Seasonal synchronization and unpredictability in epidemic models with waning immunity and healthcare thresholds

This paper explores a model integrating healthcare capacity thresholds and seasonal effects to investigate the synchronization of epidemic cycles with seasonal transmission rates, using parameters reflective of the COVID-19 pandemic. Through bifurcation analysis in the epi-seasonal domain, we identify regions of significant seasonal synchronization related to transmission rate fluctuations, waning immunity, and healthcare capacity thresholds. The model highlights four sources of unpredictability: chaotic regimes, quasiperiodicity, proximity to SNIC or transcritical bifurcations, and bistability. Our findings reveal that chaotic regimes are more predictable than quasiperiodic regimes in epidemiological terms. Synchronizing outbreaks with seasonal cycles, even in chaotic regimes, predominantly results in significant winter outbreaks. Conversely, quasiperiodicity allows outbreaks to occur at any time of the year. Near eradication unpredictability aligns with historical pertussis data, underscoring the model's relevance to real-world epidemics and vaccine schedules. Additionally, we identify a bistability region with potential for abrupt shifts in disease prevalence, triggered by superspreading events or migration.