Symmetry in a multi-strain epidemiological model with distributed delay as a general cross-protection period and disease enhancement factor

Important biological features of viral infectious diseases caused by multiple agents with interacting strain dynamics continue to pose challenges for mathematical modelling development. Motivated by dengue fever epidemiology, we study a system of Integro-Differential Equations (IDE) considering strain structure of pathogens. Knowing that complex dynamics observed in dengue models are driven by the combination of two biological features, the temporary cross-immunity (TCI) and disease enhancement via the antibody-dependent enhancement process (ADE), our IDE system incorporates the TCI with a general time delay term, and the ADE effect by a constant factor to differentiate the susceptibility of individuals experiencing a primary or a secondary infection. Aiming at analysing the effect of the symmetry on dengue serotypes in the IDE framework, a detailed qualitative analysis of the model is performed and the instability of the coexistence steady state is shown using the perturbation theory approach. Numerical simulations identify the bifurcation structures and confirm the stability analysis. Results for the symmetric and asymmetric models are discussed.