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What if I try to model the mortality rate of a certain province and then to relate it to Differential Equations, the analysis on the rate of change will be expressed to a DE like the death is proportional to the population (just an example) as an end goal. Is this plausible or is there already a DE expressing the proportionality of death rate to something? My point is, out of the time-to-time analysis of death rate, I'd like to create a DE out of it and find the general formula that estimates future number of death in t time just like population growth rate. Is this possible? Or there are already given solutions/formulas to finding or estimating future death numbers? Thanks.

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It's plausible and there's been a huge amount of work along these lines already. See for example Mathematical Models in Population Biology and Epidemiology by Brauer and Castillo-Chavez, an excellent book.

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