Marcin Choiński, Warsaw University of Life Sciences, Warsaw, Poland
Joanna Rencławowicz, Polish Academy of Sciences, Warsaw, Poland
Urszula Skwara, University of Warsaw, Poland

Abstract: In this article we model two-strain dynamics of dengue transmission by both mosquitoes and humans with vertical transmission to larvae in the mosquito population. We include secondary infections, causing a severe form of disease. Mathematical analysis of proposed model is conducted - we study existence and local stability of equilibria of the system. While analysing the model, unusual properties emerged which lead us to implement its simplifications and obtain different results. Theoretical outcomes are accomplished with numerical simulations. They suggest that vertical transmission has a negligible impact on the dengue spread.

Keywords: dengue model, vertical transmission, disease-free equilibrium, endemic equilibrium, local stability of solutions