Stochastic extension of a two-strain SIR model with non-monotone incidence functions: Analysis of stochastic thresholds and disease dynamics

In this manuscript, we consider a two-strain SIR epidemic model with two non-monotonic transmission processes, moving from a deterministic to a stochastic differential framework with noise incorporated into the incidence functions. Within the stochastic regime, we identify two stochastic critical thresholds that dictate the dynamics of the disease, steering it towards either extinction or persistence in mean over time. We establish the existence of a unique positive solution using stochastic Lyapunov functions and corroborate our theoretical findings with numerical simulations, providing a comprehensive insight into the complex disease dynamics under stochastic influences. • Proposes a stochastic two-strain SIR model with non-monotone incidence. • Derives two stochastic thresholds governing extinction or mean persistence. • Establishes a unique global positive solution via Lyapunov techniques. • Numerical experiments confirm theory and illustrate complex dynamics. • Provides insights for public-health responses to multi-strain disease outbreaks.