A highly accurate peak time formula of epidemic outbreak from the SIR model

Forecasting the epidemic peak time right from the origination of a disease is vital to take over dynamical behaviour of its spread over time. The decision of isolation, social distance and lock down strategic progresses does all rely on an accurate prediction of the peak time so that reduction of the time of peak or of the infected size of population will be made possible. Therefore, recent efforts concentrated on deriving elaborative and analytically accessible expressions representing the peak time of the infected compartment from the classical SIR epidemic mathematical model. In this research paper, two closed-form formulae are introduced to yield a straightforward computation of peak time of an infectious disease with no restrictions on the SIR quantities. In addition to this, the calculations can be implemented on a usual calculator, without requiring the use of advanced mathematical functions, having provided the initial fractions of infected and susceptible populations as well as the recovery to infectious ratio. A comparison including the COVID-19 data is fulfilled with the very recent formulas available in the open literature. With the proposed new scalings, evaluation of the peak time is reduced only to two parameter space and the accuracy of the present formulas in reduced form is ultimately confirmed yielding an error of order of magnitude 10−4 valid for the complete regime of the set of SIR model parameters. Even in the case of an endemic, the past peak time of the illness can also be captured accurately by the given formulae. Two simple approximations in terms of usual geometric series are also provided. These can be safely used with a pocket calculator without sophisticated laboratory equipments.

Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages.

Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics, however, most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious period. This paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control strategies. For this purpose, we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period: the first one is an exponential distribution model (EDM), and the other one is a gamma distribution model (GDM); explicit formula of peak time of the EDM is presented via our analytical approach. By data fitting with the COVID-19 (Omicron) epidemic in Spain and Norway, it seems that Spain is more suitable for EDM while Norway is more suitable for GDM. Finally, we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates, and increase of primary course rate (PCR) and booster dose rate (BDR).

Modeling COVID-19 dynamics in the sixteen West African countries.

The COVID-19 pandemic is currently causing several damages to the world, especially in the public health sector. Due to identifiability problems in parameters' estimation of complex compartmental models, this study considered a simple deterministic susceptible-infectious-recovered (SIR)-type model to characterize the first wave and predict the future course of the pandemic in the West African countries. We estimated some specific characteristics of the disease's dynamics, such as its initial conditions, reproduction numbers, true peak and peak of the reported cases, with their corresponding times, final epidemic size and time-varying attack ratio. Our findings revealed a relatively low proportion of susceptible individuals in the region and the different countries ( 1.2 % across West Africa). The detection rate of the disease was also relatively low ( 0.9 % for West Africa as a whole) and < 2 % for most countries, except for Gambia (12.5 %), Cape-Verde ( 9.5 % ), Mauritania ( 5.9 % ) and Ghana ( 4.4 % ). The reproduction number varied between 1.15 (Burkina-Faso) and 4.45 (Niger), and most countries' peak time of the first wave of the pandemic was between June and July. Generally, the peak time of the reported cases came a week (7-8 days) after the true peak time. The model predicted for the first wave, 222,100 actual active cases in the region at the peak time, while the final epidemic size accounted for 0.6 % of the West African population (2,526,700 individuals). The results showed that COVID-19 has not severely affected West Africa as in other regions. However, current control measures and standard operating procedures should be maintained over time to accelerate a decline in the observed trends of the pandemic.

R-WAVE PEAK TIME AS A NEW PREDICTOR OF MYOCARDIAL INJURY IN PATIENTS INFECTED WITH COVID-19

Objectives: Myocardial injury is closely associated with the poor prognosis of patients infected with coronavirus disease 2019 (COVID-19). Early diagnosis of cardiovascular complications that develop during the process of COVID-19 is crucial. R-wave peak time (RWPT) is an electrocardiographic parameter in which myocardial involvement caused by various situations is shown. This study was designed to assess the predictive value of RWPT in patients infected with COVID-19 who developed a myocardial injury. Methodology: A total of 138 patients diagnosed with COVID-19 were enrolled in this prospective study. The patients were classified according to their troponin values ??? study group (SG, n= 52) with high troponin and control group (CG, n= 86) without elevated troponin. All data obtained from patients were compared. Results: QRS duration (101 +/- 5 ms vs. 99 +/- 6 ms, p= .013) and RWPT (43 +/- 6 ms vs. 38 +/- 5 ms, p<0.001) were significantly longer in SG than in the CG. In multivariate analysis, C -reactive protein (OR: 1.109, 95% CI: 1.058-1.163;p<0.001), ejection fraction (OR: .844, 95% CI: .765-.931;p=0.001), and RWPT (OR: 1.211, 95% CI: 1.096-1.339;p<0.001) were independent predictors of myocardial injury in COVID-19-infected individuals. The ROC analysis revealed a cut-off value of RWPT for myocardial injury of 40.5 ms, with a sensitivity of 63.5% and a specificity of 62.8% (AUC: 0.730, 95% CI: 0.641-0.819, p<0.001). Conclusion: RWPT is a significant predictor of myocardial injury and may benefit in better identifying patients with myocardial injury in COVID-19.

A Design Science Approach to Blood Donation Apps

The COVID-19 pandemic has put additional pressure on the healthcare systems worldwide. It also led to a significant shortage of blood products. Delaying surgeries resulted in an increased demand at peak times that aligned with a decrease in blood donations at the same time. While being crucial for many surgeries and also certain types of treatments, blood cannot be produced artificially, but healthcare systems rely on voluntary donations. The relatively short shelf-life of most products makes a close matching of demand and supply necessary. We argue that smartphone applications can help to motivate donors to donate blood when necessary, giving access to all relevant information and services. By applying the design science research methodology, we derived design principles for effective smartphone applications and present a conceptual model in the form of mock-ups. We performed two design cycles and evaluated the design principles and the conceptual model with regular, lapsed, first-time and non-donors from Germany in a focus group discussion. © 2022, Springer Nature Switzerland AG.

Random forest to predict eucalyptus as a potential herb in preventing coviD19

The covid-19 pandemic had been on the rise since the beginning of 2020. In Indonesia itself, the first case was identified on 3rd March 2020, then peaked at around the end of January 2021. Even though the recent number of covid-19 cases is not as much as the peak time, the positive case has been increasing from around 2600 to 6300 cases every day in the last month. This phenomenon is urging people to take better care of their health. One of the alternatives Indonesian takes to maintain and increase their health is using herbal medicine. Indonesia is one of the countries with a flourishing number of herbal species. Eucalyptus is one of herbal plants with lots of benefits. Even before the pandemic eucalyptus oil has been used for daily use by many in Indonesia. In this study, we predict the compounds in eucalyptus which have any interaction with protein in SARS-COV-2 virus using machine learning method, namely Random Forest. This is one of the applications of the drug-discovery method, drug repurposing, which used existing drug-target interaction data as a model to predict drug compounds with unidentified interaction with targets. Applying this method, we predicted some compounds found in eucalyptus, such as alpha-terpinene, and 1,8-cineole might have an interaction with covid-19 protein thus eucalyptus can be used as a preventive measure. © 2021 IEEE.

Developing a Calibrated Discrete Event Simulation Model of Shops of a Dutch Phone and Subscription Retailer during COVID-19 to Evaluate Shift Plans to Reduce Waiting Times

Belsimpel deals with large waiting times during peak times under COVID-19 circumstances compared to non-COVID-19 times. Therefore, a discrete event simulation model of the Belsimpel shops has been developed. However, the model is not validated due to data scarcity. This paper proposes a model calibration procedure based on the idea that service times decrease during high-demanded hours and increase otherwise. The results show that the proposed procedure enables the generation of realistic Key Performance Indicator values. The calibrated simulation model can be used for analyzing the performance of possible improvements. Accordingly, the calibrated model is applied to investigate the impact of an improved employee scheduling. The results show that the mean waiting time decreases by 20-33 %, the maximum waiting time decreases by 12-20 %, and the mean service level increases by 3-11 %. These improvements enhance customer satisfaction while scheduling the same number of working hours. © 2021 IEEE.

Effects of COVID-19 on individuals in Opioid Addiction Recovery

Opioid Use Disorder (OUD) is one of the most severe health care problems in the USA. People addicted to opioids need various treatments, including Medication-Assisted Treatment (MAT), proper counseling, and behavioral therapies. However, during the peak time of the COVID-19 pandemic, the supply of emergency medications was disrupted seriously. Patients faced severe medical care scarcity since many pharmaceutical companies, drugstores, and local pharmacies were closed. Import-export was also canceled to consent to the government emergency law, i.e., lockdown, quarantine, and isolation. These circumstances and their negative effects on OUD patient's psychology could have led them to a drop out of MAT medications and persuaded to resume illicit opioid use. This project involves collecting and analyzing a large volume of Twitter data related to MAT medications for OUD patients. We discover the Active MAT Medicine Users (AMMUs) on twitter. For this, we build a seed dictionary of words related to OUD and MAT and apply association rules to expand it. Further, AMMUs' tweet posts are studied 'before the pandemic' (BP) and 'during the pandemic' (DP) to understand how the drug behaviors and habits have changed due to COVID-19. We also perform sentiment analysis on Tweets to determine the impact of the COVID-19 pandemic on the psychology of AMMUs. Our analysis shows that the use of MAT medications has decreased around 30.54%, where the use of illicit drugs and other prescription opioids increased 18.06% and 12.12%, respectively, based on AMMUs' tweets posted during the lockdown compared with before the lockdown statistics. The COVID-19 pandemic and lockdown may result in the resumption of illegal and prescription opioid abuse by OUD patients. Necessary steps and precautions should be taken by health care providers to ensure the emergency supply of medicines and also psychological support and thus prevent patients from illicit opioid use. © 2021 IEEE.

Sentiment Analysis of Cancer Patients About Their Treatment During the Peak Time of Pandemic COVID-19

Social media has become a valuable tool for users to express their opinion and for researchers to analyze public sentiment more efficiently. People respond much quickly towards any issue on social than any other traditional platform. Observing the patient's opinion on social media about the hospital medical facilities is a new trend that several hospitals are adopting recently in the modern world to improve their heal care facilities. After the pandemic of SARS-CoV-2, it has influenced the health care practices of all the world. Initial investigations indicate that patients with comorbidities are more fragile to this SARS-CoV-2 infection. Medical experts suggested postponing the routine treatment of cancer patients. However, few meta-analyses suggested evidence are not sufficient to hold the claim of the frailty of cancer patients to COVID-19. They were not in favor of shelving the scheduled treatments. On the other hand, some medical experts favored postponing cancer patients' scheduled treatments like chemotherapy, which could be a dangerous decision for cancer patients. We conducted the sentiment analysis of the patients with various comorbidities (diseases like diabetes, obesity, and cancer in which patient has to visit the hospital more often) to understand their point of view whether they were satisfied during the pandemic with their treatment or not? How Covid-19 affected their scheduled appointments. To serve the purpose, we gathered more than 150000 relevant tweets from Twitter (Jan 2020 to April 2020) to analyze the sentiment of cancer patients around the world. Our findings demonstrate a surge in the argument about cancer and its treatment after the outbreak of COVID-19. Most of the tweets are reasonable (52.6%) compared to negative ones (24.3%). We developed polarity and subjectivity distribution to better recognize the positivity/negativity in the sentiment. The results reveal that the polarity range of positive tweets is within the range of 0 to 0.5. That means the tendency in the tweets is not negative (it is above zero) nor so much positive too. It is statistical evidence supporting how natural language processing (NLP) can be used to better understand the patient's behavior in real-time. It may facilitate the medical professionals to make better decisions to organize the routine management of cancer patients. © 2021 IEEE.

Assessment of P Wave Peak Time and P Wave Dispersion in Patients with COVID-19 Infection

Objective: This study aims to evaluate P wave distribution (PD) and P wave peak time (PWPT) in COVID-19 patients. Materials and Methods: A total of 140 participants were recruited in our study. The COVID-19 group included 74 subjects, and the control group included 66 individuals. Between the two groups, PD was compared for electrocardiographic P-wave measurements, including abnormal P wave axis, P wave terminal force in V1 (PWTF), P wave max duration (P max), and PWPT. Results: It was determined that the P max and PD values of the patients infected with the COVID-19 virus were higher than the control group (p<0.001). PWPTD2 (p<0.001), PWPTV1 (p<0.001) and abnormal P wave axis ratio (p<0.05) were found to be significantly longer in COVID-19 patients. Serum CRP and WBC values were found to be significantly higher in COVID-19 patients (p<0.001, p<0.001, respectively). Also, a significant and positive correlation was detected between CRP and P max, PD, PWPTD2 and PWPTV1. There was the same correlation relationship between WBC with P max, PD, PWPTD2 and PWPTV1. Conclusion: Significant prolongation of PWPT and PD in COVID-19 patients may be predictive in determining the risk of developing atrial fibrillation.

Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?

An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible-infectious-recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.

Explicit formulae for the peak time of an epidemic from the SIR model.

Reducing the peak time of an epidemic disease in order for slowing down the eventual dynamics and getting prepared for the unavoidable epidemic wave is utmost significant to fight against the risks of a contagious epidemic disease. To serve to this purpose, the well-documented infection model of SIR is examined in the current research to propose an analytical approach for providing an explicit formula associated with a straightforward computation of peak time of outbreak. Initially, the time scale from the relevant autonomous SIR epidemic model is formulated analytically via an integral based on the fractions of susceptible and infected compartments. Afterwards, through a series expansion of the logarithmic term of the resultant integrand, the peak time is shown to rely upon the fraction of susceptible, the infectious ratio as well as the initial fractions of ill and susceptible individuals. The approximate expression is shown to rigorously capable of capturing the time threshold of illness for an epidemic from the semi-time SIR epidemiology. Otherwise, it is also successful to predict the peak time from a past history of a disease when all-time epidemic model is adopted. Accuracy of the derived expressions are initially confirmed by direct comparisons with recently reported approximate formulas in the literature. Several other epidemic disease samples including the COVID-19 often studied in the recent literature are eventually attacked with favourable performance of the presented formulae for assessing the peak time occurrence of an epidemic. A quick evaluation of the peak time of a disease certainly enables the governments to take early effective epidemic precautions.

Current trends and future prediction of novel coronavirus disease (COVID-19) epidemic in China: a dynamical modeling analysis.

The novel coronavirus disease 2019 (COVID-19) infection broke out in December 2019 in Wuhan, and rapidly overspread 31 provinces in mainland China on 31 January 2020. In the face of the increasing number of daily confirmed infected cases, it has become a common concern and worthy of pondering when the infection will appear the turning points, what is the final size and when the infection would be ultimately controlled. Based on the current control measures, we proposed a dynamical transmission model with contact trace and quarantine and predicted the peak time and final size for daily confirmed infected cases by employing Markov Chain Monte Carlo algorithm. We estimate the basic reproductive number of COVID-19 is 5.78 (95%CI: 5.71-5.89). Under the current intervention before 31 January, the number of daily confirmed infected cases is expected to peak on around 11 February 2020 with the size of 4066 (95%CI: 3898-4472). The infection of COVID-19 might be controlled approximately after 18 May 2020. Reducing contact and increasing trace about the risk population are likely to be the present effective measures.

A data driven epidemic model to analyse the lockdown effect and predict the course of COVID-19 progress in India.

We propose a data driven epidemic model using the real data on the infection, recovery and death cases for the analysis of COVID-19 progression in India. The model assumes continuation of existing control measures such as lockdown and quarantines, the suspected and confirmed cases and does not consider the scenario of 2nd surge of the epidemic due to any reason. The model is arrived after least square fitting of epidemic behaviour model based on theoretical formulation to the real data of cumulative infection cases reported between 24 March 2020 and 30May 2020. The predictive capability of the model has been validated with real data of infection cases reported during June 1-10, 2020. A detailed analysis of model predictions in terms of future trend of COVID-19 progress individually in 18 states of India and India as a whole has been attempted. Infection rate in India, as a whole, is continuously decreasing with time and has reached 3 times lower than the initial infection rate after 6 weeks of lock down suggesting the effectiveness of the lockdown in containing the epidemic. Results suggest that India, as a whole, could see the peak and end of the epidemic in the month of July 2020 and March 2021 respectively as per the current trend in the data. Active infected cases in India may touch 2 lakhs or little above at the peak time and total infected cases may reach over 19 lakhs as per current trend. State-wise results have been discussed in the manuscript. However, the prediction may deviate particularly for longer dates, as assumptions of model cannot be met always in a real scenario. In view of this, a real time application (COV-IND Predictor) has been developed which automatically syncs the latest data from the national COVID19 dash board on daily basis and updates the model input parameters and predictions instantaneously. This real time application can be accessed from the link: https://docs.google.com/spreadsheets/d/1fCwgnQ-dz4J0YWVDHUcbEW1423wOJjdEXm8TqJDWNAk/edit?usp=sharing and can serve as a practical tool for policy makers to track peak time and maximum active infected cases based on latest trend in data for medical readiness and taking epidemic management decisions.

Why is it difficult to accurately predict the COVID-19 epidemic?

Since the COVID-19 outbreak in Wuhan City in December of 2019, numerous model predictions on the COVID-19 epidemics in Wuhan and other parts of China have been reported. These model predictions have shown a wide range of variations. In our study, we demonstrate that nonidentifiability in model calibrations using the confirmed-case data is the main reason for such wide variations. Using the Akaike Information Criterion (AIC) for model selection, we show that an SIR model performs much better than an SEIR model in representing the information contained in the confirmed-case data. This indicates that predictions using more complex models may not be more reliable compared to using a simpler model. We present our model predictions for the COVID-19 epidemic in Wuhan after the lockdown and quarantine of the city on January 23, 2020. We also report our results of modeling the impacts of the strict quarantine measures undertaken in the city after February 7 on the time course of the epidemic, and modeling the potential of a second outbreak after the return-to-work in the city.