J Math Biol. 2026 Jul 9;93(2):16. doi: 10.1007/s00285-026-02434-x.
ABSTRACT
Strain evolution poses a global threat, yet medical resources often fall short of meeting the demands of such public health emergencies. To examine how constrained medical resources and random factors influence disease transmission dynamics, this study incorporates the limited number of hospital beds into a stochastic infectious disease model that accounts for strain evolution and transmission rate affected by the logarithmic Ornstein-Uhlenbeck process. The primary contributions include deriving sufficient conditions that guarantee the existence, uniqueness and boundedness of the positive global solution for the stochastic model, identifying thresholds governing disease extinction and persistence and establishing sufficient conditions for the existence of a stationary distribution, based on which we compute the probability density function of the model to quantify the final size of the disease from a statistical perspective. Numerical simulations indicate that: (i) when strain 1 exhibits dominant transmissibility, it secures a dominant competitive position via its transmission advantage, while strain 2 sustains endemic transmission by exploiting recovered individuals, enabling the long-term coexistence of both strains. By contrast, when the two strains have comparable transmissibility, strain 1, which depends exclusively on susceptible individuals for transmission and survival, is eliminated via competitive exclusion by strain 2 (which can infect individuals recovered from strain 1), and is ultimately driven to extinction; (ii) for epidemic prevention and control, we should not only constrain the mean transmission rate of the disease below the epidemic threshold, but also reserve an adequate control safety margin against stochastic fluctuations in transmission rate; (iii) in the early stage of an epidemic when medical resources are scarce, it is necessary to rapidly expand hospital bed capacity. Once resource supply matches the epidemic demand, the focus of prevention and control should be shifted to optimizing the efficiency of resource scheduling. These results have certain significance for preventing and controlling diseases with such transmission patterns.
PMID:42426308 | DOI:10.1007/s00285-026-02434-x
