COVID-19 and SARS-CoV-2. Modeling the present, looking at the future

Abstract

Since December 2019 the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has produced an outbreak of pulmonary disease which has soon become a global pandemic, known as COronaVIrus Disease-19 (COVID-19). The new coronavirus shares about 82% of its genome with the one which produced the 2003 outbreak (SARS CoV-1). Both coronaviruses also share the same cellular receptor, which is the angiotensin-converting enzyme 2 (ACE2) one. In spite of these similarities, the new coronavirus has expanded more widely, more faster and more lethally than the previous one. Many researchers across the disciplines have used diverse modeling tools to analyze the impact of this pandemic at global and local scales. This includes a wide range of approaches – deterministic, data-driven, stochastic, agent-based, and their combinations – to forecast the progression of the epidemic as well as the effects of non-pharmaceutical interventions to stop or mitigate its impact on the world population. The physical complexities of modern society need to be captured by these models. This includes the many ways of social contacts – (multiplex) social contact networks, (multilayers) transport systems, metapopulations, etc. – that may act as a framework for the virus propagation. But modeling not only plays a fundamental role in analyzing and forecasting epidemiological variables, but it also plays an important role in helping to find cures for the disease and in preventing contagion by means of new vaccines. The necessity for answering swiftly and effectively the questions: could existing drugs work against SARS CoV-2? and can new vaccines be developed in time? demands the use of physical modeling of proteins, protein-inhibitors interactions, virtual screening of drugs against virus targets, predicting immunogenicity of small peptides, modeling vaccinomics and vaccine design, to mention just a few. Here, we review these three main areas of modeling research against SARS CoV-2 and COVID-19: (1) epidemiology; (2) drug repurposing; and (3) vaccine design. Therefore, we compile the most relevant existing literature about modeling strategies against the virus to help modelers to navigate this fast-growing literature. We also keep an eye on future outbreaks, where the modelers can find the most relevant strategies used in an emergency situation as the current one to help in fighting future pandemics.

Side effect of a 6 p.m curfew for preventing the spread of SARS-CoV-2: A modeling study from Toulouse, France

“…Our model is a discretized version of a susceptible infectious and recovered (SIR)-type model ( 6 ). These compartmental models are well suited to studies of the spread of SARS-CoV-2 in different populations ( 7 , 8 ). Our model ( 3 , 5 , 9 ) includes a diffusion/transmission coefficient that varies with the likelihood of contagion, and a reduction coefficient that accounts for the impact of public health measures on virus transmission in the French city of Toulouse.…”

First Consistent Determination of the Basic Reproduction Number for the First Covid-19 Wave in 71 Countries from the SIR-Epidemics Model with a Constant Ratio of Recovery to Infection Rate

“…The SIR system is the simplest and most fundamental of the compartmental models and its variations (for a recent review see ref. 5 ).…”

“…It is convenient to introduce with I(t) = i(t)/N, S(t) = s(t)/N and R(t) = r(t)/N the infected, susceptible and recovered/removed fractions of persons involved in the infection at time t, with the sum requirement I(t) + S(t) + R(t) = 1. In terms of the reduced time , accounting for arbitrary but given time-dependent infection rates, and the medically interesting daily rate of new infections (5) where the dot denotes a derivative with respect to t, the SIR-model equations can be written as (6) with and the dimensionless For the special and important case of a time independent ratio K(t) = k = const., new analytical results of the SIR-model (6) have been recently derived. 4 For a growing epidemics with time the constant ratio k < 1 has to be smaller than unity corresponding to the initial infection rate at time t = 0 being larger than the initial recovery rate , both in units of days .…”

“…These values are significantly smaller than the estimates of R 0 ∈ [2.4, 5.6] in the mainstream literature on Covid-19 based on the monitored effective reproduction factors. 5,9 It is the purpose of the present manuscript to resolve this discrepancy by calculating the relation between the SIR-basic reproduction number and the value of the ratio . It is shown that this relationship is different from the simple microscopic = 1 relationship.…”

“…The inverse of this ratio is often referred to as the inverse microscopic SIRbasic reproduction number. 5 However, the recent application 8 of analytical approximations of the solution of the SIR-model to the monitored death and infection rates in many countries provided values of > 0.9 close to unity for the majority of countries investigated corresponding to microsciopic SIR-basic reproduction numbers R 0 = 1/ < 1.11 only slightly greater than unity. These values are significantly smaller than the estimates of R 0 ∈ [2.4, 5.6] in the mainstream literature on Covid-19 based on the monitored effective reproduction factors.…”