{"id":435202,"date":"2020-05-20T09:41:20","date_gmt":"2020-05-20T13:41:20","guid":{"rendered":"http:\/\/www.rochester.edu\/newscenter\/?p=435202"},"modified":"2020-05-20T10:08:24","modified_gmt":"2020-05-20T14:08:24","slug":"mathematical-model-monitor-spread-covid-19-435202","status":"publish","type":"post","link":"https:\/\/www.rochester.edu\/newscenter\/mathematical-model-monitor-spread-covid-19-435202\/","title":{"rendered":"Mathematical model will monitor spread of COVID-19"},"content":{"rendered":"<div style=\"width: 75%; font-size: 150%; font-face: arial; font-weight: bold; line-height: 125%; margin-bottom: 0.5em;\">National Science Foundation grant enables Rochester computational scientists to develop the tool for policymakers.<\/div>\n<p><a href=\"https:\/\/www.rochester.edu\">Ä¢¹½´«Ã½<\/a> researchers are using their expertise in mathematical modeling to help answer one of the biggest questions surrounding the pandemic and quarantine: When is this going to end?<\/p>\n<p><a href=\"http:\/\/www.pas.rochester.edu\/people\/faculty\/ghoshal_gourab\/index.html\">Gourab Ghoshal<\/a>, an associate professor of physics, mathematics, and computer science, and <a href=\"http:\/\/www.hajim.rochester.edu\/che\/people\/faculty\/white_andrew\/index.html\">Andrew White<\/a>, an assistant professor of chemical engineering, recently received a National Science Foundation grant to create a mathematical model that will monitor the spread of COVID-19. Both White and Ghoshal are computational researchers and are able to conduct their research remotely during the campus shutdown. Combining their expertise in modeling both epidemiology and molecular simulation, the researchers hope to create a unique tool that will help policymakers make informed decisions about reopening the country.<\/p>\n<p>\u201cWe need to turn on the lights to get more information to eradicate this disease,\u201d Ghoshal says. \u201cThis is very difficult because we have to scale up testing, do contact tracing, convince people to make behavioral changes. It would be helpful to have an estimate for how transmissible the disease is in real time.\u201d<\/p>\n<h4><b>Measuring infection rates: R<sub>0<\/sub> versus R effective<\/b><\/h4>\n<p>As anyone who has seen the 2011 movie <i>Contagion<\/i> knows, the estimate of a virus\u2019s infection rate is represented by the mathematical term \u201cR<sub>0<\/sub>,\u201d pronounced \u201cR naught.\u201d If R<sub>0 <\/sub>equals five, for example, every person who is infected with a virus will infect an average of five people. If R<sub>0. <\/sub>is greater than one, the virus is spreading and the outbreak will continue, but if R<sub>0<span class=\"Apple-converted-space\">\u00a0 <\/span><\/sub>is less than one, the disease is declining and will eventually die out.<\/p>\n<p>While R<sub>0<span class=\"Apple-converted-space\">\u00a0 <\/span><\/sub>is used to describe the intensity of a disease outbreak, it is really only relevant at the beginning of a pandemic. As the pandemic progresses, other factors, such as social distancing or quarantines, affect the infection rate.<\/p>\n<p>\u201cAt every point in time, you want to monitor the effective transmissibility of the disease, independent of how many people actually have it: what is the likelihood that somebody goes out and who do they infect?\u201d Ghoshal says.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<div class=\"pullquote\">To account for fluctuations over the course of the pandemic, the model will produce what is known as R effective, or the number of people who can be infected by an individual at any given time.<\/div>\n<p>In order to take into account fluctuating situations and behaviors over the course of a pandemic, Ghoshal and White\u2019s model will produce what is known as R effective, which is R<sub>0<span class=\"Apple-converted-space\">\u00a0 <\/span><\/sub>as a function of time: the number of people who can be infected by an individual at any given time. At the beginning of a pandemic, for example, R effective may be five, but once a quarantine is in place and progresses, R effective could be less than one.<\/p>\n<p>\u201cThat is good because it means you\u2019re in a situation where the pandemic might die down, but then the moment you start easing lockdowns, there\u2019s a good chance that can take off again,\u201d Ghoshal says. \u201cOur model might be able to give you what R effective is in real time.\u201d<\/p>\n<p>Local officials will be able to use Ghoshal and White\u2019s model to monitor infection rates on a day-to-day basis, and will better be able to determine whether opening businesses causes infection rates to spike.<\/p>\n<p>\u201cThe mayor of a specific town would know the R effective today and tomorrow and can say, \u2018Ok, I\u2019ll open up all the coffee shops\u2019 and can see what the R effective is, and can open up more businesses if the R effective stays down or close things if the R effective goes up,\u201d Ghoshal says.<\/p>\n<h4><b>The challenge of speed and accuracy<\/b><\/h4>\n<p>Researchers are able to calculate R<sub>0<\/sub> and R effective by inputting data into mathematical models. There are several data variables that are used to most accurately calculate R effective: (S)usceptible; (E)xposed; (A)symptomatic but infectious; symptomatic and (I)nfectious; (R)ecovered; and (D)eceased.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>The problem with many of the current models that use this SEAIRD framework is that they are a trade-off between accuracy and simplicity: as models become increasingly sophisticated, they become more data intensive so they can\u2019t be deployed quickly. Simple models, on the other hand, require fewer data inputs and can be deployed more quickly, but they are often not as accurate.<\/p>\n<div class=\"pullquote\">A statistical framework called maximum entropy biasing will help maximize the speed and accuracy of COVID-19 data.<\/div>\n<p>Ghoshal and White hope to develop a model that is somewhere in between.<\/p>\n<p>\u201cOur model will be easily deployable and will make reasonably accurate predictions really fast, in a scalable fashion,\u201d Ghoshal says.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>To do this, the researchers are taking the epidemiology models Ghoshal works on and feeding them into a framework called maximum entropy biasing that White has successfully used to simulate molecular dynamics.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>The researchers input into the model the two variables they find to be most reliable\u2014the mortality rates and hospitalization rates, which are numbers easily obtained from open source data at the state and county level. A maximum entropy biasing framework allows the model to account for any other variables that are unknown\u2014individuals who don\u2019t show any symptoms, but are still able to infect others, for instance\u2014so researchers don\u2019t have to input every factor.<\/p>\n<p>\u201cMaximum entropy basically means that we aren\u2019t going to find all the parameters, so we\u2019re going to put on this bias term that accounts for things we don\u2019t know,\u201d White says. \u201cThis is a new direction that people haven\u2019t explored.\u201d<\/p>\n<p>Inputting just these two variables and using maximum entropy biasing will produce the R effective for a region at any point in time. The nature of the model means it could also be deployed for future disease outbreaks as well.<\/p>\n<p>\u201cAnother pandemic is bound to happen unless we change our ways,\u201d Ghoshal says. \u201cIn the initial phase, when there\u2019s very little data available, we hope this particular tool can start to turn the lights on, if not in the entire apartment, at least in one room, before more people die.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Computational scientists win a National Science Foundation grant to develop a tool to provide accurate, timely information to local-level policymakers monitoring the spread of COVID-19.<\/p>\n","protected":false},"author":912,"featured_media":435232,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[116],"tags":[34352,18842,18802,23492,18662,36412,18632,6106,16072],"class_list":["post-435202","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sci-tech","tag-andrew-white","tag-department-of-chemical-and-sustainability-engineering","tag-department-of-computer-science","tag-department-of-mathematics","tag-department-of-physics-and-astronomy","tag-gourab-ghoshal","tag-hajim-school-of-engineering-and-applied-sciences","tag-national-science-foundation","tag-school-of-arts-and-sciences"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mathematical model will monitor spread of COVID-19<\/title>\n<meta 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