CTMC epidemic project
Construct a continuous-time Markov chain for an SIS epidemic. From state \(i\), infection and recovery occur at rates
\[b(i)=\beta\frac{i(N-i)}N,\qquad d(i)=\gamma i.\]The total rate is \(a(i)=b(i)+d(i)\). The waiting time to the next event satisfies
\[\tau\sim\operatorname{Exp}(a(i)).\]Conditional on an event, infection occurs with probability \(b(i)/a(i)\), otherwise recovery occurs.
Algorithm
Starting at \(i_0\), draw a waiting time, select the event, update \(i\), advance time and repeat until the final time or extinction.
Analysis
Repeat the CTMC simulation to estimate extinction probability, outbreak size distributions and time-dependent moments.
Project outcome. Build an event-driven epidemic simulation directly from biological transition rates.