Accurate stochastic simulation algorithm for multiscale models of infectious diseases

In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In cases where small numbers or noise play a crucial role, these differential equations are replaced with memoryless Markovian models, where discrete individuals can be members of a compartment and transition stochastically. Classic stochastic simulation algorithms, such as Gillespie's algorithm and the next reaction method, can be employed to solve these Markovian models exactly. The intricate coupling between models at different scales underscores the importance of multiscale modelling in infectious diseases. However, several computational challenges arise when the multiscale model becomes non-Markovian. In this paper, we address these challenges by developing a novel exact stochastic simulation algorithm. We apply it to a showcase multiscale system where all individuals share the same deterministic within-host model while the population-level dynamics are governed by a stochastic formulation. We demonstrate that as long as the within-host information is harvested at a reasonable resolution, the novel algorithm we develop will always be accurate. Moreover, the novel algorithm we develop is general and can be easily applied to other multiscale models in (or outside) the realm of infectious diseases.
Comment: 23 pages, 7 figures