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)

May 15, 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.
This model employs a type of feedback mechanism. The rate of reported cases (i.e., the number of individuals who are sick, test positive, and are subsequently isolated per day) affects the rate of susceptible individuals moving into social distancing. When the number of reported cases increases, the number of people in social distancing will increase. However, when the daily number of reported new cases reaches a low level, social distancing mandates are relaxed, allowing population members to move back into the Susceptible compartment with a higher transmission rate. The forecasts below illustrate that this decrease in social distancing could result in a second wave of cases in Knox County.

Figure 1: Flow Diagram Illustrating Transitions among the Population Compartments

Figure 1: Flow Diagram Illustrating Transitions among the Population Compartments

Results

Figure 2: Cumulative Numbers of Cases and Deaths through 9 August 2020

Figure 2: Cumulative numbers of cases and deaths through 9 august 2020 figure 2: cumulative numbers of Cases and Deaths through 9 August 2020
In Figure 2, we present forecasts for the cumulative numbers of cases and deaths through 9 August 2020. The blue points denote the exact values of these variables obtained from the Knox County Health Department. Given the current values of the crucial rates of our model (estimated given the data from Knox County), most importantly that of social distancing adherence, the forecasts predict a second resurgence of the outbreak beginning in June 2020.

Figure 3: 

Left - Active Cases depending on the Level of Social Distancing.

Right - Number of Individuals in Social Distancing under Level 1 Social Distancing.

Active Cases depending on the level of social distancing number of individuals in social distancing under level 1 social distancing
Figure 3 examines the dependence of the number of active cases on the degree of social distancing observed in Knox County. In the left plot of Figure 3, each forecast shows the effect of a different level of social distancing policy, with Level 1 suggesting the weakest social distancing guidelines (a natural increase in adherence as the number of cases increases) and Level 4 implying the strongest (strict social distancing policy mandates). In the right plot of Figure 3, we forecast the number of individuals observing social distancing at a given time under Level 1 social distancing guidelines. Recalling the feedback mechanism of our model and the nature of Level 1 measures, we observe that a decrease in the number of individuals practicing social distancing allows for a subsequent increase in the active number of cases.

Figure 4: Forecasts for Late 2020 Given Increased Relaxation of Social Distancing  and Variation in the Reduction Factor r of the Transmission Rate

Forecasts for late 2020 given increased relaxation of social distancing and variation in the reduction factor of the transmission rate Figure 4: Forecasts for Late 2020 Given Increased Relaxation of Social Distancing and Variation in the Reduction Factor of the Transmission Rate
Finally, we consider projections for the duration of 2020, with the aim of studying how the reintroduction of the students in the Fall 2020 semester might affect the dynamics of the outbreak in Knox County, Tennessee. In Figure 4, we explore possible scenarios that might arise if social distancing practice is weakened to a basic level even below that of Level 1 above. This corresponds to increased relaxation of the social distancing parameter qs The individual scenarios displayed were generated by varying the reduction factor of the transmission rate. In the top plot of Figure 4, the vertical axis measures the current number of reported active cases (the size of the Infected, Isolated compartment of our model) at a given time. The bottom plot of Figure 4 reports the cumulative number of reported active cases at each time. It is worth noting that, in each case, a third peak occurs, having magnitude comparable to, or sometimes significantly greater than, that of the first peak. We remark that the parameters in the scenarios considered in Figure 4 were fit to recent data, except, of course, the reduction factor and relaxation of social distance qs.  As a result, Figure 4 (and Figures 2 and 3 for the same reason) likely underpredict the number of active cases due to low numbers of testing performed.
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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