An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models.

Seasonal variations in the incidence of infectious diseases are a well-established phenomenon, driven by factors such as climate changes, social behaviors, and ecological interactions that influence host susceptibility and transmission rates. While seasonality plays a significant role in shaping epidemiological dynamics, it is often overlooked in both empirical and theoretical studies. Incorporating seasonal parameters into mathematical models of infectious diseases is crucial for accurately capturing disease dynamics, enhancing the predictive power of these models, and developing successful control strategies. In this paper, I highlight key modeling approaches for incorporating seasonality into disease transmission, including sinusoidal functions, periodic piecewise linear functions, Fourier series expansions, Gaussian functions, and data-driven methods. These approaches are evaluated in terms of their flexibility, complexity, and ability to capture distinct seasonal patterns observed in real-world epidemics. A comparative analysis showcases the relative strengths and limitations of each method, supported by real-world examples. Additionally, a stochastic Susceptible-Infected-Recovered (SIR) model with seasonal transmission is demonstrated through numerical simulations. Important outcome measures, such as the basic and instantaneous reproduction numbers and the probability of a disease outbreak derived from the branching process approximation of the Markov chain, are also presented to illustrate the impact of seasonality on disease dynamics.