Influence of asymptomatic people on malaria transmission: a mathematical model for a low-transmission area case

Malaria remains a primary parasitic disease in the tropical world, generating high morbidity and mortality in human populations. Recently, community surveys showed a high proportion of asymptomatic cases, which are characterized by a low parasitemia and a lack of malaria symptoms. Until now, the asymptomatic population is not treated for malaria and thus remains infective for a long time. In this paper, we introduce a four-dimensional mathematical model to study the influence of asymptomatic people on malaria transmission in low-transmission areas, specifically using data from Brazil. The equilibrium points of the system are calculated, and their stability is analyzed. Via numerical simulations, more in-depth analyzes of the space of some crucial parameters on the asymptomatic population are done, such as the per capita recovery rates of symptomatic and asymptomatic people, the ratio of the density of mosquitoes to that of humans, the mortality rate of mosquitoes and the probability of undergoing asymptomatic infection upon an infectious mosquito bite. Our results indicate that the disease-free equilibrium is inside the stability region if asymptomatic people are treated and/or the ratio of the density of mosquitoes to that of humans is decreased and/or the mortality rate of mosquitoes is increased.