Integrate-and-fire model of disease transmission

We create an epidemiological susceptible-infected-susceptible model of disease transmission using integrate-and-fire nodes on a network, allowing memory of previous interactions and infections. Agents in the network sum infectious matter from their nearest neighbors at every time step, until they exceed their infection threshold, at which point they "fire" and become infected for as long as the recovery time. The model has memory of previous interactions by tracking the amount of infectious matter carried by agents as well as just binary infected or susceptible states, and the model has memory of previous infections by modeling immunity as increasing the infection threshold after recovery. Creating a simulation of the model on networks with a power-law degree distribution and homogeneous agent parameters, we find a single strain version of the model matches well with the England COVID-19 case data, with a root-mean-squared error of 0.014%. A simulation of a multistrain version of the model (where there is cross-strain immunity) matches well with the influenza strain A and strain B case numbers in Canada, with a root-mean-squared error of 0.002% and 0.0012%, respectively, though due to the coupling in the model, both strains peak in phase. Since the dynamics of the model successfully capture real-life transmission dynamics, we test interventions to study their effect on case numbers, with both quarantining and social gathering restrictions lowering the peak. Since the model has memory, the stricter the intervention, the higher the secondary peak when the restriction is removed, showing that interventions change only the shape of the curves and not the overall number infected in the population.