The impact of hospital resources and environmental perturbations on the dynamics of a disease transmission model with density-dependent demographics

Taking into account environmental fluctuations and the availability of public health resources, we develop both deterministic and stochastic models of the XYZN type. Deterministic model exhibit complex and diverse dynamics. In particular, the threshold ϕ suggests that sustained disease transmission and associated mortality can reduce the equilibrium population size below the environment’s carrying capacity, or even lead to population extinction in extreme cases. Our findings suggest that the persistence or eradication of this disease, within the stochastic model framework, is determined by the basic reproduction number $R_{0}^{s}$ . If $R_{0}^{s}<1$ , the disease is eradicated with probability 1, while $R_{0}^{s}>1$ implies the disease is almost surely stochastically permanent. In the part of numerical simulation, we selected data from Delhi, India during the COVID-19 period to verify our results.