Quest for a reductionist model in mathematical epidemiology: generalizing an extant proof of concept

In view of completeness in mathematical epidemiology, classic compartmental models have increasingly interlinked metapopulations, thus overburdening the system of coupled time-dependent ordinary differential equations and jeopardizing generalization. On the contrary, science often pursuits unified descriptions of natural phenomena and attempts to embed simplicity in complexity, which may trigger paradigm shifts to be unbiasedly explored. The present work considered an extent proof of concept (POC) in mathematical epidemiology that proposed and numerically solved a single partial differential equation (PDE) to rule disease spread. Besides time dependence, this reductionist PDE relies on generalized coordinates in a multidisciplinary – ultimately One-Health – hyperspace to categorize individuals in heterogeneous populations. Another novelty refers to modeling disease spread analogous to species transfer in a continuum host medium (namely, whole population). As the latter is allowed to ‘flow’ in the generalized hyperspace, disordered (i.e. diffusive) as well as ordered (i.e. convective) disease spread can be modeled in this epidemic analogue. Given this transport-phenomena-inspired POC, a theoretical roadmap then is attempted toward One Health while limitations are addressed about a reductionist path for in silico epidemiology targeting Sustainable Development Goal 3.