Using machine learning to enhance pandemic modeling: case study of COVID-19 dynamics in Ghana
TL;DR
Modified Patankar–Runge–Kutta (MPRK) methods are applied to approximate the solutions of the resulting system of nonlinear ordinary differential equations (ODEs) representing each model to produce unconditionally positive approximations and to preserve the conservative part of the ODEs.
Abstract
In this study, five distinct COVID-19 models developed in different countries, each designed to reflect the prevailing epidemiological condition at the time of formulation, are examined. The models are reformulated while still maintaining their original compartmental structure, using their common transmissions from one compartment to the other. Modified Patankar–Runge–Kutta (MPRK) methods are then applied to approximate the solutions of the resulting system of nonlinear ordinary differential equations (ODEs) representing each model to produce unconditionally positive approximations and to preserve the conservative part of the ODEs. In particular, we incorporate the numerical solution into a cost function to improve the estimates for the non-autonomous model hyperparameters. In a first step we obtain piecewise constant parameters that fit real data. Later we perform a WENO reconstruction in a post-process to approximate the true time-dependent coefficients inside the ODEs. As a proof-of-concept, we apply our approach to improve the parameters of a paper concerned with modeling COVID-19 in Ghana, where we can make 5-day predictions within a 10% error range.