Host-vector dynamics of dengue with asymptomatic, isolation and vigilant compartments: insights from modelling

The important role of isolation and awareness in controlling dengue outbreak cannot be overemphasized. However, limited attention has been paid to the aspect of mathematical modelling of dengue incorporating these control factors. In this work, a nonlinear mathematical model of dengue dynamics in the presence of asymptomatic, isolation and vigilant compartments is developed and rigorously analysed. Based on positivity and boundedness of solutions, the model is shown to be mathematically well posed. The effective reproduction number of the model is calculated analytically. Further qualitative analysis suggests that the model exhibits the backward bifurcation property in the presence of the rate of immunity loss. However, it is shown that the absence of immunity loss can lead to the elimination of backward bifurcation property exhibited by the model. Using Lyapunov function method, the global asymptotic dynamics of the dengue model is shown. Sensitivity analysis is carried out to identify the key parameters that drive the dynamics of dengue transmission and spread in the population. Numerical simulations are carried out to investigate the effects of most sensitive parameters on the dynamics of dengue spread in the interacting populations. Without isolation, the disease's situation is seen to be much worse and the number of infected cases is seen to be fast increasing. Therefore, the study suggests that increasing the rates of isolation for symptomatic and asymptomatic infected individuals and fraction of vigilant individuals reduce dengue disease burden significantly.