Transmission dynamics of zika virus in presence of vertical transmission and some preventive measures

Abstract

Zika virus (ZIKV) infection is a vector-born human disease which enhances the chance of various types of neurological complications in affected individual. In this work we have studied a mathematical model of ZIKV by incorporating vector, direct (sexual) and vertical transmission paths of the virus. In our model also we have considered different kind of preventive measures like as: protection of susceptible individuals from mosquito bites, isolation of infected individuals from mosquito, protection of susceptible individuals from sexual interaction with infected individuals, and mosquitoes control effort. We have found the analytical expression of basic reproduction number and studied the stability of the disease free equilibrium point. Existence of endemic equilibrium point and its stability are also studied. The proposed model exhibits a backward bifurcation when the virus transmission probability from infected human to mosquito crosses the crucial value. We have fitted the model to real data and estimated the key model parameters and their 95% confidence interval which depict the ZIKV outbreak in French Polynesia in 2013-14. We also have estimated the basic reproduction number using first nine epidemic weeks (EW) data and the estimated value is 2.87 with lower and upper values are 2.47 and 3.32 respectively. The effective reproduction number of the outbreak also has been studied and which decreases gradually from 5.404 to 0.2499 during the period 11th October, 2013 and 28th March, 2014. According to our sensitivity analysis, the basic reproduction number is the most sensitive with controllable parameters, biting rate, mosquito recruitment rate, mosquito death rate and recovery rate from infection. Finally, numerically we have studied the impact of different parameters on the basic reproduction number and on the number of infected human population.