A study on epidemic modelling using deterministic and stochastic SIR compartmental models

Abstract

Epidemic modelling is imperative as it provides predictions that aid timely interventions during a disease outbreak. Most works in the field adopt the SIR compartmental model as a foundation, before employing various deterministic and stochastic strategies to simulate the dynamics of an epidemic. In our research, we have chosen to apply the deterministic ODE and stochastic complex networks, with Higher-Ordered Interactions (HOIs) approaches. Through experiments using ODEs on different r0 and initial conditions, we identified a threshold r0 that could result in the infection of an entire population, thus serving as an indicator for epidemic monitoring. However, as ODEs assume homogeneity in interactions, they are generally considered unrealistic. To circumvent this, the stochastic complex networks (with HOIs) were developed to study virus reproducibility. Among all networks considered, the BA network in particular has shown to consistently demonstrate spikes in epidemic reproduction at the onset, suggesting higher vulnerability to epidemic spreading for real-world communal structures with properties akin to the BA network. In the model, an infectibility parameter, rℓ was also found to be closely related in estimating actual virus transmission, and larger values of rℓ were shown to potentially outweigh effects by an epidemic infectious period. Lastly, HOIs were integrated on the networks and a group transmissibility (psc) > pairwise (pT = 0.1) was shown to steer the course of an epidemic and change actual virus reproducibility for different networks, highlighting the need to reduce group interactions to curb epidemic spreading. Through the constructs of our project, we hope to further develop a more comprehensive epidemic modelling framework that would provide insightful estimates on virus reproducibility when an outbreak ensues