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 epi...
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AIMS Press
2025-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2025013 |
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| author | Mahmudul Bari Hridoy |
| author_facet | Mahmudul Bari Hridoy |
| author_sort | Mahmudul Bari Hridoy |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e2b38e24882d44b0947ae7988c1909de |
| institution | DOAJ |
| issn | 1551-0018 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e2b38e24882d44b0947ae7988c1909de2025-08-20T03:16:58ZengAIMS PressMathematical Biosciences and Engineering1551-00182025-01-0122232435410.3934/mbe.2025013An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic modelsMahmudul Bari Hridoy0Department of Mathematics & Statistics, Texas Tech University, Lubbock, Texas 79409-1042, USASeasonal 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.https://www.aimspress.com/article/doi/10.3934/mbe.2025013seasonalitybranching processmarkov chaininfectious diseasestime-varying parameterstemporal dynamics |
| spellingShingle | Mahmudul Bari Hridoy An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models Mathematical Biosciences and Engineering seasonality branching process markov chain infectious diseases time-varying parameters temporal dynamics |
| title | An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models |
| title_full | An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models |
| title_fullStr | An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models |
| title_full_unstemmed | An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models |
| title_short | An exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models |
| title_sort | exploration of modeling approaches for capturing seasonal transmission in stochastic epidemic models |
| topic | seasonality branching process markov chain infectious diseases time-varying parameters temporal dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2025013 |
| work_keys_str_mv | AT mahmudulbarihridoy anexplorationofmodelingapproachesforcapturingseasonaltransmissioninstochasticepidemicmodels AT mahmudulbarihridoy explorationofmodelingapproachesforcapturingseasonaltransmissioninstochasticepidemicmodels |