Minimum Vector Control Intensity to Get a Stable Fixed Point in a Mosquito Dynamic Model

ABSTRACT

Vector-borne diseases are a cause of concern all around the world, especially in Brazil. In the past few years, the Brazilian health system faced recurrent epidemics such as Dengue and Malaria as well as new cases of Chikungunya, Zika and Yellow Fever. Vector control continues to be one of the most important counter measures against these types of diseases. Mathematical models are important tools for planning vector control strategies. In this work we present an approach in order to calculate what is the minimum vector control intensity to obtain stability in a simple population’s dynamics model of mosquitoes. We combined numerical simulations with analytic results. Transcritical bifurcations appear in our analysis considering different control’s parameters values for the eggs, larvae, pupae and adults mosquitoes populations. A discussion about combined strategies of vector control was also showed.

Keywords:
modelling; population dynamic; stability; simulation