Stray dog culling for rabies control: a stochastic modelling study

A stochastic continuous-time Markov chain (CTMC) model, rooted in a deterministic approach, investigates rabies dynamics within human and stray dog populations. Stability analysis confirms the disease-free equilibrium is globally asymptotically stable for $R_e<1$, while an endemic equilibrium persists for $R_e>1$. Through a Galton-Watson branching process, the stochastic threshold is derived, providing extinction probabilities that align closely with 10,000 numerical sample paths. The CTMC model predicts two distinct outcomes, disease extinction or persistence, and demonstrates a positive probability of rabies extinction in finite time even when $R_e>1$. This contrast is significant because the deterministic model predicts a certain outbreak under identical conditions, whereas the stochastic framework captures the possibility of early extinction due to demographic fluctuations. Sensitivity analysis identifies the natural death rate and culling intensity as the most influential parameters. Results show a direct correlation between culling intensity and the probability of rabies elimination.