Extinction of Disease Pathogenesis in Infected Population and Its Subsequent Recovery: A Stochastic Approach

Table 1

Hypothesized transition rates for the stochastic version.

Event	Transition	Transition rates
Birth of a susceptible host	(𝑚,𝑛)→(𝑚+1,𝑛)	𝜆1(𝑚,𝑛)=𝑏1𝑚−𝑏2(𝑚+𝑛)𝑚+𝛿𝑛
Death of a susceptible host	(𝑚,𝑛)→(𝑚−1,𝑛)	𝜇1(𝑚,𝑛)=𝑑1𝑚+𝑑2(𝑚+𝑛)𝑚
Infection of an uninfected host	(𝑚,𝑛)→(𝑚−1,𝑛+1)	𝛾2(𝑚,𝑛)=𝜆+𝛼/𝛽+𝑚𝑚𝑛
Death or recovery of an infected host	(𝑚,𝑛)→(𝑚,𝑛−1)	𝜇2(𝑚,𝑛)=(𝑑𝐼+𝛿)𝑛