A new conceptual disease triangle DST framework for balancing two extremes: Disease eradication and species...

Understanding the drivers of extinction risk in endangered species requires addressing the interplay of disease, population dynamics, and environmental stochasticity. In this study, we developed a disease-ecological model that integrates Allee effects into susceptible-infected-recovered (SIR) dynamics and stochasticity to explore their combined impact. Using Canine Distemper in African wild dogs as the main system, we introduce the Disease-Stochasticity-Tipping (DST) triangle, a framework capturing vulnerabilities that emerge from interactions among disease resilience, stochasticity, and tipping phenomena. Our analysis shows that these forces rarely act independently; their interplay shapes disease eradication and species extinction. Key findings along the disease resilience-tipping edge, weak Allee strength stabilizes populations at endemic equilibria, allowing population recovery, while strong Allee strength may trigger extinction via homoclinic bifurcation, though sufficient disease resilience can prevent collapse. On the disease resilience-stochasticity edge, strong resilience limits the influence of stochastic effects on disease persistence. Stochasticity-tipping edge illustrates at low noise levels, bistable dynamics allow populations to coexist or become extinct depending on initial population sizes, but higher noise intensity drives a shift toward noise-induced tipping. The DST triangle, thus, provides a robust, novel framework for guiding disease management and conservation efforts under stochasticity and the Allee effect.