A Novel Mathematical Model That Predicts the Protection Time of SARS-CoV-2 Antibodies.

Infectious diseases such as SARS-CoV-2 pose a considerable threat to public health. Constructing a reliable mathematical model helps us quantitatively explain the kinetic characteristics of antibody-virus interactions. A novel and robust model is developed to integrate antibody dynamics with virus dynamics based on a comprehensive understanding of immunology principles. This model explicitly formulizes the pernicious effect of the antibody, together with a positive feedback stimulation of the virus-antibody complex on the antibody regeneration. Besides providing quantitative insights into antibody and virus dynamics, it demonstrates good adaptivity in recapturing the virus-antibody interaction. It is proposed that the environmental antigenic substances help maintain the memory cell level and the corresponding neutralizing antibodies secreted by those memory cells. A broader application is also visualized in predicting the antibody protection time caused by a natural infection. Suitable binding antibodies and the presence of massive environmental antigenic substances would prolong the protection time against breakthrough infection. The model also displays excellent fitness and provides good explanations for antibody selection, antibody interference, and self-reinfection. It helps elucidate how our immune system efficiently develops neutralizing antibodies with good binding kinetics. It provides a reasonable explanation for the lower SARS-CoV-2 mortality in the population that was vaccinated with other vaccines. It is inferred that the best strategy for prolonging the vaccine protection time is not repeated inoculation but a directed induction of fast-binding antibodies. Eventually, this model will inform the future construction of an optimal mathematical model and help us fight against those infectious diseases.

More or less deadly? A mathematical model that predicts SARS-CoV-2 evolutionary direction.

SARS-CoV-2 has caused tremendous deaths globally. It is of great value to predict the evolutionary direction of SARS-CoV-2. In this paper, we proposed a novel mathematical model that could predict the evolutionary trend of SARS-CoV-2. We focus on the mutational effects on viral assembly capacity. A robust coarse-grained mathematical model is constructed to simulate the virus dynamics in the host body. Both virulence and transmissibility can be quantified in this model. A delicate equilibrium point that optimizes the transmissibility can be numerically obtained. Based on this model, the virulence of SARS-CoV-2 might further decrease, accompanied by an enhancement of transmissibility. However, this trend is not continuous; its virulence will not disappear but remains at a relatively stable range. A virus assembly model which simulates the virus packing process is also proposed. It can be explained why a few mutations would lead to a significant divergence in clinical performance, both in the overall particle formation quantity and virulence. This research provides a novel mathematical attempt to elucidate the evolutionary driving force in RNA virus evolution.

mRNA COVID-19 Vaccines-Facts and Hypotheses on Fragmentation and Encapsulation.

BACKGROUND: The adventure of the mRNA vaccine began thirty years ago in the context of influenza. This consisted in encapsulating the mRNA coding for a viral protein in a lipid particle. We show how the mRNA encoding S protein has been modified for that purpose in the context of the anti-SARS-CoV-2 vaccination. RESULTS: by using data coming from genetic and epidemiologic databases, we show the theoretical possibility of fragmentation of this mRNA into small RNA sequences capable of inhibiting important bio-syntheses such as the production of beta-globin. DISCUSSION: we discuss two aspects related to mRNA vaccine: (i) the plausibility of mRNA fragmentation, and (ii) the role of liposomal nanoparticles (LNPs) used in the vaccine and their impact on mRNA biodistribution. CONCLUSION: we insist on the need to develop lipid nanoparticles allowing personalized administration of vaccines and avoiding adverse effects due to mRNA fragmentation and inefficient biodistribution. Hence, we recommend (i) adapting the mRNA of vaccines to the least mutated virus proteins and (ii) personalizing its administration to the categories of chronic patients at risk most likely to suffer from adverse effects.

Mathematical Modelling of the Spatial Distribution of a COVID-19 Outbreak with Vaccination Using Diffusion Equation.

The formulation of mathematical models using differential equations has become crucial in predicting the evolution of viral diseases in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China, which causes a severe and potentially fatal respiratory syndrome. Since then, it has been declared a pandemic by the World Health Organization and has spread around the globe. A reaction−diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process, in which different substances are transformed, and a diffusion process, which causes their distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic using the bias of reaction−diffusion equations. Both local and global asymptotic stability conditions for the equilibria were determined using a Lyapunov function, and the nature of the stability was determined using the Routh−Hurwitz criterion. Furthermore, we consider the conditions for the existence and uniqueness of the model solution and show the spatial distribution of the model compartments when the basic reproduction rate R0<1 and R0>1. Thereafter, we conducted a sensitivity analysis to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations and investigating the impact of vaccination, together with the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. Therefore, we offer to the public health policymakers a better understanding of COVID-19 management.

Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic.

BACKGROUND: The age of infection plays an important role in assessing an individual's daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article's main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model. RESULTS: We present some results of the parameters' identification of the model when all the eigenvalues are known. This method was applied to Japan's third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month. CONCLUSION: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.

Statistical analysis supports UTR (untranslated region) deletion theory in SARS-CoV-2.

It was noticed that the mortality rate of SARS-CoV-2 infection experienced a significant declination in the early stage of the epidemic. We suspect that the sharp deterioration of virus toxicity is related to the deletion of the untranslated region (UTR) of the virus genome. It was found that the genome length of SARS-CoV-2 engaged a significant truncation due to UTR deletion after a mega-sequence analysis. Sequence similarity analysis further indicated that short UTR strains originated from its long UTR ancestors after an irreversible deletion. A good correlation was discovered between genome length and mortality, which demonstrated that the deletion of the virus UTR significantly affected the toxicity of the virus. This correlation was further confirmed in a significance analysis of the genetic influence on the clinical outcomes. The viral genome length of hospitalized patients was significantly more extensive than that of asymptomatic patients. In contrast, the viral genome length of asymptomatic was considerably longer than that of ordinary patients with symptoms. A genome-level mutation scanning was performed to systematically evaluate the influence of mutations at each position on virulence. The results indicated that UTR deletion was the primary driving force in alternating virus virulence in the early evolution. In the end, we proposed a mathematical model to explain why this UTR deletion was not continuous.

A Model for the Lifespan Loss Due to a Viral Disease: Example of the COVID-19 Outbreak.

The end of the acute phase of the COVID-19 pandemic is near in some countries as declared by World Health Organization (WHO) in January 2022 based on some studies in Europe and South Africa despite unequal distribution of vaccines to combat the disease spread globally. The heterogeneity in individual age and the reaction to biological and environmental changes that has been observed in COVID-19 dynamics in terms of different reaction to vaccination by age group, severity of infection per age group, hospitalization and Intensive Care Unit (ICU) records show different patterns, and hence, it is important to improve mathematical models for COVID-19 pandemic prediction to account for different proportions of ages in the population, which is a major factor in epidemic history. We aim in this paper to estimate, using the Usher model, the lifespan loss due to viral infection and ageing which could result in pathological events such as infectious diseases. Exploiting epidemiology and demographic data firstly from Cameroon and then from some other countries, we described the ageing in the COVID-19 outbreak in human populations and performed a graphical representation of the proportion of sensitivity of some of the model parameters which we varied. The result shows a coherence between the orders of magnitude of the calculated and observed incidence numbers during the epidemic wave, which constitutes a semi-quantitative validation of the mathematical modelling approach at the population level. To conclude, the age heterogeneity of the populations involved in the COVID-19 outbreak needs the consideration of models in age groups with specific susceptibilities to infection.

Age Dependent Epidemic Modeling of COVID-19 Outbreak in Kuwait, France, and Cameroon.

Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible-Infectious-Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0-19 years, 20-64 years, and >64 years, but in this article, we only consider two (20-64 years and >64 years) age groups because the group 0-19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible-Infectious-Goneanewsusceptible-Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.

Modeling Vaccine Efficacy for COVID-19 Outbreak in New York City.

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-19 epidemics from reported cases data. Given an epidemiological model, we developed in previous studies a method that allowed the computation of an instantaneous transmission rate that produced an exact fit of reported cases data of the COVID-19 outbreak. In this article, we improve the method by incorporating vaccination data. More precisely, we develop a model in which vaccination is variable in its effectiveness. We develop a new technique to compute the transmission rate in this model, which produces an exact fit to reported cases data, while quantifying the efficacy of the vaccine and the daily number of vaccinated. We apply our method to the reported cases data and vaccination data of New York City.

What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below 3.5 from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below 3.5, which implies that it is sufficient to vaccinate 71% of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate 75-80% to eliminate COVID-19 in each state or country.

Analysis of Reproduction Number R0 of COVID-19 Using Current Health Expenditure as Gross Domestic Product Percentage (CHE/GDP) across Countries.

(1) Background: Impact and severity of coronavirus pandemic on health infrastructure vary across countries. We examine the role percentage health expenditure plays in various countries in terms of their preparedness and see how countries improved their public health policy in the first and second wave of the coronavirus pandemic; (2) Methods: We considered the infectious period during the first and second wave of 195 countries with their current health expenditure as gross domestic product percentage (CHE/GDP). An exponential model was used to calculate the slope of the regression line while the ARIMA model was used to calculate the initial autocorrelation slope and also to forecast new cases for both waves. The relationship between epidemiologic and CHE/GDP data was used for processing ordinary least square multivariate modeling and classifying countries into different groups using PC analysis, K-means and hierarchical clustering; (3) Results: Results show that some countries with high CHE/GDP improved their public health strategy against virus during the second wave of the pandemic; (4) Conclusions: Results revealed that countries who spend more on health infrastructure improved in the tackling of the pandemic in the second wave as they were worst hit in the first wave. This research will help countries to decide on how to increase their CHE/GDP in order to properly tackle other pandemic waves of the present COVID-19 outbreak and future diseases that may occur. We are also opening up a debate on the crucial role socio-economic determinants play during the exponential phase of the pandemic modelling.

Estimation of Daily Reproduction Numbers during the COVID-19 Outbreak

(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R0 is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes.

Unpredictable, Counter-Intuitive Geoclimatic and Demographic Correlations of COVID-19 Spread Rates.

We present spread parameters for first and second waves of the COVID-19 pandemic for USA states, and for consecutive nonoverlapping periods of 20 days for the USA and 51 countries across the globe. We studied spread rates in the USA states and 51 countries, and analyzed associations between spread rates at different periods, and with temperature, elevation, population density and age. USA first/second wave spread rates increase/decrease with population density, and are uncorrelated with temperature and median population age. Spread rates are systematically inversely proportional to those estimated 80-100 days later. Ascending/descending phases of the same wave only partially explain this. Directions of correlations with factors such as temperature and median age flip. Changes in environmental trends of the COVID-19 pandemic remain unpredictable; predictions based on classical epidemiological knowledge are highly uncertain. Negative associations between population density and spread rates, observed in independent samples and at different periods, are most surprising. We suggest that systematic negative associations between spread rates 80-100 days apart could result from confinements selecting for greater contagiousness, a potential double-edged sword effect of confinements.

Factors associated with the spatial heterogeneity of the first wave of COVID-19 in France: a nationwide geo-epidemiological study.

BACKGROUND: The objective of this study was to better understand the factors associated with the heterogeneity of in-hospital COVID-19 morbidity and mortality across France, one of the countries most affected by COVID-19 in the early months of the pandemic. METHODS: This geo-epidemiological analysis was based on data publicly available on government and administration websites for the 96 administrative departments of metropolitan France between March 19 and May 11, 2020, including Public Health France, the Regional Health Agencies, the French national statistics institute, and the Ministry of Health. Using hierarchical ascendant classification on principal component analysis of multidimensional variables, and multivariate analyses with generalised additive models, we assessed the associations between several factors (spatiotemporal spread of the epidemic between Feb 7 and March 17, 2020, the national lockdown, demographic population structure, baseline intensive care capacities, baseline population health and health-care services, new chloroquine and hydroxychloroquine dispensations, economic indicators, degree of urbanisation, and climate profile) and in-hospital COVID-19 incidence, mortality, and case fatality rates. Incidence rate was defined as the cumulative number of in-hospital COVID-19 cases per 100 000 inhabitants, mortality rate as the cumulative number of in-hospital COVID-19 deaths per 100 000, and case fatality rate as the cumulative number of in-hospital COVID-19 deaths per cumulative number of in-hospital COVID-19 cases. FINDINGS: From March 19 to May 11, 2020, hospitals in metropolitan France notified a total of 100 988 COVID-19 cases, including 16 597 people who were admitted to intensive care and 17 062 deaths. There was an overall cumulative in-hospital incidence rate of 155·6 cases per 100 000 inhabitants (range 19·4-489·5), in-hospital mortality rate of 26·3 deaths per 100 000 (1·1-119·2), and in-hospital case fatality rate of 16·9% (4·8-26·2). We found clear spatial heterogeneity of in-hospital COVID-19 incidence and mortality rates, following the spread of the epidemic. After multivariate adjustment, the delay between the first COVID-19-associated death and the onset of the national lockdown was positively associated with in-hospital incidence (adjusted standardised incidence ratio 1·02, 95% CI 1·01-1·04), mortality (adjusted standardised mortality ratio 1·04, 1·02-1·06), and case fatality rates (adjusted standardised fatality ratio 1·01, 1·01-1·02). Mortality and case fatality rates were higher in departments with older populations (adjusted standardised ratio for populations with a high proportion older than aged >85 years 2·17 [95% CI 1·20-3·90] for mortality and 1·43 [1·08-1·88] for case fatality rate). Mortality rate was also associated with incidence rate (1·0004, 1·0002-1·001), but mortality and case fatality rates did not appear to be associated with baseline intensive care capacities. We found no association between climate and in-hospital COVID-19 incidence, or between economic indicators and in-hospital COVID-19 incidence or mortality rates. INTERPRETATION: This ecological study highlights the impact of the epidemic spread, national lockdown, and reactive adaptation of intensive care capacities on the spatial distribution of COVID-19 morbidity and mortality. It provides information for future geo-epidemiological analyses and has implications for preparedness and response policies to current and future epidemic waves in France and elsewhere. FUNDING: None.

Towards unified and real-time analyses of outbreaks at country-level during pandemics.

The management of public health and the preparedness for health emergencies partly rely on the collection and analysis of surveillance data, which become crucial in the context of an emergency such as the pandemic caused by COVID-19. For COVID-19, typically, numerous national and global initiatives have been set up from this perspective. Here, we propose to develop a shared vision of the country-level outbreaks during a pandemic, by enhancing, at the international scale, the foundations of the analysis of surveillance data and by adopting a unified and real-time approach to monitor and forecast the outbreak across time and across the world. This proposal, rolled out as a web platform, should contribute to strengthen epidemiological understanding, sanitary democracy as well as global and local responses to pandemics.

SARS-CoV-2 and miRNA-like inhibition power.

(1) Background: RNA viruses and especially coronaviruses could act inside host cells not only by building their own proteins, but also by perturbing the cell metabolism. We show the possibility of miRNA-like inhibitions by the SARS-CoV-2 concerning for example the hemoglobin and type I interferons syntheses, hence highly perturbing oxygen distribution in vital organs and immune response as described by clinicians; (2) Hypothesis: We hypothesize that short RNA sequences (about 20 nucleotides in length) from the SARS-CoV-2 virus genome can inhibit the translation of human proteins involved in oxygen metabolism, olfactory perception and immune system. (3) Methods: We compare RNA subsequences of SARS-CoV-2 protein S and RNA-dependent RNA polymerase genes to mRNA sequences of beta-globin and type I interferons; (4) Results: RNA subsequences longer than eight nucleotides from SARS-CoV-2 genome could hybridize subsequences of the mRNA of beta-globin and of type I interferons; (5) Conclusions: Beyond viral protein production, COVID-19 might affect vital processes like host oxygen transport and immune response.

Inverted Covariate Effects for First versus Mutated Second Wave Covid-19: High Temperature Spread Biased for Young.

(1) Background: Here, we characterize COVID-19's waves, following a study presenting negative associations between first wave COVID-19 spread parameters and temperature. (2) Methods: Visual examinations of daily increases in confirmed COVID-19 cases in 124 countries, determined first and second waves in 28 countries. (3) Results: The first wave spread rate increases with country mean elevation, median population age, time since wave onset, and decreases with temperature. Spread rates decrease above 1000 m, indicating high ultraviolet lights (UVs) decrease the spread rate. The second wave associations are the opposite, i.e., spread increases with temperature and young age, and decreases with time since wave onset. The earliest second waves started 5-7 April at mutagenic high elevations (Armenia, Algeria). The second waves also occurred at the warm-to-cold season transition (Argentina, Chile). Second vs. first wave spread decreases in most (77%) countries. In countries with late first wave onset, spread rates better fit second than first wave-temperature patterns. In countries with ageing populations (for example, Japan, Sweden, and Ukraine), second waves only adapted to spread at higher temperatures, not to infect the young. (4) Conclusions: First wave viruses evolved towards lower spread. Second wave mutant COVID-19 strain(s) adapted to higher temperature, infecting younger ages and replacing (also in cold conditions) first wave COVID-19 strains. Counterintuitively, low spread strains replace high spread strains, rendering prognostics and extrapolations uncertain.

Temperature Decreases Spread Parameters of the New Covid-19 Case Dynamics.

(1) Background: The virulence of coronavirus diseases due to viruses like SARS-CoV or MERS-CoV decreases in humid and hot weather. The putative temperature dependence of infectivity by the new coronavirus SARS-CoV-2 or covid-19 has a high predictive medical interest. (2) Methods: External temperature and new covid-19 cases in 21 countries and in the French administrative regions were collected from public data. Associations between epidemiological parameters of the new case dynamics and temperature were examined using an ARIMA model. (3) Results: We show that, in the first stages of the epidemic, the velocity of contagion decreases with country- or region-wise temperature. (4) Conclusions: Results indicate that high temperatures diminish initial contagion rates, but seasonal temperature effects at later stages of the epidemy remain questionable. Confinement policies and other eviction rules should account for climatological heterogeneities, in order to adapt the public health decisions to possible geographic or seasonal gradients.