The University of Tennessee, Knoxville.
Predictive Modeling of the COVID-19 Outbreak in
Knox County, Tennessee:
Effects of Social Distancing Policies 

A Policy Brief by the Howrd H. Baker Jr. Center for Public Policy in Partnership with the Coronavirus-19 Outbreak Response Experts (CORE-19)

Updated: Aug 11, 2020
Tennessee State Capitol and Flag
Using publicly available data from emerging research on COVID-19, this brief was written and reviewed by the Coronavirus-19 Outbreak Response Experts (CORE-19) at the University of Tennessee, Knoxville.  In this brief we utilized compartmental modeling techniques to forecast COVID-19 outbreak in Knox County, Tennessee. Through these forecasts, we see the strong impact of various policy-dependent parameters on the disease dynamics. We highlight the importance of policy supporting consistent social distancing guidelines. The model predicts a significant second peak of the outbreak should a relaxation of social distancing measures occur.

Introduction

This brief uses compartmental modeling techniques and COVID-19 data from the Knox County Health Department to forecast outbreak dynamics three months into the future. In addition, it investigates the efficacy of social distancing policy, forecasting additional peaks for the outbreak if social distancing mandates are relaxed.

Methods

We utilized a compartmental model to generate the forecasts below. This model studies the dynamics of the COVID-19 outbreak by regarding rates of change among the following compartments of the population.
  • Susceptible - members of the population who are susceptible to COVID-19, have not yet been exposed, and are not actively practicing social distancing.
  • Susceptible, but Social Distancing - members of the population who are susceptible to and have not been exposed to COVID-19, but are practicing social distancing
  • Exposed - members of the population who have been exposed to COVID-19 but are not yet infected
  • Infected - members of the population who are infected (includes those who are asymptomatic or only exhibiting mild symptoms) but have not been tested, confirmed positive, and consequently isolated
  • Infected and Isolated - members of the population who are infected, tested positive and were isolated
    • We assume that all individuals who, upon testing, test positive are immediately isolated.
  • Recovered - members of the population who were infected and have recovered
The model structure is adopted from that of Aslan et al.. To accurately capture the local outbreak dynamics in Knox County, Tennessee, the key rates of the model were estimated using data available from the Knox County Health Department. The rates of disease transmission, disease progression, and social distancing adherence were estimated from the Knox County data.  These rates are chosen so that the simulated number of cumulative cases matches closely with the cumulative cases in the Knox County data.

Figure 1: Flow Diagram Illustrating Transitions among the Population Compartments

Figure 1: Flow Diagram Illustrating Transitions among the Population Compartments
In Figure 1, we summarize how individuals of the population move among the compartments of our model. The individuals in the susceptible and social distancing compartment are exposed to the disease via λ(t) = I(t)/N(t), where I(t) denotes the size of infected compartment and N(t) denotes the size of population at time t. Note that since the individuals practicing social distancing and/or wearing masks become exposed less frequently, a reduction factor r on their transmission rate is introduced. After an incubation period 1/α, exposed individuals become infected at a rate of α. The infected individuals will either recover at rate of γi, are tested and consequently isolated at a rate of iq or die due to the disease at a rate of μi. The individuals who are infected and isolated either recover at rate of γq or die due to the disease at a rate of μq.

Results

Since we consider the phases of relaxing restrictions involving social distancing or wearing masks, we fit the model to the data in multiple time phases and made a 14-day forecast with 10% and 50% reduction in the transmission rate. Figure 2 shows the results of the fit and the 14-day forecast.

Figure 2: Cumulative Numbers of Cases, Recovered, Deaths and Active cases

Figure 3: cumulative numbers of cases, deaths, recoveries, and active cases forecasted for 14 days
Send additional questions regarding predictive modeling to Dr. Agricola Odoi or to the CORE-19 research team. 
aodoi@utk.edu | core19@utk.edu | 865-321-1299

Coronavirus-19 Outbreak Response Experts (CORE-19) 

Collaborating Authors
Dr. Agricola Odoi

Dr. Agricola Odoi, BVM, MSc, PhD

Odoi is a professor of epidemiology at the University of Tennessee College of Veterinary Medicine. He teaches quantitative and geographical epidemiology and his research interests are in population health and impact of place on health and access to health services. He was a public health epidemiologist before joining academia. Odoi is a member of the CORE-19 Steering Committee. 
Dr. Suzanne Lenhart

Dr. Suzanne Lenhart, PhD

Lenhart is a Chancellor’s Professor and the James R. Cox Professor of Mathematics the University of Tennessee, Knoxville, and is the Associate Director for Education and Outreach at the National Institute for Mathematical and Biological Synthesis (NIMBioS, funded by the National Science Foundation). She is currently also a member of the UT Center for Wildlife Health. She was a part-time member of the research staff at Oak Ridge National Laboratory for 22 years.
Dr. ibrahim Halil Aslan

Dr. ibrahim Halil Aslan, PhD

Aslan is an UT Math Department, Alumni and Research associate at Department of Mathematics in Batman University, West Ramada, Turkey. His research focus is Mathematical modeling in biological system and data science.
Dr. Mahir Dehir

Dr. Mahir Demir, PhD

Demir is an UT Math Department, Alumni. He is now a postdoc at Department of Fisheries and Wildlife/Quantitative Fishery Center at Michigan State University. His research interests are biological data analysis and modeling; infectious diseases and optimal control strategies; ecosystem-based (fishery) management strategies.
Dr. Michael Morgan Wise

Dr. Michael Morgan Wise, PhD, NASM-CPT

Wise is a scientist in the Advanced Technologies Integration Department of Dynetics, Inc. in Huntsville, Alabama. His primary research interests include numerical analysis of differential equations, numerical linear algebra, and high-performance computing. He is an alumnus of the Department of Mathematics at the University of Tennessee, Knoxville.
Coronavirus Outbreak Response Experts (CORE-19)
Steering Committee
Dr. Kathleen Brown

Dr. Kathleen C. Brown, PhD, MPH

Brown is an Associate Professor of Practice in the Department of Public Health and the Program Director for the Master's in Public Health (MPH) degree. Her research focuses on the health and well-being of individuals and communities. She has experience in local public health in epidemiology, risk reduction and health promotion.
Dr. Katie Cahill

Dr. Katie A. Cahill, PhD

Cahill is the Associate Director of the Howard H. Baker Jr. Center for Public Policy. She also is the Director of the Center's Leadership & Governance program and holds a courtesy faculty position in the Department of Political Science. Her area of expertise is public health policy. She leads the Healthy Appalachia project. 
Dr. Kristina Kintziger

Dr. Kristina W. Kintziger, PhD, MPH

Kintziger is an Assistant Professor in the Department of Public Health and the co-Director of the Doctoral Program. She has worked in academia and public health practice. Prior to coming to Tennessee, she served as an epidemiologist and biostatistician at the Florida Department of Health. She is an environmental and infectious disease epidemiologist.
Dr. Matthew Murray

Dr. Matthew N. Murray, PhD

Murray is the Director of the Howard H. Baker Jr. Center for Public Policy. He also is the Associate Director of the Boyd Center for Business and Economic Research and is a professor in the Department of Economics in the Haslam College of Business. He has led the team producing Tennessee's annual economic report to the governor since 1995. 
Dr. Marcy Souza

Dr. Marcy J. Souza, DVM, MPH

Souza is an associate professor and Director of Veterinary Public Health in the UT College of Veterinary Medicine.  Her teaching and research focuses on zoonotic diseases and food safety issues. 
Disclaimer: the information in this policy brief was produced by researchers, not medical or public health professionals, and is based on their best assessment of the existing knowledge and data available on the topic. It does not constitute medical advice and is subject to change as additional information becomes available. The information contained in this brief is for informational purposes only. No material in this brief is intended to be a substitute for professional medical advice, diagnosis or treatment, and the University of Tennessee makes no warranties, expressed or implied, regarding errors or omissions and assumes no legal liability or responsibility whatsoever for loss or damage resulting from the use of information provided.
Howard H. Baker Jr Center for Public Policy
1640 Cumberland Avenue
Knoxville, TN 37996
Phone: 865-974-0931
Email: bakercenter@utk.edu
Online: bakercenter.utk.edu
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