Joanna Rencławowicz, Military University of Technology, Warsaw, Poland
Marcin Choiński, Warsaw University of Life Sciences - SGGW
Urszula Skwara, University of Warsaw, Poland

Abstract: In this study, we examine a two-strain dengue model that captures the interactions between human and mosquito populations. The proposed model incorporates the possibility of reinfection with a different strain and vertical transmission of the virus from adult mosquitoes to their offspring. We assume that the recruitment rate for susceptible larval mosquitoes is constant, which allows us to show the local stability of the disease-free equilibrium, the existence and local stability of endemic equilibrium in the case of one strain as well as the existence of two-strain stationary states. What is important, these results are obtained despite the non-constant size of mosquito population. To support our findings, we present numerical simulations with realistic dengue parameters that reflect biological phenomena.

Keywords: dengue, constant recruitment, vertical transmission, two-strain equilibrium, local stability