Dengue disease, basic reproduction number and control

TL;DR

This paper models dengue transmission dynamics, analyzes stability conditions, and demonstrates how insecticide control can keep the basic reproduction number below one to prevent outbreaks.

Contribution

It introduces a comprehensive transmission model with control parameters and applies it to a real outbreak case to inform vector control strategies.

Findings

The model identifies conditions for disease eradication.

Insecticide application can effectively reduce the reproduction number.

Case study confirms the model's practical relevance.

Abstract

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.