Simulation model for the dynamics of dengue with asymptomatic transmission and the effect of temperature

Abstract

Background: One of the fastest spreading vector-borne diseases in tropical and subtropical regions is dengue, which generates cost overruns for public health entities. Several factors can influence the dynamics of dengue virus transmission: environmental and climatic (abundance of vectors), interactions between hosts (infections by asymptomatic individuals), and population immunological factors. Given these conditions, it is necessary to carry out theoretical studies based on meteorological factors and asymptomatic transmission that are associated with both the existence of the vector and its incidence, in order to provide a scientific basis for health entities in decision-making. Methods: A mathematical model based on nonlinear ordinary differential equations is proposed to interpret the dynamics of dengue transmission in humans coupled to the dynamics of the Aedes aegypti species, considering the population of symptomatic and asymptomatic infected humans and the effect of temperature variability. The basic reproduction number was found and some simulation results based on the Runge-Kutta numerical method were obtained. Results: The simulations showed that the temperature had a directly proportional relationship with the basic reproduction number. The cases of infected people and carrier mosquitoes increased when the temperature peaks increased drastically; in low temperatures the infection persisted with low morbidity due to the survival of asymptomatic people. Conclusions: High temperatures tolerable by mosquitoes increase their life expectancy and their numbers in the environment which, together with a reservoir of asymptomatic infected people, leads to a higher incidence of the dengue virus in certain seasons or maintains its circulation in seasons of low temperatures, despite lower vector survival rates.