Davies, Kale J

Day, Judy D

Lanzas, Cristina

Lenhart, Suzanne

English

VCU Scholars Compass

Deriving ODE approximations for spatial networks: modeling environmentally transmitted infections

Virginia Commonwealth UniversityVCU Scholars CompassBiology and Medicine Through MathematicsConference 2018Jun 1st, 11:00 AM - 11:30 AMDeriving ODE approximations for spatialnetworks: modeling environmentally transmittedinfectionsKale J. DaviesNorth Carolina State University, kjdavies@ncsu.eduCristina LanzasNorth Carolina State University, clanzas@ncsu.eduSuzanne LenhartThe University of Tennessee, Knoxville, lenhart@math.utk.eduSee next page for additional authorsFollow this and additional works at: https://scholarscompass.vcu.edu/bammPart of the Life Sciences Commons, Medicine and Health Sciences Commons, and the PhysicalSciences and Mathematics CommonsThis Event is brought to you for free and open access by the Dept. of Mathematics and Applied Mathematics at VCU Scholars Compass. It has beenaccepted for inclusion in Biology and Medicine Through Mathematics Conference by an authorized administrator of VCU Scholars Compass. Formore information, please contact libcompass@vcu.edu.https://scholarscompass.vcu.edu/bamm/2018/friday/13Presenter InformationKale J. Davies, Cristina Lanzas, Suzanne Lenhart, and Judy D. DayThis event is available at VCU Scholars Compass: https://scholarscompass.vcu.edu/bamm/2018/friday/13AbstractDeriving ODE approximations for spatial networks: modelingenvironmentally transmitted infectionsPrimarily, mathematical modeling of epidemiology has focused on directlytransmitted infections. While much progress has been made, there are manyinfections that are spread via environmental pathogens, without requiring host-to-host contact. While models for environmental transmission exist, they havegenerally been constructed intuitively, with their structure being analogous tostandard models for direct transmission. As model insights are generally sensi-tive to the underlying assumptions, it is important that we are able understandthe details and consequences of these assumptions. Starting from a networkmodel, we rigorously derive systems of ordinary differential equations (ODEs).These ODEs approximate the dynamics of the network model and are derivedvia three key assumptions: continuity, homogeneity and independence. By vary-ing these assumptions, we can develop more sophisticated systems of ODEs,decreasing the errors due to the assumptions at the expense of increasing thenumber of equations in the system. We compare these ODE models to a stochas-tic implementation of the network model, demonstrating that the accuracy ofthe approximations are somewhat predictable based on the chosen parametersand assumptions of the model.

https://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=1224&context=bamm

Deriving ODE approximations for spatial networks: modeling environmentally transmitted infections

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