Epidemic Dynamics and Non-Pharmaceutical Interventions: A Mathematical Approach

We present a comparative analysis of three compartmental mathematical models aimed at capturing the dynamics of directly transmitted infectious diseases while explicitly incorporating social behaviour and non-pharmaceutical interventions (NPIs). The models are extensions of the classical SEIR framework and introduce heterogeneous social behaviours, behaviour switching mechanisms over time, and vaccination strategies. In Model 1, we consider a closed population with two subgroups differing in their adherence to NPIs. Model 2 incorporates vital dynamics and a hospitalization compartment, allowing long-term analysis. Model 3 further extends the framework by including vaccination and dynamic behavioural changes driven by the evolution of the epidemic. Through numerical simulations, we assess the impact of behavioural heterogeneity, timing of vaccination, and post-recovery behaviour on epidemic curves. The results show that early adoption of NPIs and timely vaccination significantly reduce infection peaks and cumulative cases. Behavioural transitions, if not sustained, can lead to secondary outbreaks. Our findings reinforce the importance of integrating behavioural and social aspects into epidemiological models to better inform public health policies and intervention planning.