A Contact-Explicit Covid-19 Epidemic and Response Assessment Model

We formulate a refined SEIR epidemic model that explicitly includes a contact class C that either thwarts pathogen invasion and returns to the susceptible class S or progresses successively through latent, asymptomatic, and symptomatic classes L, A, and I. Individuals in both A and I may go directly to an immune class V, and in I to a dead class D. We extend this SCLAIV formulation by including a set of drivers that can be used to develop policy to manage current Covid-19 and similar type disease outbreaks. These drivers include surveillance, social distancing (rate and efficacy), social relaxation, quarantining (linked to contact tracing), patient treatment/isolation and vaccination processes, each of which can be represented by a non-negative constant or an s-shaped switching flow. The latter are defined in terms of onset and switching times, initial and final values, and abruptness of switching. We built a Covid-19NMB-DASA web app to generate both deterministic and stochastic solutions to our SCLAIV and drivers model and use incidence and mortality data to provide both maximum-likelihood estimation (MLE) and Bayesian MCMC fitting of parameters. In the context of South African and English Covid-19 incidence data we demonstrate how to both identify and evaluate the role of drivers in ongoing outbreaks. In particular, we show that early social distancing in South Africa likely averted around 80,000 observed cases (actual number is double if only half the cases are observed) during the months of June and July. We also demonstrated that incidence rates in South Africa will increase to between a conservative estimate of 15 and 30 thousand observed cases per day (at a 50% surveillance level) by the end of August if stronger social distancing measures are not effected during July and August, 2020. On different a note, we show that comparably good local MLE fits of the English data using surveillance, social distancing and social relaxation drivers can represent very different kinds of outbreaks--one with close to 90% and another with under 8% immune individuals. This latter result provides a cautionary tale of why fitting SEIR-like models to incidence or prevalence data can be extremely problematic when not anchored by other critical measures, such as levels of immunity in the population. Our presentation illustrates how our SCLAIV formulation can be used to carry out forensic and scenario analyses of disease outbreaks such as Covid-19 in well defined regions.