal control problem, to find the suitable cost-effective and time-dependent control strategies to reduce the number of infectives in a desired interval of time.