Robustness of a two-strain dengue fever model with respect to asymmetry

We analyse the effects of symmetry of a two-strain compartmental dengue fever model. The model is an extension of the classical compartmental susceptible--infected--recovered (SIR) model where the exchange between the compartments is described by ordinary differential equations (ODE's). Two-strains of the virus exist so that a primary infection with one strain and secondary infection by the other strain can occur. There is life-long immunity to the primary infection strain, temporary cross-immunity followed by life-long immunity to the other strain after the secondary infection. Susceptible individuals can become infected with two different infection rates depending from whom they are getting the infection. In the previously studied models [1,2] the two stains identical with respect to their epidemiological functioning: that is the epidemiological process parameters of the two strains were assumed equal. As a result the mathematical model possesses a mathematical symmetry property.