Please click above image to view slide. ↑
Memo to help understand the lecture PPT slides (as of June 18, 2020)
Slide Number (#) 1
- Course title: Health Technology II
Title of lecture series: Measures against large-scale epidemics：
Title of (1st of 4 lectures): Mathematical modeling of pandemics
- Prepared and presented by Byung-Kwang (BK) Yoo, M.D., M.S., Ph.D.
- Professor at Center for Innovation Policy, Kanagawa University of Human Services
- This lecture was given on June 18, 2020
Slide Number (#) 2
- My first key message is “please do not get overwhelmed by new information on COVID-19 coming every day.”
- This is partly because new information released today will be outdated next week or even tomorrow.
- Therefore, my lectures will focus more on basic methods and approaches for an epidemic in general. These methods and approaches will NOT be outdated at least in the next 10 years or so.
- Goal of today’s class is to study the roles and the limitations of mathematical modeling in making pandemic-related policies.
Slide Number (#) 3
Today’s Road Map.
- Introduction of Presenter (and Students)
- Basic Backgrounds of the COVID-19
- Mathematical Modeling
- Next Week
Slide Number (#) 4
- Presenter’s introduction
- 1st MD, PhD (health economics) among 300,000+ MDs in Japan
- Medical resident (orthopedic surgery) in Japan
- MS (Harvard Univ.) PhD (Johns Hopkins Univ.) in US (since 1995)
- worked for Stanford Univ. in CA, US federal agency Centers for Disease Control and Prevention (CDC) in GA, Univ. Rochester in NY., Univ. of California Davis in CA,
- (Since April 2020) Kanagawa University of Human Services
- Research: Preventive behavior change ((a) Infectious Disease (esp. Flu Vaccine) and (b) Chronic disease prevention (esp. Diet and Physical Activity), Tele-health, Workforce supply, Long term care (dementia), Health insurance
Slide Number (#) 5
In today’s Road Map, we move on to (II) Basic Backgrounds of the COVID-19
Slide Number (#) 6
- Basic Backgrounds of the COVID-19 from the WHO website
(as of May 28, 2020)
- Global impacts
5.6 Million (M) Confirmed cases, 0.25M deaths
- Japan’s case
16,683 Confirmed cases, 867 deaths
- The most important background is that thus far there is no effective vaccine or treatment confirmed by WHO.
- As a result, a primary prevention is and going to be a major counter-measure against the COVID-19.
- By definition, a primary prevention aims to reduce an infection risk.
- A general example of a primary prevention is Behavior change, which will mitigate the negative impacts of COVID-19.
- As you know, a more specific example is Social distancing
– (Q for students) Other options of Behavior change?
Slide Number (#) 7
- There are 3 types of basic Measures against the COVID-19
- Primary prevention (to reduce infection risk)
Behavior change to mitigate the negative impacts of COVID-19
Social distancing (Long-term commitment like obesity prevention)
Vaccination (One-time commitment; Simple??: available after spring 2021?)
- Secondary prevention (if close contact w/ infected)
Detect early enough to improve outcome
- Tertiary Prevention
Treatment after infected & w/ serious symptoms
Slide Number (#) 8
- In Road Map, we move on to
- Mathematical Modeling
Slide Number (#) 9
- Goals of Mathematical Modeling are summarized in this table
- First, please look at the cell in the row of “Evaluation” and the column of “Epidemic path/impacts”.
- The cell shows that one goal is to estimate the “Past/ Current Severity” an epidemic.
- A very popular example of such estimation is “Reproduction rate.”
- I believe that you had many chances to hear this term in the mass media reports in Japan so far.
- The next slide explains what a “Reproduction rate” is.
Slide Number (#) 10
- This figure illustrates implications of a basic reproduction number of R0=4, as an example.
- If the population is entirely “susceptible” --- which mean that “can be infected” --, incidence increase exponentially, four-hold each generation.
- Each generation is indicated by (t) in this figure.
- Incidence increase until the accumulation of immunes slows the process.
- “Immunes” indicate people who will not be infected when exposed to viruses in the case of COVID-19.
Slide Number (#) 11
- This slide is a modified version of the previous slide.
- This new figure illustrates implications of a basic reproduction number of R0=4, which is the same assumption as in the previous slide.
- But, int this slide, 75% of the population is “immune,” shown as a shaded square being different from a blanc circle indicating “susceptible.”
- If 75% of the population is “immune”, then only 25% of the contacts lead to successful transmissions.
- In this figure, there are 2 types of arrows. Regular arrows show a transmission. On the other hand, dotted arrows show “no transmission.”
- As a result, the net (or effective) reproduction number
Rn = R0x(s: proportion of population) = 4x25% =1.
Slide Number (#) 12
- There are 3 specific policy goals based on the reproduction number.
- Goal 1 is to monitor the net/effective reproduction number “EVERY DAY” to see if Rn < 1 or not. This is because if Rn < 1, the infection will disappear (die down/out).
- (Question for students) Does the government report the net/effective reproduction number “EVERY DAY”?
- Goal 2 is to exceed crude herd immunity threshold.
- Herd immunity threshold is defined by 1 – (1/R0)
- Example of “herd immunity threshold” is already shown in the previous slide.
- In the previous slide, 75% is the crude herd immunity threshold. Please remember that R0=4, 75% is immune, and Rn=1.
- Namely, when 75% of the total population is immune, the epidemic severity will remain at the same level. In other words, for each generation, the total # of infected will be the same.
- In this example, if more than 75% (e.g., 80% or greater) among the total population is immune, Rn will become less than 1, i.e.., the epidemic will die down.
Slide Number (#) 13
- Once you are familiar with the concept of “herd immunity threshold,” the next Goal 3 is to achieve immunity among to the total population by vaccination.
- If we use the same example in the previous slide again, once vaccines are available, Vaccination program’s target is to vaccine the proportion of “crude herd immunity threshold” (e.g., at least 75% in the previous example) of the total population
- When vaccines are not available yet, what are the options?
- One option is an actual nation-wide policy to exceed Crude herd immunity threshold by infection. This option was adopted by (past) UK, Sweden and other nations. As you may know, this option has seriously failed so far in the US and Sweden, which was officially admitted by these governments’ officials.
- Next question is what kind of criteria are available to judge whether an option succeeds or fails? One criterion is whether the collapse of health care (HC) system is observed. Please note that there are two types of the collapse of HC. These are below.
- Patients beyond the capacity (= excess demand for HC)
- HC providers (e.g. physicians (MDs) and nurses) become infected (= reduced supply of HC)
I will get back to this problem again in later slides.
Slide Number (#) 14
- This slide summarizes “basic reproduction number” and “herd immunity threshold” of various diseases.
- A popular example is influenza in the 2nd row. As you know, seasonal influenza occurs every winter with the basic reproduction numbers, ranging between 2 and 4. As we learned in an earlier slider slide including a nice cartoon, when the basic reproduction number is 4, the herd immunity threshold is 75%. Likewise, when the basic reproduction number is 2, the herd immunity threshold is 50%.
- Although most people do not care about seasonal influenza, around 30% or more of the population is infected by influenza virus every year. However, due to relatively less sever clinical symptoms, people do not care about seasonal influenza.
- (Question for students) What is the value of the basic reproduction number of the ongoing COVID-19?
- Thus far, the basic reproduction number is reported to be around 2.5 in European countries. On the other hand, in East Asian countries including Japan, the basic reproduction number is reported to be around 1.7, which is clearly lower than the 2.5 values in European countries.
- Therefore, at least in terms of the basic reproduction number, the ongoing COVID-19 is close to influenza in this table.
- There is another column of “serial interval” (also called “case to case interval”). The exact definition of “serial interval” is explained in the next slide.
Slide Number (#) 15
- This slide summary of the definitions of the pre-infectious (latent), incubation and infectious periods for an infection.
- The dotted lines refer to the infectious period and the shaded blocks refer to clinical disease.
- The very bottom arrow indicates “serial interval (also called “case to case interval”),” starting from “day 1 of the first patient’s clinical symptoms” and ending on “day 1 of the second patient’s clinical symptoms” in this figure. (source: Vyunncyky 2020, p.3)
Slide Number (#) 16
- The following slides will explain the importance of the net reproduction number (Rn) using the figures of a hypothetical epidemic path. Therefore, please note that the numbers in ths hypothetical example are “not” true at all.
- In this slide, Y axis indicates the “proportion of the infected per day where the unit is [% total population].”
- X axis indicates time where the unit is [day].
- For instance, Y = 0.1% on Day=t, Y = 0.2% on Day=t+1
Slide Number (#) 17
- This slide is the extension of the previous slide.
- As explained in the previous point, this bell-shape curve indicates the proportion of the infected for each day. Therefore, if you sum up the value of Y for all days from “Day 1 of an epidemic” to “the final Day of this epidemic”, you can obtain the accumulated proportion of the infected among the total population, which is also called a “final size” of an epidemic.
- In this figure, the final size is illustrated by the shaded area under the curve.
- (Any question so far?)
Slide Number (#) 18
- This slide is the extension of the previous slide, too.
- Please remember that we are learning how to interpret this figure in order to understand the importance of the net reproduction number (Rn).
- Also, please note that all numbers in this hypothetical example are “not” true but used for learning how to interpret this figure.
- If you compare two curves in this figure, you will learn the importance of reducing the net reproduction number (Rn). The left curve is based on Rn=1.7, while the right curve on Rn=1.3.
- There are 4 points to compare the impacts of two Rn, 1.7 and 1.3.
- First, concerning Upsurge-Speed, it is slower in the lower-RN-curve.
- Second, regarding Peak-Timing, it is Delayed in the lower-RN-curve.
- In the X-axis, T2 is later than T1.
- Third, as to the Peak-Level, it is Lower in the lower-RN-curve
- (Question for students) Regarding the total proportion of infected (“area under curve” or “final size”), are these curves the same?
- The answer is “NO”. The curve of lower Rn has smaller “final size.” The next slide explains more details.
Slide Number (#) 19
- Please note that the numbers in this slide’s table are “true”, although we still talk about the same hypothetical example, extending the previous slides.
- Assuming that Rn is constant and that vaccines are not available, the total proportion of the infected (area under curve or final size) i
= Crude herd immunity threshold (CHIT)
= 23% (if Rn =1.3), being smaller than 41% (Rn =1.7)
- Therefore, in all of four comparing points, the impacts of an epidemic with a lower Rn is smaller than those with a higher Rn.
- This is why our primary policy goal is to reduce Rn during an epidemic.
Slide Number (#) 20
- This slide explains the importance of lowering the peak-level of an epidemic. This is because the peak level is directly related to the collapse of health care system
- Let us assume that the capacity of health care system is 0.3%, which is shown by the RED horizontal line in this figure (note: this is hypothetical #, not true).
- For instance, the currently available ICU beds will be fully (100%) occupied on day-T1 if 0.3% of the total population is infected on day-T1 --- and some of the infected need the ICU care.
- As a result, infected patients within the RED area in this figure cannot access to or receive the ICU care. This RED area is defined by “area under the curve” and “area above the RED horizontal line.”
- Please do not mis-interpret that no patient can receive health care on day-T1. Instead, some “lucky” patient in the GREEN are on the say day-T1 can receive the ICU care under the curve with a higher Rn of 1.7. This GREEN area is defined by “area under the curve” and “area below the RED horizontal line.”
- Then, a very serious ethical issue comes up. Who can receive the health care when the health care resource is in shortage or lower than the healthcare supply. We can discuss this issue further later in this class or the final class.
Slide Number (#) 21
- There are two types of options to reduce the risk of the health care system collapse.
- One is to reduce the “Reproduction number (RN),” or a Demand Side approach.
- A more specific option is to reduce the infection risk among high risk subpopulations (institutionalized, essential workers)
- The other type option is to increase the “Capacity of health care,” or a Supply Side approach.
- Facility/Equipment: # of beds, respirators
- Workforce: # of MDs, nurses, labo tech etc.
- ↓ infection risk of health care workers
Slide Number (#) 22
- From this slide, we focus more on the “prediction” function of mathematical modeling.
- As discussed in the past slides, we have a better chance to avoid the risk of the health care system, if we can predict the future epidemic path and impacts.
- Moreover, mathematical modeling can evaluate the effectiveness of specific measures, such as vaccination programs, social distancing and treatments (when available).
- However, please note that in general, it is very difficult to evaluate a specific measure’s unique effectiveness.
- Unfortunately, there are so many published studied with a very poor method, which tend to be highly biased in estimating the unique effect of, say, social distancing.
Slide Number (#) 23
- The following slides are from my past research entitled,
“Public Avoidance and the Epidemiology of novel H1N1 Influenza A”
Byung-Kwang Yoo, et al.
National Bureau of Economic Research (NBER) (*)
Working Paper, 2010, (www.nber.org/papers/w15752).
- (*) NBER is the nation's leading nonprofit economic research organization. 16 of the 31 American Nobel Prize winners in Economics and 6 of the past Chairmen of the President's Council of Economic Advisers have been researchers at the NBER.
(To be updated)