A forecasting model of disease prevalence based on the McKendrick–von Foerster equation
•A new approach to forecasting disease-specific prevalence is developed.•Approach is based on McKendrick–von Foerster's partial differential eqns.•Analytical solutions of formulas for disease prevalence are provided.•Approach uses minimal simplifying assumptions.•Validated through comparison of...
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| Veröffentlicht in: | Mathematical biosciences 2019-05, Vol.311, p.31-38 |
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| container_title | Mathematical biosciences |
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| creator | Akushevich, I. Yashkin, A. Kravchenko, J. Fang, F. Arbeev, K. Sloan, F. Yashin, A.I. |
| description | •A new approach to forecasting disease-specific prevalence is developed.•Approach is based on McKendrick–von Foerster's partial differential eqns.•Analytical solutions of formulas for disease prevalence are provided.•Approach uses minimal simplifying assumptions.•Validated through comparison of observed and predicted data for diabetes prevalence.
A new model for disease prevalence based on the analytical solutions of McKendric–von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data. The computational scheme for parameter estimations using Medicare data, analytical properties of the model, application for diabetes prevalence, and relationship with partitioning models are described and discussed. The model allows natural generalization for the case of several diseases as well as for modeling time trends in cause-specific mortality rates. |
| doi_str_mv | 10.1016/j.mbs.2018.12.017 |
| format | Article |
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A new model for disease prevalence based on the analytical solutions of McKendric–von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data. The computational scheme for parameter estimations using Medicare data, analytical properties of the model, application for diabetes prevalence, and relationship with partitioning models are described and discussed. The model allows natural generalization for the case of several diseases as well as for modeling time trends in cause-specific mortality rates.</description><identifier>ISSN: 0025-5564</identifier><identifier>EISSN: 1879-3134</identifier><identifier>DOI: 10.1016/j.mbs.2018.12.017</identifier><identifier>PMID: 30597156</identifier><language>eng</language><publisher>United States: Elsevier Inc</publisher><subject>Age ; Computer applications ; Diabetes mellitus ; Diabetes Mellitus, Type 2 - epidemiology ; Differential equations ; Disease ; Exact solutions ; Forecasting ; Government programs ; Health care ; Humans ; Lee-Carter ; Mathematical models ; Medicare ; Medicare - statistics & numerical data ; Models, Theoretical ; Parameter estimation ; Partial differential equations ; Partitioning ; Prevalence ; Projections ; Time series ; Trends ; Type II Diabetes ; United States</subject><ispartof>Mathematical biosciences, 2019-05, Vol.311, p.31-38</ispartof><rights>2018</rights><rights>Copyright © 2018. Published by Elsevier Inc.</rights><rights>Copyright Elsevier Science Ltd. May 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c479t-6f9408c3f14bf345d3f3949fda0145d2687b0552e733c4cbac12786c08e137cb3</citedby><cites>FETCH-LOGICAL-c479t-6f9408c3f14bf345d3f3949fda0145d2687b0552e733c4cbac12786c08e137cb3</cites><orcidid>0000-0002-1185-148X ; 0000-0002-4195-7832</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.mbs.2018.12.017$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,315,781,785,886,3551,27929,27930,46000</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/30597156$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Akushevich, I.</creatorcontrib><creatorcontrib>Yashkin, A.</creatorcontrib><creatorcontrib>Kravchenko, J.</creatorcontrib><creatorcontrib>Fang, F.</creatorcontrib><creatorcontrib>Arbeev, K.</creatorcontrib><creatorcontrib>Sloan, F.</creatorcontrib><creatorcontrib>Yashin, A.I.</creatorcontrib><title>A forecasting model of disease prevalence based on the McKendrick–von Foerster equation</title><title>Mathematical biosciences</title><addtitle>Math Biosci</addtitle><description>•A new approach to forecasting disease-specific prevalence is developed.•Approach is based on McKendrick–von Foerster's partial differential eqns.•Analytical solutions of formulas for disease prevalence are provided.•Approach uses minimal simplifying assumptions.•Validated through comparison of observed and predicted data for diabetes prevalence.
A new model for disease prevalence based on the analytical solutions of McKendric–von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data. The computational scheme for parameter estimations using Medicare data, analytical properties of the model, application for diabetes prevalence, and relationship with partitioning models are described and discussed. The model allows natural generalization for the case of several diseases as well as for modeling time trends in cause-specific mortality rates.</description><subject>Age</subject><subject>Computer applications</subject><subject>Diabetes mellitus</subject><subject>Diabetes Mellitus, Type 2 - epidemiology</subject><subject>Differential equations</subject><subject>Disease</subject><subject>Exact solutions</subject><subject>Forecasting</subject><subject>Government programs</subject><subject>Health care</subject><subject>Humans</subject><subject>Lee-Carter</subject><subject>Mathematical models</subject><subject>Medicare</subject><subject>Medicare - statistics & numerical data</subject><subject>Models, Theoretical</subject><subject>Parameter estimation</subject><subject>Partial differential equations</subject><subject>Partitioning</subject><subject>Prevalence</subject><subject>Projections</subject><subject>Time series</subject><subject>Trends</subject><subject>Type II Diabetes</subject><subject>United States</subject><issn>0025-5564</issn><issn>1879-3134</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNp9kcFu1DAQhi0EokvhAbggS1x6SeqxYzsRElJVUUAt4gIHTpbjTFovSby1k5W49R36hn0SvNq2Ag6crLG_-TXjj5DXwEpgoI7X5dimkjOoS-AlA_2ErKDWTSFAVE_JijEuCylVdUBepLRmmQBQz8mBYLLRINWK_DihfYjobJr9dEnH0OFAQ087n9AmpJuIWzvg5JC2ue5omOh8hfSLO8epi979vLu53ebLs4AxzRgpXi929mF6SZ71dkj46v48JN_PPnw7_VRcfP34-fTkonCVbuZC9U3Faid6qNpeVLITvWiqpu8sg1xxVeuWSclRC-Eq11oHXNfKsRpBaNeKQ_J-n7tZ2hE7h9Mc7WA20Y82_jLBevP3y-SvzGXYGtWA4lLmgKP7gBiuF0yzGX1yOAx2wrAkwzNWNVLWO_TtP-g6LHHK6xnOudJK6hoyBXvKxZBSxP5xGGBmJ86sTRZnduIMcJO15J43f27x2PFgKgPv9gDmv9x6jCY5v_PS-axvNl3w_4n_Da5_qk0</recordid><startdate>20190501</startdate><enddate>20190501</enddate><creator>Akushevich, I.</creator><creator>Yashkin, A.</creator><creator>Kravchenko, J.</creator><creator>Fang, F.</creator><creator>Arbeev, K.</creator><creator>Sloan, F.</creator><creator>Yashin, A.I.</creator><general>Elsevier Inc</general><general>Elsevier Science Ltd</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QL</scope><scope>7QO</scope><scope>7QP</scope><scope>7SN</scope><scope>7TK</scope><scope>7TM</scope><scope>7U9</scope><scope>8FD</scope><scope>C1K</scope><scope>FR3</scope><scope>H94</scope><scope>M7N</scope><scope>P64</scope><scope>RC3</scope><scope>7X8</scope><scope>5PM</scope><orcidid>https://orcid.org/0000-0002-1185-148X</orcidid><orcidid>https://orcid.org/0000-0002-4195-7832</orcidid></search><sort><creationdate>20190501</creationdate><title>A forecasting model of disease prevalence based on the McKendrick–von Foerster equation</title><author>Akushevich, I. ; Yashkin, A. ; Kravchenko, J. ; Fang, F. ; Arbeev, K. ; Sloan, F. ; Yashin, A.I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c479t-6f9408c3f14bf345d3f3949fda0145d2687b0552e733c4cbac12786c08e137cb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Age</topic><topic>Computer applications</topic><topic>Diabetes mellitus</topic><topic>Diabetes Mellitus, Type 2 - epidemiology</topic><topic>Differential equations</topic><topic>Disease</topic><topic>Exact solutions</topic><topic>Forecasting</topic><topic>Government programs</topic><topic>Health care</topic><topic>Humans</topic><topic>Lee-Carter</topic><topic>Mathematical models</topic><topic>Medicare</topic><topic>Medicare - statistics & numerical data</topic><topic>Models, Theoretical</topic><topic>Parameter estimation</topic><topic>Partial differential equations</topic><topic>Partitioning</topic><topic>Prevalence</topic><topic>Projections</topic><topic>Time series</topic><topic>Trends</topic><topic>Type II Diabetes</topic><topic>United States</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Akushevich, I.</creatorcontrib><creatorcontrib>Yashkin, A.</creatorcontrib><creatorcontrib>Kravchenko, J.</creatorcontrib><creatorcontrib>Fang, F.</creatorcontrib><creatorcontrib>Arbeev, K.</creatorcontrib><creatorcontrib>Sloan, F.</creatorcontrib><creatorcontrib>Yashin, A.I.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Bacteriology Abstracts (Microbiology B)</collection><collection>Biotechnology Research Abstracts</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Ecology Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Genetics Abstracts</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Mathematical biosciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Akushevich, I.</au><au>Yashkin, A.</au><au>Kravchenko, J.</au><au>Fang, F.</au><au>Arbeev, K.</au><au>Sloan, F.</au><au>Yashin, A.I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A forecasting model of disease prevalence based on the McKendrick–von Foerster equation</atitle><jtitle>Mathematical biosciences</jtitle><addtitle>Math Biosci</addtitle><date>2019-05-01</date><risdate>2019</risdate><volume>311</volume><spage>31</spage><epage>38</epage><pages>31-38</pages><issn>0025-5564</issn><eissn>1879-3134</eissn><abstract>•A new approach to forecasting disease-specific prevalence is developed.•Approach is based on McKendrick–von Foerster's partial differential eqns.•Analytical solutions of formulas for disease prevalence are provided.•Approach uses minimal simplifying assumptions.•Validated through comparison of observed and predicted data for diabetes prevalence.
A new model for disease prevalence based on the analytical solutions of McKendric–von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data. The computational scheme for parameter estimations using Medicare data, analytical properties of the model, application for diabetes prevalence, and relationship with partitioning models are described and discussed. The model allows natural generalization for the case of several diseases as well as for modeling time trends in cause-specific mortality rates.</abstract><cop>United States</cop><pub>Elsevier Inc</pub><pmid>30597156</pmid><doi>10.1016/j.mbs.2018.12.017</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0002-1185-148X</orcidid><orcidid>https://orcid.org/0000-0002-4195-7832</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Age Computer applications Diabetes mellitus Diabetes Mellitus, Type 2 - epidemiology Differential equations Disease Exact solutions Forecasting Government programs Health care Humans Lee-Carter Mathematical models Medicare Medicare - statistics & numerical data Models, Theoretical Parameter estimation Partial differential equations Partitioning Prevalence Projections Time series Trends Type II Diabetes United States |
| title | A forecasting model of disease prevalence based on the McKendrick–von Foerster equation |
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