Inverse problems and ebola virus disease using an age of infection model

Abstract

Parameter estimation problems in ordinary and partial differential equations constitute a large class of models described by ill-posed operator equations. A considerable number of such problems come from epidemiology and infectious disease modeling, with Ebola Virus Disease (EVD) being a very important example. While it is not difficult to find a solution of an SEIJCR ODE constrained least squares problem, this problem is extremely unstable and a number of different parameter combinations produce essentially the same case curve. This is a serious obstacle in the study of the Ebola virus epidemics, since reliable approximations of system parameters are important for the proper assessment of existing control measures as well as for the forward projections aimed at testing a variety of contact tracing policies. In this paper, we attempt a stable estimation of system parameters with the use of iterative regularization along with a special algorithm for computing initial values. The numerical study is illustrated by data fitting and forward projections for the most recent EVD outbreak in Sierra Leone and Liberia.