A Theoretical Investigation of the SARS-CoV-2Model via Fractional Order Epidemiological Model

We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.

Development of the second version of Global Prediction System for Epidemiological Pandemic

Coronavirus disease 2019(COvID-19)is a severe global public health emergency that has caused a major cri-sis in the safety of human life,health,global economy,and social order.Moreover,CovID-19 poses significant challenges to healthcare systems worldwide.The prediction and early warning of infectious diseases on a global scale are the premise and basis for countries to jointly fight epidemics.However,because of the complexity of epidemics,predicting infectious diseases on a global scale faces significant challenges.In this study,we developed the second version of Global Prediction System for Epidemiological Pandemic(GPEP-2),which combines statis-tical methods with a modified epidemiological model.The GPEP-2 introduces various parameterization schemes for both impacts of natural factors(seasonal variations in weather and environmental impacts)and human so-cial behaviors(government control and isolation,personnel gathered,indoor propagation,virus mutation,and vaccination).The GPEP-2 successfully predicted the COVID-19 pandemic in over 180 countries with an average accuracy rate of 82.7%.It also provided prediction and decision-making bases for several regional-scale CovID-19 pandemic outbreaks in China,with an average accuracy rate of 89.3%.Results showed that both anthropogenic and natural factors can affect virus spread and control measures in the early stages of an epidemic can effectively control the spread.The predicted results could serve as a reference for public health planning and policymaking.

Influence of Quince Rootstocks on Entomosporium Leaf Spot （Entomosporium mespili） Susceptibility in European Pear cv. Abate Fetel

Entomosporium leaf spot （ELS） is caused by the fungus Fabraea maculata （anamorph： Entomosporium mespili） and affects most pear cultivars and quince rootstocks in Brazil. The aim of this study was to characterize the effect of Adams, EMA and EMC quince rootstocks on ELS in European pear cultivar ＂Abate Fetel＂ in Southern Brazil, during the 2009/2010, 2010/2011 and 2011/2012 growing season. The incidence and severity of disease was quantified weekly in 100 randomly leaves distributed in four medium-height branches per plant with eight replications. Disease progress curves of ELS were constructed and the epidemics compared according to： （1） the beginning of symptoms appearance （BSA）; （2） the time to reach the maximum disease incidence and severity （TRMDI and TRMDS）; （3） area under the incidence and severity disease progress curve （AUIDPC and AUSDPC）. The data were analyzed by linear regression and adjusted for three empirical models： Logistic, Monomolecular and Gompertz. The Abate Fetel cultivar under all rootstocks evaluated was susceptible to E. mespili. However, there were significant differences in ELS intensity among rootstocks evaluated. The highest ELS intensities were observed in combinations with EMA and Adams quince rootstock. Abate Fetel cultivar grafted on EMC quince rootstock showed all epidemiological variables results significantly different when compared with EMA quince rootstock. EMC quince rootstock induced late resistance compared with the other considerated rootstocks. The Logistic model was the most appropriates to describe the ELS progress of Abate Fetel cultivar under all rootstocks evaluated in the edafoclimatic conditions of Southern Brazil, during the 2009/2010, 2010/2011 and 2011/2012 growing season.

Deep Learning Applications for COVID-19 Analysis:A State-of-the-Art Survey

The COVID-19 has resulted in catastrophic situation and the deaths of millions of people all over the world.In this paper,the predictions of epidemiological propagation models,such as SIR and SEIR,are introduced to analyze the earlier COVID-19 propagation.The deep learning methods combined with transfer learning are familiar with classification-detection approaches based on chest X-ray and CT images are presented in detail.Besides,deep learning approaches have also been applied to lung ultrasound(LUS),which has been shown to be more sensitive than chest X-ray and CT images in detecting COVID-19.In the absence of a vaccine,the machine learning-related approaches are applied to analyze vaccine candidates in the realm of biology and medicine.The telehealth system played a major role in combating the pandemic from all aspects and reducing contact with patients during this period.Natural language processing-related methods are utilized to analyze tweets related to the COVID-19 epidemic on social media,and further analyze public sentiment and subject modeling,so as to arrange corresponding measures to appease public sentiment.In particular,this survey is to summarize and analyze the contributions made in various fields during the COVID-19 pandemic by considering both the contribution of deep learning in chest X-ray and CT images,as well as the application of the latest LUS during the COVID-19 pandemic.Telehealth and the importance of public sentiment analysis during a pandemic were also described in detail.

ANALYSIS OF AN SIS EPIDEMIOLOGIC MODEL WITH VARIABLE POPULATION SIZE AND A DELAY

Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.

Epidemiologic Evolution Platform Using Integrated Modeling and Geographic Information System

At the international level, a major effort is being made to optimizethe flow of data and information for health systems management. The studiesshow that medical and economic efficiency is strongly influenced by the levelof development and complexity of implementing an integrated system of epidemiological monitoring and modeling. The solution proposed and describedin this paper is addressed to all public and private institutions involved inthe fight against the COVID-19 pandemic, using recognized methods andstandards in this field. The Green-Epidemio is a platform adaptable to thespecific features of any public institution for disease management, based onopen-source software, allowing the adaptation, customization, and furtherdevelopment of “open-source” applications, according to the specificities ofthe public institution, the changes in the economic and social environment andits legal framework. The platform has a mathematical model for the spreadof COVID-19 infection depending on the location of the outbreaks so thatthe allocation of resources and the geographical limitation of certain areascan be parameterized according to the number and location of the real-timeidentified outbreaks. The social impact of the proposed solution is due to theplanned applications of information flow management, which is a first stepin improving significantly the response time and efficiency of people-operatedresponse services. Moreover, institutional interoperability influences strategicsocietal factors.

An evaluation of mathematical models for the outbreak of COVID-19

Mathematical modelling performs a vital part in estimating and controlling the recent outbreak of coronavirus disease 2019(COVID-19).In this epidemic,most countries impose severe intervention measures to contain the spread of COVID-19.The policymakers are forced to make difficult decisions to leverage between health and economic development.How and when tomake clinical and public health decisions in an epidemic situation is a challenging question.The most appropriate solution is based on scientific evidence,which is mainly dependent on data and models.So one of the most critical problems during this crisis is whether we can develop reliable epidemiological models to forecast the evolution of the virus and estimate the effectiveness of various intervention measures and their impacts on the economy.There are numerous types of mathematical model for epidemiological diseases.In this paper,we present some critical reviews on mathematical models for the outbreak of COVID-19.Some elementary models are presented as an initial formulation for an epidemic.We give some basic concepts,notations,and foundation for epidemiological modelling.More related works are also introduced and evaluated by considering epidemiological features such as disease tendency,latent effects,susceptibility,basic reproduction numbers,asymptomatic infections,herd immunity,and impact of the interventions.

Turing instability in a diffusive SIS epidemiological model

Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible （SIS） type of epidemiological disease model with self- and cross-diffusion are investigated. We study the effect of diffusion on the stability of the endemic equilibrium with disease-induced mortality and nonlinear incidence rate, In the absence of diffusion the stationary solution stays stable but becomes unstable with respect to diffusion and that Turing instability takes place. We show that a standard （self-diffusion） system may be either stable or unstable, cross-diffusion response can stabilize an unstable standard system or decrease a ＂ihlring space （the space which the emergence of spatial patterns is holding） compared to the ~lhlring space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges. Numerical simulations are provided to illustrate and extend the theoretical results.

Mathematical modelling of the spread of COVID-19 on a university campus

In this paper we present a deterministic transmission dynamic compartmental model for the spread of the novel coronavirus on a college campus for the purpose of analyzing strategies to mitigate an outbreak.The goal of this project is to determine and compare the utility of certain containment strategies including gateway testing,surveillance testing,and contact tracing as well as individual level control measures such as mask wearing and social distancing.We modify a standard SEIR-type model to reflect what is currently known about COVID-19.We also modify the model to reflect the population present on a college campus,separating it into students and faculty.This is done in order to capture the expected different contact rates between groups as well as the expected difference in outcomes based on age known for COVID-19.We aim to provide insight into which strategies are most effective,rather than predict exact numbers of infections.We analyze effectiveness by looking at relative changes in the total number of cases as well as the effect a measure has on the estimated basic reproductive number.We find that the total number of infections is most sensitive to parameters relating to student behaviors.We also find that contact tracing can be an effective control strategy when surveillance testing is unavailable.Lastly,we validate the model using data from Villanova University's online COVID-19 Dashboard from Fall 2020 and find good agreement between model and data when superspreader events are incorporated in the model as shocks to the number of infected individuals approximately two weeks after each superspreader event.

Modelling SARS-CoV-2 unreported cases in Italy: Analysis of serological survey and vaccination scenarios

Objectives:Aim of the present paper is the study of the large unreported component,characterizing the SARS-CoV-2 epidemic event in Italy,taking advantage of the Istat survey.Particular attention is devoted to the sensitivity and specificity of the serological test and their effects.Methods:The model satisfactory reproduces the data of the Italian survey showing a relevant predictive power and relegating in a secondary position models which do not include,in the simulation,the presence of asymptomatic groups.The corrections due to the serological test sensitivity(in particular those ones depending on the symptoms onset)are crucial for a realistic analysis of the unreported(and asymptomatic)components.Results:The relevant presence of an unreported component during the second pandemic wave in Italy is confirmed and the ratio of reported to unreported cases is predicted to be roughly 1:4 in the last months of year 2020.A method to correct the serological data on the basis of the antibody sensitivity is suggested and systematically applied.The asymptomatic component is also studied in some detail and its amount quantified.A model analyses of the vaccination scenarios is performed confirming the relevance of a massive campaign(at least 80000 immunized per day)during the first six months of the year 2021,to obtain important immunization effects within August/September 2021.

Systematic comparison of epidemic growth patterns using two different estimation approaches

Background:Different estimation approaches are frequently used to calibrate mathematical models to epidemiological data,particularly for analyzing infectious disease outbreaks.Here,we use two common methods to estimate parameters that characterize growth patterns using the generalized growth model(GGM)calibrated to real outbreak datasets.Materials and methods:Data from 31 outbreaks are used to fit the GGM to the ascending phase of each outbreak and estimate the parameters using both least squares(LSQ)and maximum likelihood estimation(MLE)methods.We utilize parametric bootstrapping to construct confidence intervals for parameter estimates.We compare the results including RMSE,Anscombe residual,and 95%prediction interval coverage.We also evaluate the correlation between the estimates from both methods.Results:Comparing LSQ and MLE estimates,most outbreaks have similar parameter estimates,RMSE,Anscombe,and 95%prediction interval coverage.Parameter estimates do not differ across methods when the model yields a good fit to the early growth phase.However,for two outbreaks,there are systematic deviations in model fit to the data that explain differences in parameter estimates(e.g.,residuals represent random error rather than systematic deviation).Conclusion:Our findings indicate that utilizing LSQ and MLE methods produce similar results in the context of characterizing epidemic growth patterns with the GGM,provided that the model yields a good fit to the data.

Adult female syphilis prevalence,congenital syphilis case incidence and adverse birth outcomes,Mongolia 2000e2016:Estimates using the Spectrum STI tool

Introduction:Mongolia's health ministry prioritizes control of Sexually Transmitted Infections,including syphilis screening and treatment in antenatal care(ANC).Methods:Adult syphilis prevalence trends were fitted using the Spectrum-STI estimation tool,using data from ANC surveys and routine screening over 1997e2016.Estimates were combined with programmatic data to estimate numbers of treated and untreated pregnant women with syphilis and associated incidence congenital syphilis(CS)and CS-attributable adverse birth outcomes(ABO),which we compared with CS case reports.Results:Syphilis prevalence in pregnant women was estimated at 1.7%in 2000 and 3.0%in 2016.We estimated 652 CS cases,of which 410 ABO,in 2016.Far larger,annually increasing numbers of CS cases and ABO were estimated to have been prevented:1654 cases,of which 789 ABO in 2016
thanks to increasing coverages of ANC(99%in 2016),ANC-based screening(97%in 2016)and treatment of women diagnosed(81%in 2016).The 42 CS cases reported nationally over 2016(liveborn infants only)represented 27%of liveborn infants with clinical CS,but only 7%of estimated CS cases among women found syphilis-infected in ANC,and 6%of all estimated CS cases including those born to women with undiagnosed syphilis.Discussion/Conclusion:Mongolia's ANC-based syphilis screening program is reducing CS,but maternal prevalence remains high.To eliminate CS(target:<50 cases per 100,000 live births),Mongolia should strengthen ANC services,limiting losses during referral for treatment,and under-diagnosis of CS including still-births and neonatal deaths,and expand syphilis screening and prevention programs.

Will the large-scale vaccination succeed in containing the COVID-19 pandemic and how soon?

Background:The availability of vaccines provides a promising solution to contain the COVID-19 pandemic.However,it remains unclear whether the large-scale vaccination can succeed in containing the COVID-19 pandemic and how soon.We developed an epidemiological model named SUVQC(Suceptible-Unquarantined-Vaccined-Quarantined-Conflrmed)to quantitatively analyze and predict the epidemic dynamics of COVID-19 under vaccination.Methods:In addition to the impact of non-pharmaceutical interventions(NPIs),our model explicitly parameterizes key factors related to vaccination,including the duration of immunity,vaccine efficacy,and daily vaccination rate etc.The model was applied to the daily reported numbers of confirmed cases of Israel and the USA to explore and predict trends under vaccination based on their current epidemic statuses and intervention measures.We further provided a formula for designing a practical vaccination strategy,which simultaneously considers the effects of the basic reproductive number of COVID-19,intensity of NPIs,duration of immunological memory after vaccination,vaccine efficacy and daily vaccination rate.Results:In Israel,53.83%of the population is fully vaccinated,and under the current NPI intensity and vaccination scheme,the pandemic is predicted to end between May 14,2021,and May 16,2021,assuming immunity persists for 180 days to 365 days.If NPIs are not implemented after March 24,2021,the pandemic will end later,between July 4,2021,and August 26,2021.For the USA,if we assume the current vaccination rate(0.268%per day)and intensity of NPIs,the pandemic will end between January 20,2022,and October 19,2024,assuming immunity persists for 180 days to 365 days.However,assuming immunity persists for 180 days and no NPIs are implemented,the pandemic will not end and instead reach an equilibrium state,with a proportion of the population remaining actively infected.Conclusions:Overall,the daily vaccination rate should be decided according to vaccine efficacy and immunity duration to achieve herd immunity.In some situations,vaccination alone cannot stop the pandemic,and NPIs are necessary to supplement vaccination and accelerate the end of the pandemic.Considering that vaccine efficacy and duration of immunity may be reduced for new mutant strains,it is necessary to remain cautiously optimistic about the prospect of,ending the pandemic under vaccination.

Modeling analytics in COVID-19: prediction, prevention, control, and evaluation

The outbreak of COVID-19 has attracted attention from all around the world.Governments and institutions have adopted ways to fight COVID-19, but itsprevalence is still strong. The SIR model has important reference value for thenovel coronavirus epidemic, offering both preventive measures and the ability topredict future trends. Based on an analysis of the classical epidemiological SIRmodel along with key parameters, this paper aims to analyze the patterns ofCOVID-19, to discuss potential anti-COVID-19 measures, and to explain whywe need to conduct appropriate measures against COVID-19. The use of theSIR model can play an important role in public health emergencies. Among theparameters of the SIR model, the contact ratio and the reproduction ratio arethe factors that have the potential to mitigate the consequences of COVID-19.Anti-COVID-19 measures include wearing a mask, washing one’s hands,keeping social distance, and staying at home if possible.

An assessment of the potential impact of the Omicron variant of SARS-CoV-2 in Aotearoa New Zealand

New Zealand delayed the introduction of the Omicron variant of SARS-CoV-2 into the community by the continued use of strict border controls through to January 2022.This allowed time for vaccination rates to increase and the roll out of third doses of the vaccine(boosters)to begin.It also meant more data on the characteristics of Omicron became available prior to the first cases of community transmission.Here we present a mathematical model of an Omicron epidemic,incorporating the effects of the booster roll out and waning of vaccine-induced immunity,and based on estimates of vaccine effectiveness and disease severity from international data.The model considers differing levels of immunity against infection,severe illness and death,and ignores waning of infection-induced immunity.This model was used to provide an assessment of the potential impact of an Omicron wave in the New Zealand population,which helped inform government preparedness and response.At the time the modelling was carried out,the date of introduction of Omicron into the New Zealand community was unknown.We therefore simulated outbreaks with different start dates,as well as investigating different levels of booster uptake.We found that an outbreak starting on 1 February or 1 March led to a lower health burden than an outbreak starting on 1 January because of increased booster coverage,particularly in older age groups.We also found that outbreaks starting later in the year led to worse health outcomes than an outbreak starting on 1 March.This is because waning immunity in older groups started to outweigh the increased protection from higher booster coverage in younger groups.For an outbreak starting on 1 February and with high booster uptake,the number of occupied hospital beds in the model peaked between 800 and 3,300 depending on assumed transmission rates.We conclude that combining an accelerated booster programme with public health measures to flatten the curve are key to avoid overwhelming the healthcare system.

A vaccination model for COVID-19 in Gauteng,South Africa

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection,and we investigate these strategies in early-stage outbreak dynamics.The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies.Using a system of ordinary differential equations,we model the outbreak in the province of Gauteng,assuming that several parameters vary over time.Analyzing data from the time period before vaccination gives the approximate dates of parameter changes,and those dates are linked to government policies.Unknown parameters are then estimated from available case data and used to assess the impact of each policy.Looking forward in time,possible scenarios give projections involving the implementation of two different vaccines at varying times.Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

Modelling the effect of non-pharmaceutical interventions on COVID-19 transmission from mobility maps

The world has faced the COVID-19 pandemic for over two years now,and it is time to revisit the lessons learned from lockdown measures for theoretical and practical epidemiological improvements.The interlink between these measures and the resulting change in mobility(a predictor of the disease transmission contact rate)is uncertain.We thus propose a new method for assessing the efficacy of various non-pharmaceutical interventions(NPI)and examine the aptness of incorporating mobility data for epidemiological modelling.Facebook mobility maps for the United Arab Emirates are used as input datasets from the first infection in the country to mid-Oct 2020.Dataset was limited to the pre-vaccination period as this paper focuses on assessing the different NPIs at an early epidemic stage when no vaccines are available and NPIs are the only way to reduce the reproduction number(R_(0)).We developed a travel network density parameterβ_(t)to provide an estimate of NPI impact on mobility patterns.Given the infection-fatality ratio and time lag(onset-to-death),a Bayesian probabilistic model is adapted to calculate the change in epidemic development withβt.Results showed that the change inβ_(t)clearly impacted R_(0).The three lockdowns strongly affected the growth of transmission rate and collectively reduced R_(0)by 78%before the restrictions were eased.The model forecasted daily infections and deaths by 2%and 3%fractional errors.It also projected what-if scenarios for different implementation protocols of each NPI.The developed model can be applied to identify the most efficient NPIs for confronting new COVID-19 waves and the spread of variants,as well as for future pandemics.

Modeling the epidemic dynamics of COVID-19: Agent-based approach including molecular dynamics simulation and SEIR type methods

In this study, we developed a SEIR model, including social interactions and individualhuman mobility in everyday activities. For this purpose, daily mobility of people wasconsidered by using the molecular dynamic method and the virus spreading was modeledemploying the ordinary SEIR scheme. Utilizing this model, the variation of populationsize, density, and health strategy as well as the effect of busy places such as malls,were considered. The results show that our flexible model is able to consider the effectsof different parameters such as distance between peoples, local population density andhealth strategy in the outbreak.

GLOBAL DYNAMICS OF A DIFFERENTIAL SUSCEPTIBILITY MODEL

An SIS epidemiological model in a population of varying size with two dissimilar groups of susceptible individuals has been analyzed. We prove that all the solutions tend to the equilibria of the system. Then we use the Poincar~ Index theorem to determine the number of the rest points and their stability properties. It has been shown that bistability occurs for suitable values of the involved parameters. We use the perturbations of the pitchfork bifurcation points to give examples of all possible dynamics of the system. Some numerical examples of bistability and hysteresis behavior of the systeIn has been also provided.

DYNAMIC ANALYSIS OF AN SIR MODEL WITH STOCHASTIC PERTURBATIONS

In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution.