Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach
Traditional compartmental models of epidemic transmission often predict an initial phase of exponential growth, assuming uniform susceptibility and interaction within the population. However, empirical outbreak data frequently show early stages of sub-exponential growth in case incidences, challengi...
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AIMS Press
2024-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2024321 |
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| author | Ping Yan Gerardo Chowell |
| author_facet | Ping Yan Gerardo Chowell |
| author_sort | Ping Yan |
| collection | DOAJ |
| description | Traditional compartmental models of epidemic transmission often predict an initial phase of exponential growth, assuming uniform susceptibility and interaction within the population. However, empirical outbreak data frequently show early stages of sub-exponential growth in case incidences, challenging these assumptions and indicating that traditional models may not fully encompass the complexity of epidemic dynamics. This discrepancy has been addressed through models that incorporate early behavioral changes or spatial constraints within contact networks. In this paper, we propose the concept of 'frailty', which represents the variability in individual susceptibility and transmission, as a more accurate approach to understanding epidemic growth. This concept shifts our understanding from a purely exponential model to a more nuanced, generalized model, depending on the level of heterogeneity captured by the frailty parameter. By incorporating this type of heterogeneity, often overlooked in traditional models, we present a novel mathematical framework. This framework enhances our understanding of how individual differences affect key epidemic metrics, including reproduction numbers, epidemic size, likelihood of stochastic extinction, impact of public health interventions, and accuracy of disease forecasts. By accounting for individual heterogeneity, our approach suggests that a more complex and detailed understanding of disease spread is necessary to accurately predict and manage outbreaks. |
| format | Article |
| id | doaj-art-596234d8cf4843d29b58cc27f62b8846 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-596234d8cf4843d29b58cc27f62b88462025-01-23T07:48:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182024-10-0121107278729610.3934/mbe.2024321Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approachPing Yan0Gerardo Chowell1Department of Statistics and Actuarial Science, University of Waterloo, Ontario, CanadaSchool of Public Health, Georgia State University, Atlanta, Georgia, USATraditional compartmental models of epidemic transmission often predict an initial phase of exponential growth, assuming uniform susceptibility and interaction within the population. However, empirical outbreak data frequently show early stages of sub-exponential growth in case incidences, challenging these assumptions and indicating that traditional models may not fully encompass the complexity of epidemic dynamics. This discrepancy has been addressed through models that incorporate early behavioral changes or spatial constraints within contact networks. In this paper, we propose the concept of 'frailty', which represents the variability in individual susceptibility and transmission, as a more accurate approach to understanding epidemic growth. This concept shifts our understanding from a purely exponential model to a more nuanced, generalized model, depending on the level of heterogeneity captured by the frailty parameter. By incorporating this type of heterogeneity, often overlooked in traditional models, we present a novel mathematical framework. This framework enhances our understanding of how individual differences affect key epidemic metrics, including reproduction numbers, epidemic size, likelihood of stochastic extinction, impact of public health interventions, and accuracy of disease forecasts. By accounting for individual heterogeneity, our approach suggests that a more complex and detailed understanding of disease spread is necessary to accurately predict and manage outbreaks.https://www.aimspress.com/article/doi/10.3934/mbe.2024321epidemic modelingsub-exponential growthfrailty modelparameter identifiabilityheterogeneitytransmission dynamicsgeneralized growth modelinfectious diseasesstochastic modelingforecasting |
| spellingShingle | Ping Yan Gerardo Chowell Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach Mathematical Biosciences and Engineering epidemic modeling sub-exponential growth frailty model parameter identifiability heterogeneity transmission dynamics generalized growth model infectious diseases stochastic modeling forecasting |
| title | Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach |
| title_full | Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach |
| title_fullStr | Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach |
| title_full_unstemmed | Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach |
| title_short | Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach |
| title_sort | modeling sub exponential epidemic growth dynamics through unobserved individual heterogeneity a frailty model approach |
| topic | epidemic modeling sub-exponential growth frailty model parameter identifiability heterogeneity transmission dynamics generalized growth model infectious diseases stochastic modeling forecasting |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2024321 |
| work_keys_str_mv | AT pingyan modelingsubexponentialepidemicgrowthdynamicsthroughunobservedindividualheterogeneityafrailtymodelapproach AT gerardochowell modelingsubexponentialepidemicgrowthdynamicsthroughunobservedindividualheterogeneityafrailtymodelapproach |