So I'm reading this paper about modeling the spread of a disease and the paper describes pretty much every other variable that they're using in this particular equation (that gives us the $\lambda_i$ for an exponential distribution used for a stochastic model), except for the last integral which I'm not sure I completely understand. I've taken a class in which we worked with some stochastic calculus, though not in detail, so it looks moderately like a stochastic integral to me, but I'm not exactly sure. Can someone confirm this?
The equation is this: $$\lambda_i(t) = C(t)\bigg(1-\frac{N(t)}{N_{pop}}\bigg)R_iF(t-T_{I,i} - T_{iso,i }) \int^{t+\delta t}_{t} W(\tau-T_{I,i})d\tau$$
where $\lambda_i(t)$ is the mean for a Poisson distribution at each time step, $C(t)$ is the transmission rate of the disease, $1-\frac{N(t)}{N_{pop}}$ is the amount of the population that is at risk for the disease at time $t$, $T_{iso}$ is the time taken to isolate after infection, and $T_I$ is the time at which some individual gets infected. Lastly, $F(t)$ is a function that describes the reduction of transmission of the disease, described by another function that I am not mentioning here because it does not add much to the question I'm asking.
The only thing not mentioned or described is the integral at the end, and I thinkkk that it's a stochastic/ito integral, but I'm not completely sure. If it was though, how would I calculate an answer for this for example, taking a specific time step, and working for that? I know it's different from regular integration, however, I can't seem to understand how to get an answer for this.
Could anyone help explain?
Thank you!!