Mathematical analysis of the impact of community ignorance on the population dynamics of dengue

Abstract

This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.