Abstract
The stochastic SIS epidemic model is well-known for its critical threshold Rs, indicating the transition between disease eradication (Rs < 1) and epidemic outbreaks (Rs > 1). However, the scenario where Rs = 1 has been uncertain. We present a definitive resolution to this pivotal issue. Additionally, we introduce advancements in analyzing the disease-free state of equilibrium when Rs < 1 to deepen our understanding of the system dynamics. To validate our theoretical developments and provide visual evidence, extensive computer simulations are conducted, enhancing the comprehensiveness and applicability of our findings to the broader field of epidemiology and infectious disease modeling. The implications of our results extend to public health policies and interventions aimed at effectively managing and controlling infectious diseases in different communities where Rs hovers around the critical value.
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