Dengue transmission is shaped by multiple viral serotypes, temporary cross-immunity (TCI), antibody-dependent enhancement (ADE), and repeated exposure in endemic populations. Classical multi-strain models usually assume lifelong protection against reinfection with the same serotype. However, recent evidence suggests that homologous dengue reinfections, although rare, can occur. Their population-level consequences remain poorly understood.

We extend a two-infection, two-strain dengue model with TCI and ADE-mediated transmission differences to include homologous reinfections. Homologous reinfection is represented by two parameters: relative susceptibility to reinfection with the same serotype and relative infectiousness during homologous reinfection. Using equilibrium analysis, bifurcation diagrams, simulations, and phase-space projections, we examine how these parameters affect dengue dynamics under intermediate and long TCI durations, with and without seasonality.

The results indicate that rare homologous reinfection pathways can influence long-term dengue dynamics when interacting with immune history, TCI, ADE-mediated transmission differences, and seasonal variation. Incorporating such pathways may improve understanding of recurrent outbreaks and irregular incidence patterns in highly exposed populations.

In this talk we study the dynamics of two recently introduced mean-field models representing the behavior of

heterogeneous all-to-all coupled quadratic integrate-and-fire neural networks.

Firstly we study the phenomena that when there are synaptic dynamics in the model, which allows a delay in synaptic transmission, it seems to reduce the emergence of

chaotic dynamics by increasing the synaptic time constant and maintains a phase-locked state in the form of bursting dynamics in the mean-field model. We examine in depth the different dynamical

behaviors that can be found in both mean-field models (spiking, bursting, and Rossler-like chaotic behaviors) and study in detail the bifurcations underlying their appearance and disappearance.

Moreover, we relate the disappearance of various behaviors with the recently introduced geometric bifurcations.

And secondly, we focus on the use of mean-field models in a theoretical study of tonic-clonic epileptic seizures. These are a particularly important class of epilepsy and have previously been theorised to arise in systems with an instability from one temporal rhythm to another via a quasi-periodic transition. We show that a recently introduced class of next generation neural field models has a sufficiently rich bifurcation structure to support such behaviour. 

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