Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases
The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary diffe...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1475 |
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| author | Sara Y. Del Valle J. M. Hyman Nakul Chitnis |
| author_facet | Sara Y. Del Valle J. M. Hyman Nakul Chitnis |
| author_sort | Sara Y. Del Valle |
| collection | DOAJ |
| description | The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. We apply the analysis to the spread of a smallpox-like disease, derive the formula for the reproduction number, $\Re_{0}$, and based on this threshold parameter, show the level of human behavioral change required to control the epidemic.We analyze how different mixing patterns can affect the disease prevalence, the cumulative number of new infections, and the final epidemic size.Our analysis indicates that the combination of residual immunity and behavioral changes during a smallpox-like disease outbreak can play a key role in halting infectious disease spread; and that realistic mixing patterns must be included in the epidemic model for the predictions to accurately reflect reality. |
| format | Article |
| id | doaj-art-238e0977309642e7907579a8ec58840d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-238e0977309642e7907579a8ec58840d2025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61475149710.3934/mbe.2013.10.1475Mathematical models of contact patterns between age groups for predicting the spread of infectious diseasesSara Y. Del Valle0J. M. Hyman1Nakul Chitnis2Los Alamos National Laboratory, Los Alamos, NM 87545Tulane University, New Orleans, LA, 70118Swiss Tropical and Public Health Institute, 4002 BaselThe spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. We apply the analysis to the spread of a smallpox-like disease, derive the formula for the reproduction number, $\Re_{0}$, and based on this threshold parameter, show the level of human behavioral change required to control the epidemic.We analyze how different mixing patterns can affect the disease prevalence, the cumulative number of new infections, and the final epidemic size.Our analysis indicates that the combination of residual immunity and behavioral changes during a smallpox-like disease outbreak can play a key role in halting infectious disease spread; and that realistic mixing patterns must be included in the epidemic model for the predictions to accurately reflect reality.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1475social networkssegregate mixing.proportional mixingreproduction numbermathematical epidemiologycontact patterns |
| spellingShingle | Sara Y. Del Valle J. M. Hyman Nakul Chitnis Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases Mathematical Biosciences and Engineering social networks segregate mixing. proportional mixing reproduction number mathematical epidemiology contact patterns |
| title | Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases |
| title_full | Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases |
| title_fullStr | Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases |
| title_full_unstemmed | Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases |
| title_short | Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases |
| title_sort | mathematical models of contact patterns between age groups for predicting the spread of infectious diseases |
| topic | social networks segregate mixing. proportional mixing reproduction number mathematical epidemiology contact patterns |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1475 |
| work_keys_str_mv | AT saraydelvalle mathematicalmodelsofcontactpatternsbetweenagegroupsforpredictingthespreadofinfectiousdiseases AT jmhyman mathematicalmodelsofcontactpatternsbetweenagegroupsforpredictingthespreadofinfectiousdiseases AT nakulchitnis mathematicalmodelsofcontactpatternsbetweenagegroupsforpredictingthespreadofinfectiousdiseases |