the number of new cases of a disease occuring during a period of time
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Incidence and prevalence The incidence $i(t)$ of an infectious disease at time $t$ is the rate at which new infections are occurring at that time. The prevalence $P(t)$ at time $t$ is the total number of infected individuals at that time. Let's suppose that $P(0)=0$ . (a) Express the total number of new infections between times $t=0$ and $t=a$ as a definite integral. (b) Suppose that all individuals either die or recover from infection, and that $D$ is the total number that have done so between times $t=0$ and $t=a .$ Express $D$ in terms of $P(a)$ and your result from part (a). (c) Let $d(t)$ be the rate at which people are dying or recovering from infection at time $t .$ What is the relationship between $D$ and $d(t) ?$
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Prevalence is the number of cases of a disease at a ___________ in time.
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