Failure of R 0 near the epidemic threshold in the classical SIS model

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Abstract The primary predictor of a disease outbreak and severity is the basic reproduction number R 0 , which represents the average number of secondary cases produced by introducing an infected individual into an entirely susceptible population. According to the classical SIS model, a disease with R 0 less than one will eventually die out and persist if R 0 is greater than one. Using the pair-approximation method, we reconstruct the classical SIS model by explicitly accounting for neighbourhood interactions between susceptible and infected individuals. Specifically, the disease can only be transmitted, with some transmission probability, if a susceptible individual is surrounded by at least one infected individual within its direct neighborhoods. Despite the simplicity of the SIS model present here, results produced by the pair-approximation model deviates significantly from predictions by the mean-field approximation model, particularly near the epidemic threshold. Contrasting the standard SIS model based on the mean-field approach, we find scenarios where the disease dies out even if R 0 is greater than one. We suggest a crucial need for redefining the basic reproduction number on a smaller spatial scale and taking the average R 0 over a global scale, rather than applying it globally to an entire population. However, in the realm of more intricate models of infectious diseases, it remains an open question to what extent mean-field approximation predictions diverge from predictions produced by models that consider neighborhood interactions.

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