A Calibration Framework for Bridging Household-Structured Microscopic and Macroscopic Epidemic Models

Abstract Modeling the spread of epidemics has had two complementary paradigms: 1) a macroscopic paradigm which divides the populace into few groups of large number of statistically identical individuals and 2) a microscopic paradigm which considers each individual as a separate entity with his own contact network. The macroscopic paradigm achieves fast computation through the solution of ordinary differential equations, but cannot capture essential features of human society such as household structures. In contrast, the microscopic paradigm can capture arbitrary heterogeneities, but its computational cost can become prohibitive as population size increases. This study develops a systematic framework for bridging these paradigms while retaining the computational advantages of the macroscopic and the accuracy of the microscopic paradigm. To the best of our knowledge, this direction of research is novel. We consider a populace comprising adults and children organized into households of different sizes. Members of the same household have different contact patterns and are therefore not statistically identical. Contact rates within households are much higher than those across households, causing clustered epidemic spread. We first demonstrate that the most natural macroscopic formulation can substantially misrepresent the epidemic trajectory. We subsequently show that a specifically designed macroscopic formulation, which captures clustered household spread by calibrating parent--child interactions through a calibration parameter, can closely approximate the microscopic model. The optimum value of this parameter is obtained by minimizing the discrepancy between the microscopic and macroscopic epidemic trajectories. This discrepancy at the optimum value is small, and it can be predicted well through standard statistical techniques applied on few exact computations. The framework significantly reduces computation time while retaining accuracy of the microscopic, and provides a foundation for obtaining the same for arbitrary social networks.