Epidemiology of Pandemics: How Mathematical Modeling Informs Public Health Policy
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1. Mathematical models of disease transmission can inform public health policy responses to pandemics like COVID-19. 2. Early modeling of COVID-19 in Michigan showed that early and sustained social distancing interventions would be necessary to flatten the curve and prevent overwhelming the healthcare system. 3. These models also demonstrated that relaxing social distancing restrictions too early could lead to a second wave of infections and that some level of continued social distancing may be required until herd immunity is achieved through vaccination or widespread infections.
Epidemiology of Pandemics: How Mathematical Modeling Informs Public Health Policy
- 1. Joseph Eisenberg, PhD, MPH Department of Epidemiology School of Public Health University of Michigan Epidemiology of Pandemics: How Mathematical Modeling Informs Public Health Policy COVID -19
- 2. Overview What do we know about COVID-19? Transmission modeling: The basics Examples of models that have informed policy COVID-19: Lessons from models
- 3. COVID-19 Disease Trajectory Exposure 18 d Symptoms Death 25 d Hospital Dischar ge Incubation 5 d (2-14 d) When do people become infectious?
- 4. The continuum of infection in a population Deaths Severe Cases Symptomatic Cases (fever) Mild or Asymptomatic Cases Cases Detected DIAGNOSED INFECTIONS: TIP OF THE ICEBERG Spectrum of Coronavirus Cases, Diagnosed and Undiagnosed
- 5. Case fataily rate varies across countries: ● Timing of epidemic ● Who /how many tested ● Demography (age, comorbidties) ● Healthcare capacity COVID-19 Case-Fatality Rate by Country (Among Those with 500+ Confirmed Cases and 1+ Deaths)
- 7. How Many People in the US Are Infected? How do we estimate total cases? Reported cases and deaths (as of 4/4/2020)
- 8. Thinking through ‘How many people are infected?”
- 9. One death today means...~4 weeks ago there were 100 infections (assuming case fatality rate 1/100) or 1000 infections (assuming case fatality rate 1/1000) 1 Death
- 10. Assuming a doubling time of 1 week 1 death today means 1600-16,000 infections today. (Assume 100-1000 infections per death 4 weeks ago and a doubling time of 1 week) 1 Death
- 11. Assuming a doubling time of 1 week Example (Michigan): 500 deaths today indicates 50,000 to 500,000 estimated cases (Assuming 100 infections per death 4 weeks ago and a doubling time of 1week) 50,000 500 deaths 100,000 200,000 400,000 800,000
- 12. Probability of infection given contact Duration of infectious period (12 d) Social distancing can diminish contact Opportunity to intervene Contact rate among individuals Pathogen R0 Measles 12-18 SARS 2-5 SARS-COV-2 2-3 Seasonal Influenza 1-2 MERS <1 What Drives Transmission? Reproductive number, a measure of spread, is a product of three terms Reproductive number (R0)
- 13. How Does Spread Happen in the Real World? Idealized situation Data from SARS pandemicWuhan: Ro = 2.2 Epidemic doubles every 7 days “A” infects 33 people, most of whom don’t infect others
- 14. What Are We Up Against? ▪ 80% of cases are mild or asymptomatic ▪ Pre-symptomatic transmission is likely (maybe 2 days prior to symptoms) ▪ Dose matters ▪ 60% of population will get sick with no interventions (based on R0=2.5) Therefore, finding and quarantining cases will be difficult. Social distancing is our best option.
- 16. Three Levels of Preventive Measures ▪ Infection prevention and control in the community ▪ Social distancing measures ▪ Travel-related measures ▪ Screening (questionnaires, testing) ▪ Contact tracing and case finding, isolation and quarantine ▪ Surveillance ▪ (Vaccine 12-18 months away) ▪ Supportive/intensive care (Medication in clinical trials)
- 17. But, Does Social Distancing Work? SCALE MATTERS Measles transmission driven by school Mixed evidence of the success in school closings for Influenza A Concerts, Sporting Events Schools, Daycare Centers Restaurants, Home Gatherings
- 18. Modeling transmission helps us understand details about how disease spreads Germ theory leads to the theory of mass action Sir Ronald Ross Contact with an infectious individual Recover and become susceptible again Susceptibl e Infected
- 19. Disease spreads by direct contact with infected Susceptib le (S) Infected (I) Removed (R) Recovery and removal from transmission process Furthered framework of transmission (SIR model) When infected people recover, they can become immune
- 20. Rate of new cases depends on infectivity, but also susceptible and infected individuals 𝒅𝑰 𝒅𝒕 =SI Probability of infection given contact Contact rate among individuals Rate of generatin g new cases Product of infectious X susceptibleTransmission rate X
- 21. What can we learn from models of other diseases?
- 22. Models help us understand herd immunity Vaccinated Person Direct protection (individual effect of intervention) Indirect protection (community effect of intervention) Infectious Person B A Need a threshold of vaccine coverage to create herd immunity
- 23. Models help us understand herd protection from other interventions (not vaccine related) Indirect protection (community effect of intervention) Direct protection (individual effect of intervention) Susceptible Infectiou s As opposed to vaccines, bed nets only have effect while used.
- 24. Models help us think about policy implications Rubella vaccination. High-risk group: reproductive-age women Herd immunity (all children) is optimal, but if not feasible, vaccinate high-risk group Water treatment. High-risk group: HIV+ individuals In-home water treatment of high-risk group is optimal (cheaper) but if disease spreads from general population to high-risk group then improving
- 25. Models help us think about policy implications Contact tracing for sexually transmitted diseases. Small high risk groups (core) can drive transmission in low risk groups (non-core) Targeted tracing will be more effective
- 26. Models help us think about policy implications Determining coverage threshold for building latrines. High-risk households create community-level risks. High coverage minimizes contamination to community Communi ty Environm ent No Latrine Low-quality latrine High-quality latrine
- 27. Building a COVID-19 transmission model with the natural history of the disease
- 28. Goals for COVID-19 transmission model 1. Forecasting to assess burden on hospitals 2. Quantifying the delay between onset of intervention and changes in reported cases/deaths 3. Estimating the type and length of social distancing needed to flatten the curve a) How that will vary as a function of when intervention begins 4. Developing an adaptive strategy to keep cases and mortality minimal
- 29. Models built iteratively with greater complexity Initial step is crude characterization of social distancing: Minimal, Moderate, Intensive Add more detail in next iterations: Characterize close contact by size and duration of gathering Larger scale events (concerts, sporting events) Medium scale events (subways, dorms, nursing homes) Small scale gatherings (restaurants, households)
- 30. Initial projections for Michigan Estimating time of peak cases is difficult when in exponential phase of outbreak Michigan COVID-19 Modeling Dashboard https://epimath.github.io/covid-19-modeling/#current-forecasts
- 31. Early intervention will flatten the curve 65% reduction in contact Michigan COVID-19 Modeling Dashboard https://epimath.github.io/covid-19-modeling/#current-forecasts
- 32. Late intervention will not change the curve much 65% reduction in contact Michigan COVID-19 Modeling Dashboard https://epimath.github.io/covid-19-modeling/#current-forecasts
- 33. Strong social distancing relaxed too soon simply delays outbreak 90% reduction in contact Michigan COVID-19 Modeling Dashboard https://epimath.github.io/covid-19-modeling/#current-forecasts
- 34. Models can help us understand disease transmission dynamics Models help us think through policy implications Importantly, how much herd immunity is needed? • In homogeneous social setting – 60% of population • In a more realistic setting with social structure – less than 60% Assuming R0 = 2.5 Conclusions
- 35. Social distancing delays the epidemic Once social distancing is relaxed people are again at risk Second peak possible in fall Will seasonal changes help us? Flattening the curves relies on Continuation of social distancing Slowly building herd immunity Conclusions
- 36. Conclusions Developing an adaptive social distancing strategy 1. Wait until we observe flattening with current level of social distancing 2. Relax social distancing and observe response a) Requires good testing and contact tracing b) Need to wait to see effect (1 – 4 weeks)
- 37. Future directions Building individual-based models (IBM) to better characterize contact patterns in different work sectors Develop guidelines for low-risk conditions in different work sectors and public gatherings