A stochastic analysis of co-infection model in a finite carrying capacity population

The paper focuses on the study of an epidemic model for the evolution of diseases, using stochastic models. We demonstrated the encoding of this intricate model into formalisms suitable for analysis with advanced stochastic model checkers. A co-infection model’s dynamics were modeled as an Ito–Levy stochastic differential equations system, representing a compartmental system shaped by disease complexity. Initially, we established a deterministic system based on presumptions and disease-related traits. Through non-traditional analytical methods, two key asymptotic properties: eradication and continuation in the mean were demonstrated. Section 2 provides a detailed construction of the model. Section 3 results confirm that the outcome is biologically well-behaved. Utilizing simulations, we tested and confirmed the stability of all equilibrium points. The ergodic stationary distribution and extinction conditions of the system are thoroughly analyzed. Investigations were made into the stochastic system’s probability density function, and digital simulations were employed to illustrate the probability density function and systems’ extinction. Although infectious disease control and eradication are major public health goals, global eradication proves challenging. Local disease extinction is possible, but it may reoccur. Extinction is more feasible with a lower [Formula: see text]. Notably, our simulations showed that reducing the [Formula: see text] value significantly increases the likelihood of disease extinction and reduces the probability of future recurrence. Additionally, our study provides insights into the conditions under which a disease can persist or become extinct, contributing to more effective disease control strategies in public health.