Abstract
Compartmental equations are primary tools in the study of disease spreading processes. They provide accurate predictions for large populations but poor results whenever the integer nature of the number of agents is evident. In the latter instance, uncertainties are relevant factors for pathogen transmission. Starting from the agent-based approach, we investigate the role of uncertainties and autocorrelation functions in the susceptible–infectious–susceptible (SIS) epidemic model, including their relationship with epidemiological variables. We find new differential equations that take uncertainties into account. The findings provide improved equations, offering new insights on disease spreading processes.
Highlights
Communicable diseases are health disorders caused by pathogens transmitted from infected individuals to susceptible ones [1]
We have investigated the effects of uncertainties in the SIS epidemic model, finding new differential equations for the average density of infected agents, ρ(t), and its corresponding variance, σ2(t)
At the core of this research, we have demonstrated that uncertainty cannot be neglected in the SIS epidemic model whenever the discreteness of the population is important, even when the population comprises statistically equivalent agents
Summary
Communicable diseases are health disorders caused by pathogens transmitted from infected individuals to susceptible ones [1]. The stochastic nature of disease transmission cannot be omitted for a number of scenarios It becomes more pronounced for small populations, where the characteristics of each agent forming the population are relevant variables to the spreading process [12]. Autocorrelation functions have been used to study time series of epidemiological data and assess the impact of spatial influences on stochastic fluctuations [15,16,17,18,19,20]. The new equations provide significant improvements over the traditional compartmental equation, as they account for stochastic effects, while being far more amenable to analytical studies than the master equation of the disease spreading process.
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