Modeling of Canine Distemper Virus in Amur Tigers Via Stochastic Differential Equations

This work investigates the stochastic dynamics of the Canine Distemper Virus, a pathogen whose impact on Amur tigers underscores the critical vulnerability of endangered species to viral outbreaks. We formulate a stochastic model and develop a computational method using a non-standard finite difference scheme to generate numerical solutions. After mathematically establishing the existence of these solutions, we evaluate the model's extinction thresholds and stationary distribution. By constructing a non-negative C 2 Lyapunov function, we derive rigorous conditions that ensure disease extinction and the persistence of a stationary distribution. Additionally, we analyze the stochastic asymptotic stability of the coexistence equilibrium. To validate our theoretical results, comprehensive numerical simulations are conducted for each epidemiological class for different values of the biological parameters.