The Mathematica Book
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A new form of a linear SIR model (Susceptible-Infected-Recovered) is posed and analytical solutions are presented. It is motivated by a desire to mimic illness patterns for particular zoonotic microorganisms. In cases where person-to-person transmission of a zoonosis is generally considered to be rare (e.g., campylabacteriosis), an interaction term between Susceptible and Infected groups is not necessary, enabling a linear model to be posed. Immunity lossed and gains are accounted for, and also the possibility that infection may occur in the absence of any illness symptoms. Under realistic values of its parameters, the solutions are able to mimic two patterns often inferred from clinical trial and outbrak data: (i) that children are more susceptible to zoonotic pattogens than adults, (ii) that people in regular contact with farm animals may attain greater immunity than the ordinary public.