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Contact and Recovery Rate

by Raywat Deonandan, PhD

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    00:01 Let's talk now about two very important indicators parameters called C and R.

    00:06 These are of a contact rate and the recovery rate.

    00:11 So, we talked about S as a function of t, S of t, because the number of people in the susceptible compartment changes over time.

    00:21 But the differential equation describing the flow of individuals out of that compartment is given by minus c, multiplied by I, multiplied by S.

    00:32 It doesn't matter what that means, except to say that there is a constant at play there, that helps define the rate of flow of people from the susceptible compartment into the infectious compartment.

    00:45 And that constant is c.

    00:50 The rate of flow of infectious people out of the infection compartment is given by a more complicated expression.

    00:58 c multiplied by IS minus r multiplied by I and R is this other constant we're going to talk about, called the recovery rate.

    01:07 From the people who recover include those newly infected minus those who have been removed.

    01:14 That's why this expression is kind of important, because depending upon which expression is bigger, that tells us if the disease is waning, or waxing.

    01:27 And lastly, of course, the rate of flow of people into the recovery compartment is given by this constant called r multiplied by number of people, I.

    01:39 So, this constant c and r, their call, as I mentioned, the contact rate, or sometimes the transmission rate, and the recovery rate.

    01:46 Sometimes that's given as h, which is the healing rate because it's the rate of people who get better, who heal.

    01:53 And unlike the other aspects of this model, which are computed or imagined, c and r are often empirically measured.

    02:04 They are characteristics of the infection as observed in the population.

    02:09 The number of people that have given contact is contacting, and the number of people who are getting better in the hospital.

    02:17 These are things that can be observed and therefore estimated.

    02:22 As noted, c is how quickly people become infected.

    02:25 It's the contact rate.

    02:28 And r is how quickly people become healed or recovered.

    02:33 These are important because they also open up the opportunity to talk about levers of public health intervention.

    02:41 Because we can control how quickly people become infected.

    02:45 We can control this contact rate.

    02:48 c is much easier to control than r.

    02:51 Because you can do things like introduce personal protective equipment for healthcare workers, masks for everybody else, that reduces the contact rate.

    03:00 You're going to have people stand further apart if we're dealing here with an infection that is spread by droplets exhale through the mouth.

    03:09 Or we can implement quarantine measures to keep infected people from interacting with uninfected people.

    03:15 We can slow the rate of susceptible people becoming infectious people.

    03:21 And we do that by changing c, contact rate.

    03:26 r in the other hand, is quite difficult to change.

    03:30 because it is the rate of people who get better.

    03:33 If we knew how to make people better, that would solve so much of the problem.

    03:38 But making people better is a function of clinical power, clinical expertise, medical technologies, whether or not we have treatments, and cures available. Right? Also as a function of healthcare system responsiveness and effectiveness.

    03:55 So, a better healthcare system will have a higher rate of recovery.

    04:00 More clinical expertise give you a higher rate of recovery.

    04:05 A less overwhelmed system gives you a higher rate of recovery.

    04:12 So again, the change of S over time is given by an expression related to the contact rate.

    04:22 And the change of I over time is given to a more by more complicated expression.

    04:27 And the change of r over time is given by an expression gated by their recovery rate.

    04:32 Let's look at the middle one.

    04:34 This complicated expression for the rate of flow of infected people.

    04:40 c multiplied by IS minus r multiplied by I.

    04:44 Clearly, if that expression is greater than zero, then the pandemic is worsening.

    04:53 It means more people are entering that infectious compartment.

    04:58 We would like that number to come down, not go up.

    05:03 So, will not surprise you to know then that C and R are important for allowing us to compute their reproduction number.

    05:11 The recall that the reproduction number is the average number of new cases produced by an existing case.

    05:17 And reproduction number allows us to estimate the seriousness of an epidemic.

    05:23 The basic reproduction number is actually given by c divided by r.

    05:28 Contact rate, or how quickly people become infected via by the recovery rate, or how quickly they become healed? So again, here is our graph of a population of 500 people experiencing the SIR model.

    05:46 And this green curve, the infection curve, and the one that we care most about is actually affected by the reproduction number.

    05:58 So, the height and width of that curve will change as the value of the reproduction number changes.

    06:03 And remember, the reproduction number is dependent on these constants C and R, which we can change through interventions like mask wearing and quarantine, and healthcare system improvements.

    06:15 So, we can change the shape of this green curve by doing those interventions.


    About the Lecture

    The lecture Contact and Recovery Rate by Raywat Deonandan, PhD is from the course Pandemics.


    Included Quiz Questions

    1. cIS - rI > 0
    2. cIS - rI > 9
    3. cIS - rI <2
    4. cIS - rI > -1
    5. cIS - rI < 1
    1. Contact rate
    2. Recovery rate
    3. Healing rate
    4. Infectious rate
    5. Death rate
    1. c/r
    2. c/t
    3. r/c
    4. r/t
    5. h/r

    Author of lecture Contact and Recovery Rate

     Raywat Deonandan, PhD

    Raywat Deonandan, PhD


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