In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China and propagated worldwide as a pandemic. In the absence of preventive medicine or a ready to use vaccine, mathematical models can provide useful scientific insights about transmission patterns and targets for drug development. In this study, we propose a within-host mathematical model of SARS-CoV-2 infection considering innate and adaptive immune responses. We analyze the equilibrium points of the proposed model and obtain an expression of the basic reproduction number. We then numerically show the existence of a transcritical bifurcation. The proposed model is calibrated to real viral load data of two COVID-19 patients. Using the estimated parameters, we perform global sensitivity analysis with respect to the peak of viral load. Finally, we study the efficacy of antiviral drugs and vaccination on the dynamics of SARS-CoV-2 infection. Our results suggest that blocking the production of the virus by infected cells decreases the viral load more than reducing the infection rate of healthy cells. Vaccination is also found useful but during the vaccine development phase, blocking virus production from infected cells can be targeted for antiviral drug development.
Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host -- including the time-to-peak and the final monotonically decreasing behavior -- is chracterized as a function of the treatment initial time. Simulation results, b…
While many epidemiological models have being proposed to understand and handle COVID-19, too little has been invested to understand how the virus replicates in the human body and potential antiviral can be used to control the replication cycle. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are properly characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such a regions, formally establishe…
The COVID-19 pandemic has severely impacted health systems and economies worldwide. Significant global efforts are therefore ongoing to improve vaccine efficacies, optimize vaccine deployment, and develop new antiviral therapies to combat the pandemic. Mechanistic viral dynamics and quantitative systems pharmacology models of SARS-CoV-2 infection, vaccines, immunomodulatory agents, and antiviral therapeutics have played a key role in advancing our understanding of SARS-CoV-2 pathogenesis and transmission, the interplay between innate and adaptive immunity to influence the outcomes of infection…
Several mathematical models in SARS-CoV-2 have shown how target-cell model can help to understand the spread of the virus in the host and how potential candidates of antiviral treatments can help to control the virus. Concepts as equilibrium and stability show to be crucial to qualitatively determine the best alternatives to schedule drugs, according to effectivity in inhibiting the virus infection and replication rates. Important biological events such as rebounds of the infections (when antivirals are incorrectly interrupted) can also be explained by means of a dynamic study of the target-ce…
Within-host models of COVID-19 infection dynamics enable the merits of different forms of antiviral therapy to be assessed in individual patients. A stochastic agent-based model of COVID-19 intracellular dynamics is introduced here, that incorporates essential steps of the viral life cycle targeted by treatment options. Integration of model predictions with an intercellular ODE model of within-host infection dynamics, fitted to patient data, generates a generic profile of disease progression in patients that have recovered in the absence of treatment. This is contrasted with the profiles obtai…
Relevance: Laboratory diagnosis of the novel coronavirus (SARS-CoV-2) infection combined with quarantine for contacts of infected individuals affects the spread of SARS-CoV-2 infection and levels of related mortality. Practices for testing for SARS-CoV-2 infection vary geographically in Russia. For example, in the city of St. Petersburg, where mortality rate for COVID-19 is the highest in the Russian Federation on Oct. 25, 2020, every death for COVID-19 corresponds to 15.7 detected cases of COVID-19 in the population, while the corresponding number for the whole of Russia is 58.1, suggesting l…
The fatality rate of Covid-19 escalates with age and is larger in men than women. I show that these variations correlate strongly with the level of the viral receptor protein ACE2 in rat lungs, which is consistent with the still limited and apparently contradictory data on human ACE2. Surprisingly, lower levels of the receptor correlate with higher fatality. However, a previous mathematical model predicts that the speed of viral progression in the organism has a maximum and then declines with the receptor level. Moreover, many manifestations of severe CoViD-19, such as severe lung injury, exac…
The importance of understanding SARS-CoV-2 evolution cannot be overemphasized. Recent studies confirm that natural selection is the dominating mechanism of SARS-CoV-2 evolution, which favors mutations that strengthen viral infectivity. We demonstrate that vaccine-breakthrough or antibody-resistant mutations provide a new mechanism of viral evolution. Specifically, vaccine-resistant mutation Y449S in the spike (S) protein receptor-bonding domain (RBD), which occurred in co-mutation [Y449S, N501Y], has reduced infectivity compared to the original SARS-CoV-2 but can disrupt existing antibodies th…
Summary: The CoV-Spectrum website supports the identification of new SARS-CoV-2 variants of concern and the tracking of known variants. Its flexible amino acid and nucleotide mutation search allows querying of variants before they are designated by a lineage nomenclature system. The platform brings together SARS-CoV-2 data from different sources and applies analyses. Results include the proportion of different variants over time, their demographic and geographic distributions, common mutations, hospitalization and mortality probabilities, estimates for transmission fitness advantage and insigh…
In this article, we propose a theory to explain the reduction in vaccine effectiveness (VE) against the Delta SARS-CoV-2 variant and decreasing VE over time reported in recent studies. Using a model illustration, we show that in-host viral replication dynamics and delays in immune response could play a key role in VE. Given this, current laboratory approaches solely measuring reductions in neutralizing ability cannot fully represent the potential impact of new SARS-CoV-2 variants. We instead propose an alternative approach that incorporates viral replication dynamics into evaluations of SARS-C…
We analyzed 5,484 close contacts of COVID-19 cases from Italy, all of them tested for SARS-CoV-2 infection. We found an infection fatality ratio of 2.2% (95%CI 1.69-2.81%) and identified male sex, age >70 years, cardiovascular comorbidities, and infection early in the epidemics as risk factors for death.
Despite the availability of effective vaccines, the persistence of SARS-CoV-2 suggests that co-circulation with other pathogens and resulting multi-epidemics may become increasingly frequent. To better forecast and control the risk of such multi-epidemics, it is essential to elucidate the potential interactions of SARS-CoV-2 with other pathogens; these interactions, however, remain poorly defined. Here, we aimed to review the current body of evidence about SARS-CoV-2 interactions. To study pathogen interactions in a systematic way, we first developed a general framework to capture their major …
Tremendous effort has been given to the development of diagnostic tests, preventive vaccines, and therapeutic medicines for coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Much of this development has been based on the reference genome collected on January 5, 2020. Based on the genotyping of 6156 genome samples collected up to April 24, 2020, we report that SARS-CoV-2 has had 4459 alarmingly mutations which can be clustered into five subtypes. We introduce mutation ratio and mutation $h$-index to characterize the protein conservativen…
SARS-CoV is believed to originate from civets and was thought to have been eliminated as a threat after the 2003 outbreak. Here, we show that human SARS-CoV (huSARS-CoV) originated directly from bats, rather than civets, by a cross-species jump in 1991, and formed a human-adapted strain in 1998. Since then huSARS-CoV has evolved further into highly virulent strains with genotype T and a 29-nt deletion mutation, and weakly virulent strains with genotype C but without the 29-nt deletion. The former can cause pneumonia in humans and could be the major causative pathogen of the SARS outbreak, wher…
In this work, we aim to study that the dynamics behavior for cumulative number of SARS-CoV-2 pandemic can provide information on the overall behavior of the spread over daily time.The cumulative data can be synthesized in an empirical form obtained from a Susceptible-Infected-Recovered (SIR) model previously studied on a Euclidean network. From the study we carried out, we can conclude that the SIR model on the Euclidean network can reproduce data from several countries with a deviation of precision for given parameter values. This gives an insight into the different agents that influence the …
We quantified the probability of developing symptoms (respiratory or fever \geq 37.5 °C) and critical disease (requiring intensive care or resulting in death) of SARS-CoV-2 positive subjects. 5,484 contacts of SARS-CoV-2 index cases detected in Lombardy, Italy were analyzed, and positive subjects were ascertained via nasal swabs and serological assays. 73.9% of all infected individuals aged less than 60 years did not develop symptoms (95% confidence interval: 71.8-75.9%). The risk of symptoms increased with age. 6.6% of infected subjects older than 60 years had critical disease, with males at …
Viral transmission pathways have profound implications for public safety; it is thus imperative to establish a complete understanding of viable infectious avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air; however, this has not yet been demonstrated. Here we quantitatively analyze virion accumulation by accounting for aerosolized virion emission and destabilization. Reported superspreading events analyzed within this framework point towards aerosol mediated transmission of SARS-CoV-2. Virion exposure calculated for these events is found to trace out a single value, …
Pavelka et al. (Science, Reports, 7 May 2021) claim that a single round of population-wide antigen testing in Slovakia reduced the observed COVID-19 prevalence by 58%, and that it played a substantial role in curbing the pandemic. We argue that this estimate, which is based on incorrect assumptions, is exaggerated, and that the relief was short-lived with little effect on mitigating the pandemic.
Genomic surveillance of SARS-CoV-2 has been instrumental in tracking the spread and evolution of the virus during the pandemic. The availability of SARS-CoV-2 molecular sequences isolated from infected individuals, coupled with phylodynamic methods, have provided insights into the origin of the virus, its evolutionary rate, the timing of introductions, the patterns of transmission, and the rise of novel variants that have spread through populations. Despite enormous global efforts of governments, laboratories, and researchers to collect and sequence molecular data, many challenges remain in an…
Understanding the behaviour of hosts of SARS-CoV-2 is crucial to our understanding of the virus. A comparison of environmental features related to the incidence of SARS-CoV-2 with those of its potential hosts is critical. We examine the distribution of coronaviruses among bats. We analyse the distribution of SARS-CoV-2 in a nine-week period following lockdown in Italy, Spain, and Australia. We correlate its incidence with environmental variables particularly ultraviolet radiation, temperature, and humidity. We establish a clear negative relationship between COVID-19 and ultraviolet radiation, …
The transmission and evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are of paramount importance to the controlling and combating of coronavirus disease 2019 (COVID-19) pandemic. Currently, near 15,000 SARS-CoV-2 single mutations have been recorded, having a great ramification to the development of diagnostics, vaccines, antibody therapies, and drugs. However, little is known about SARS-CoV-2 evolutionary characteristics and general trend. In this work, we present a comprehensive genotyping analysis of existing SARS-CoV-2 mutations. We reveal that host immune response…
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been mutating since it was first sequenced in early January 2020. The genetic variants have developed into a few distinct clusters with different properties. Since the United States (US) has the highest number of viral infected patients globally, it is essential to understand the US SARS-CoV-2. Using genotyping, sequence-alignment, time-evolution, $k$-means clustering, protein-folding stability, algebraic topology, and network theory, we reveal that the US SARS-CoV-2 has four substrains and five top US SARS-CoV-2 mutations we…
The emergence of new variants of SARS-CoV-2 is a major concern given their potential impact on the transmissibility and pathogenicity of the virus as well as the efficacy of therapeutic interventions. Here, we predict the mutability of all positions in SARS-CoV-2 protein domains to forecast the appearance of unseen variants. Using sequence data from other coronaviruses, pre-existing to SARS-CoV-2, we build statistical models that do not only capture amino-acid conservation but more complex patterns resulting from epistasis. We show that these models are notably superior to conservation profile…
There is a near consensus view that SARS-CoV-2 has a natural zoonotic origin; however, several characteristics of SARS-CoV-2 taken together are not easily explained by a natural zoonotic origin hypothesis. These include: a low rate of evolution in the early phase of transmission; the lack of evidence of recombination events; a high pre-existing binding to human ACE2; a novel furin cleavage site insert; a flat glycan binding domain of the spike protein which conflicts with host evasion survival patterns exhibited by other coronaviruses, and high human and mouse peptide mimicry. Initial assumpti…
Tyshkovskiy and Panchin have recently published a commentary on our paper in which they outline several "points of disagreement with the Segreto/Deigin hypothesis". As our paper is titled "The genetic structure of SARS-CoV-2 does not rule out a laboratory origin", points of disagreement should provide evidence that rules out a laboratory origin. However, Tyshkovskiy and Panchin provide no such evidence and instead attempt to criticize our arguments that highlight aspects of SARS-CoV-2 that could be consistent with the lab leak hypothesis. Strikingly, Tyshkovskiy and Panchin's main point of cri…
Accurate and reliable forecasting of emerging dominant severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants enables policymakers and vaccine makers to get prepared for future waves of infections. The last three waves of SARS-CoV-2 infections caused by dominant variants Omicron (BA.1), BA.2, and BA.4/BA.5 were accurately foretold by our artificial intelligence (AI) models built with biophysics, genotyping of viral genomes, experimental data, algebraic topology, and deep learning. Based on newly available experimental data, we analyzed the impacts of all possible viral spike (S)…
One regards spaces of trees as stratified spaces, to study distributions of phylogenetic trees. Stratified spaces with may have cycles, however spaces of trees with a fixed number of leafs are contractible. Spaces of trees with three leafs, in particular, are spiders with three legs. One gives an elementary proof of the stickiness of intrinsic sample means on spiders. One also represents four leafs tree data in terms of an associated Petersen graph. One applies such ideas to analyze RNA sequences of SARS-CoV-2 from multiple sources, by building samples of trees and running nonparametric statis…
The devastating impact of the COVID-19 pandemic caused by SARS coronavirus 2 (SARS CoV 2) has raised important questions about viral origin, mechanisms of zoonotic transfer to humans, whether companion or commercial animals can act as reservoirs for infection, and why there are large variations in SARS-CoV-2 susceptibilities across animal species. Powerful in silico modelling methods can rapidly generate information on newly emerged pathogens to aid countermeasure development and predict future behaviours. Here we report an in silico structural homology modelling, protein-protein docking, and …
The mechanism of SARS-CoV-2 evolution and transmission is elusive and its understanding, a prerequisite to forecast emerging variants, is of paramount importance. SARS-CoV-2 evolution is driven by the mechanisms at molecular and organism scales and regulated by the transmission pathways at the population scale. In this review, we show that infectivity-based natural selection was discovered as the mechanism for SARS-CoV-2 evolution and transmission in July 2020. In April 2021, we proved beyond all doubt that such a natural selection via infectivity-based transmission pathway remained the sole m…
China adjusted the zero-COVID strategy in late 2022, triggering an unprecedented Omicron wave. We estimated the time-varying reproduction numbers of 32 provincial-level administrative divisions from December 2022 to January 2023. We found that the pooled estimate of initial reproduction numbers is 4.74 (95% CI: 4.41, 5.07).
The large-scale evolution of the SARS-CoV-2 virus has been marked by rapid turnover of genetic clades. New variants show intrinsic changes, notably increased transmissibility, as well as antigenic changes that reduce the cross-immunity induced by previous infections or vaccinations. How this functional variation shapes the global evolutionary dynamics has remained unclear. Here we show that selection induced by vaccination impacts on the recent antigenic evolution of SARS-CoV-2; other relevant forces include intrinsic selection and antigenic selection induced by previous infections. We obtain …
This article contains a series of analyses done for the SARS-CoV-2 outbreak in Rio Grande do Sul (RS) in the south of Brazil. These analyses are focused on the high-incidence cities such as the state capital Porto Alegre and at the state level. We provide methodological details and estimates for the effective reproduction number $R_t$, a joint analysis of the mobility data together with the estimated $R_t$ as well as ICU simulations and ICU LoS (length of stay) estimation for hospitalizations in Porto Alegre/RS.
The novel coronavirus SARS-CoV-2 has rapidly emerged as a significant threat to global public health, in particular because -- as is not uncommon with novel pathogens -- there is no effective pharmaceutical treatment or prophylaxis to the viral syndrome it causes. In the absence of such specific treatment modalities, the mainstay of public health response rests on non-pharmaceutical interventions (NPIs), such as social distancing. This paper contributes to the understanding of social distancing against SARS-CoV-2 by quantitatively analysing the statistical dynamics of disease propagation as a …
Currently, many countries are considering the introduction of tracing software on mobile smartphones with the main purpose to inform and alarm the mobile app user. Here, we demonstrate that, in addition to alarming and informing, mobile tracing can detect nearly all users that are infected by SARS-CoV-2. Our algorithm BETIS (Bayesian Estimation for Tracing Infection States) makes use of self-reports of the user's health status. Then, BETIS guarantees that almost all SARS-CoV-2 infections of the group of users can be detected. Furthermore, BETIS estimates the virus prevalence in the whole popul…
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the current global COVID-19 pandemic, in which millions of lives have been lost. Understanding the zoonotic evolution of the coronavirus may provide insights for developing effective vaccines, monitoring the transmission trends, and preventing new zoonotic infections. Homopolymeric nucleotide repeats (HP), the most simple tandem repeats, are a ubiquitous feature of eukaryotic genomes. Yet the HP distributions and roles in coronavirus genome evolution are poorly investigated. In this study, we characterize th…
During a long-running pandemic a pathogen can mutate, producing new strains with different epidemiological parameters. Existing approaches to epidemic modelling only consider one virus strain. We have developed a modified SEIR model to simulate multiple virus strains within the same population. As a case study, we investigate the potential effects of SARS-CoV-2 strain B.1.1.7 on the city of Moscow. Our analysis indicates a high risk of a new wave of infections in September-October 2021 with up to 35 000 daily infections at peak. We open-source our code and data.
Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；Korea University（高丽大学）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）
Digital contact tracing approaches based on Bluetooth low energy (BLE) have the potential to efficiently contain and delay outbreaks of infectious diseases such as the ongoing SARS-CoV-2 pandemic. In this work we propose a novel machine learning based approach to reliably detect subjects that have spent enough time in close proximity to be at risk of being infected. Our study is an important proof of concept that will aid the battery of epidemiological policies aiming to slow down the rapid spread of COVID-19.
