The COVID-19 pandemic as inspiration to reconsider epidemic models: A novel approach to spatially homogeneous epidemic spread modeling

Epidemic spread models are useful tools to study the spread and the effectiveness of the interventions at a population level, to an epidemic. The workhorse of spatially homogeneous class models is the SIR-type ones comprising ordinary differential equations for the unknown state variables. The transition between different states is expressed through rate functions. Inspired by -but not restricted to- features of the COVID-19 pandemic, a new framework for modeling a disease spread is proposed. The main concept refers to the assignment of properties to each individual person as regards his response to the disease. A multidimensional distribution of these properties represents the whole population. The temporal evolution of this distribution is the only dependent variable of the problem. All other variables can be extracted by post-processing of this distribution. It is noteworthy that the new concept allows an improved consideration of vaccination modeling because it recognizes vaccination as a modifier of individuals response to the disease and not as a means for individuals to totally defeat the disease. At the heart of the new approach is an infection age model engaging a sharp cut-off. This model is analyzed in detail, and it is shown to admit self-similar solutions. A hierarchy of models based on the new approach, from a generalized one to a specific one with three dominant properties, is derived. The latter is implemented as an example and indicative results are presented and discussed. It appears that the new framework is general and versatile enough to simulate disease spread processes and to predict the evolution of several variables of the population during this spread.

Relating SARS-CoV-2 shedding rate in wastewater to daily positive tests data: A consistent model based approach

During the COVID-19 pandemic, wastewater-based epidemiology (WBE) has been engaged to complement medical surveillance and in some cases to also act as an early diagnosis indicator of viral spreading in the community. Most efforts worldwide by the scientific community and commercial companies focus on the formulation of protocols for SARS-CoV-2 analysis in wastewater and approaches addressing the quantitative relationship between WBE and medical surveillance are lacking. In the present study, a mathematical model is developed which uses as input the number of daily positive medical tests together with the highly non-linear shedding rate curve of individuals to estimate the evolution of global virus shedding rate in wastewater along calendar days. A comprehensive parametric study by the model using as input actual medical surveillance and WBE data for the city of Thessaloniki (~700,000 inhabitants, North Greece) during the outbreak of November 2020 reveals the conditions under which WBE can be used as an early warning tool for predicting pandemic outbreaks. It is shown that early warning capacity is different along the days of an outbreak and depends strongly on the number of days apart between the day of maximum shedding rate of infected individuals in their disease cycle and the day of their medical testing. The present data indicate for Thessaloniki an average early warning capacity of around 2 days. Moreover, the data imply that there exists a proportion between unreported cases (asymptomatic persons with mild symptoms that do not seek medical advice) and reported cases. The proportion increases with the number of reported cases. The early detection capacity of WBE improves substantially in the presence of an increasing number of unreported cases. For Thessaloniki at the peak of the pandemic in mid-November 2020, the number of unreported cases reached a maximum around 4 times the number of reported cases.