Question

. A researcher is trying to model COVID with the following SIS model where individuals can become reinfected after acquiring disease:

\text { - } \frac{d s}{d t}=-\beta s i+v i \text { - } \frac{d i}{d t}=\beta s i-v i a. Clearly this is quite a simplification of COVID! Can you list three ways this is unrealistic? Nevertheless, the researcher decides to stick with this model. In the population of 1000 people she is studying, she knows there were 20 COVID cases on Sept 1 (t=0). She also knows that expected duration of infection for this particular COVID variant is 10 days. b. What is i。 (the initial prevalence of infection) and s̟ (the initial fraction of the population that is susceptible)? c. What is the value of v? She finds a report that estimates the long run, steady state prevalence of COVID would be 0.15. d. If she believed this report, what would be the value of ß?

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