A model for the spread of an infectious disease among mice is

where N is the size of the population of mice, a is the mortality rate due to infection, b is the mortality rate due to natural causes for infected mice, β is a transmission coefficient for the rate that infected mice infect susceptible mice, ϒ is the rate the mice recover from infection, and g is the rate that mice lose immunity. Show that the solution to this equation, with the initial condition N(0) =(a + b + v)/β, can be written as

where

Transcribed Image Text:

dN dt = TN - ar(a + b + v) V p[α = √( 1 + b + x)]