Logistic growth modelling of COVID-19 proliferation in China and its international implications

Assessing marginal effects of non-pharmaceutical interventions on the transmission of SARS-CoV-2 across Africa: a hybrid modeling study

Since 2019, a new strain of coronavirus has challenged global health systems. Due its fragile healthcare systems, Africa was predicted to be the most affected continent. However, past experiences of African countries with epidemics and other factors, including actions taken by governments, have contributed to reducing the spread of SARS-CoV-2. This study aims to assess the marginal impact of non-pharmaceutical interventions in fifteen African countries during the pre-vaccination period. To describe the transmission dynamics and control of SARS-CoV-2 spread, an extended time-dependent SEIR model was used. The transmission rate of each infectious stage was obtained using a logistic model with NPI intensity as a covariate. The results revealed that the effects of NPIs varied between countries. Overall, restrictive measures related to assembly had, in most countries, the largest reducing effects on the pre-symptomatic and mild transmission, while the transmission by severe individuals is influenced by privacy measures (more than $10\%$). Countries should develop efficient alternatives to assembly restrictions to preserve the economic sector. This involves e.g. training in digital tools and strengthening digital infrastructures.

Chaos theory in the understanding of COVID-19 pandemic dynamics

The chaos theory, a field of study in mathematics and physics, offers a unique lens through which to understand the dynamics of the COVID-19 pandemic. This theory, which deals with complex systems whose behavior is highly sensitive to initial conditions, can provide insights into the unpredictable and seemingly random nature of the pandemic's spread. In this review, we will discuss some literature data with the aim of showing how chaos theory could provide valuable perspectives in understanding the complex and dynamic nature of the COVID-19 pandemic. In particular, we will emphasize how the chaos theory can help in dissecting the unpredictable, non- linear progression of the disease, the importance of initial conditions, and the complex interactions between various factors influencing its spread. These insights are crucial for developing effective strategies to manage and mitigate the impact of the pandemic.

Machine learning algorithms for predicting determinants of COVID-19 mortality in South Africa

Background

COVID-19 has strained healthcare resources, necessitating efficient prognostication to triage patients effectively. This study quantified COVID-19 risk factors and predicted COVID-19 intensive care unit (ICU) mortality in South Africa based on machine learning algorithms.

Methods

Data for this study were obtained from 392 COVID-19 ICU patients enrolled between 26 March 2020 and 10 February 2021. We used an artificial neural network (ANN) and random forest (RF) to predict mortality among ICU patients and a semi-parametric logistic regression with nine covariates, including a grouping variable based on K-means clustering. Further evaluation of the algorithms was performed using sensitivity, accuracy, specificity, and Cohen's K statistics.

Results

From the semi-parametric logistic regression and ANN variable importance, age, gender, cluster, presence of severe symptoms, being on the ventilator, and comorbidities of asthma significantly contributed to ICU death. In particular, the odds of mortality were six times higher among asthmatic patients than non-asthmatic patients. In univariable and multivariate regression, advanced age, PF1 and 2, FiO2, severe symptoms, asthma, oxygen saturation, and cluster 4 were strongly predictive of mortality. The RF model revealed that intubation status, age, cluster, diabetes, and hypertension were the top five significant predictors of mortality. The ANN performed well with an accuracy of 71%, a precision of 83%, an F1 score of 100%, Matthew's correlation coefficient (MCC) score of 100%, and a recall of 88%. In addition, Cohen's k-value of 0.75 verified the most extreme discriminative power of the ANN. In comparison, the RF model provided a 76% recall, an 87% precision, and a 65% MCC.

Conclusion

Based on the findings, we can conclude that both ANN and RF can predict COVID-19 mortality in the ICU with accuracy. The proposed models accurately predict the prognosis of COVID-19 patients after diagnosis. The models can be used to prioritize COVID-19 patients with a high mortality risk in resource-constrained ICUs.

Solving the stochastic dynamics of population growth

Population growth is a fundamental process in ecology and evolution. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations with the deterministic predictions. We show that these deterministic equations are generically bad predictors of the average stochastic population dynamics. Specifically, deterministic predictions overestimate the simulated population sizes, especially those of populations starting with a small number of individuals. Describing population growth as a stochastic birth process, we prove that the discrepancy between deterministic predictions and simulated data is due to unclosed-moment dynamics. In other words, the deterministic approach does not consider the variability of birth times, which is particularly important with small population sizes. We show that some moment-closure approximations describe the growth dynamics better than the deterministic prediction. However, they do not reduce the error satisfactorily and only apply to some population growth models. We explicitly solve the stochastic growth dynamics, and our solution applies to any population growth model. We show that our solution exactly quantifies the dynamics of a community composed of different strains and correctly predicts the fixation probability of a strain in a serial dilution experiment. Our work sets the foundations for a more faithful modeling of community and population dynamics. It will allow the development of new tools for a more accurate analysis of experimental and empirical results, including the inference of important growth parameters.

Assessing last-mile distribution resilience under demand disruptions

The COVID-19 pandemic led to a significant breakdown of the traditional retail sector resulting in an unprecedented surge in e-commerce demand for the delivery of essential goods. Consequently, the pandemic raised concerns pertaining to e-retailers' ability to maintain and efficiently restore level of service in the event of such low-probability high-severity market disruptions. Thus, considering e-retailers' role in the supply of essential goods, this study assesses the resilience of last-mile distribution operations under disruptions by integrating a Continuous Approximation (CA) based last-mile distribution model, the resilience triangle concept, and the Robustness, Redundancy, Resourcefulness, and Rapidity (R4) resilience framework. The proposed R4 Last Mile Distribution Resilience Triangle Framework is a novel performance-based qualitative-cum-quantitative domain-agnostic framework. Through a set of empirical analyses, this study highlights the opportunities and challenges of different distribution/outsourcing strategies to cope with disruption. In particular, the authors analyzed the use of an independent crowdsourced fleet (flexible service contingent on driver availability); the use of collection-point pickup (unconstrained downstream capacity contingent on customer willingness to self-collect); and integration with a logistics service provider (reliable service with high distribution costs). Overall, this work recommends the e-retailers to create a suitable platform to ensure reliable crowdsourced deliveries, position sufficient collection-points to ensure customer willingness to self-collect, and negotiate contracts with several logistics service providers to ensure adequate backup distribution.

[Mathematical models for COVID-19 infection estimation: essential considerations and projections in Colombia]

OBJECTIVE

To estimate the COVID-19 infection behavior in Colombia using mathematical models.

METHODS

Two mathematical models were constructed to estimate imported confirmed cases and related confirmed cases of COVID-19 infection in Colombia, respectively. The phenomenology of imported confirmed cases is modeled with sigmoidal function, while related confirmed cases are modeled using a combination of exponential functions and polynomial algebraic functions. The fitting algorithms based on least squares methods and direct search methods are used to determine the parameters of the models.

RESULTS

The sigmodial model performs a highly convergent estimation of the reported confirmed cases of COVID-19 infection to May 28, 2020. This model achieved a prediction error of 0.5 % measured using the normalized root mean square error. The model of the confirmed cases reported as related shows a 3.5 % prediction error and a low bias of -0.01 associated with overestimation.

CONCLUSIONS

This work shows that the mathematical models allow to predict the behavior of the infection efficiently and effectively by COVID 19 in Colombia when the imported cases and the related cases of infection are independently considered.

Long-term temporal evolution of extreme temperature in a warming Earth

We present a new approach to modeling the future development of extreme temperatures globally and on the time-scale of several centuries by using non-stationary generalized extreme value distributions in combination with logistic functions. The statistical models we propose are applied to annual maxima of daily temperature data from fully coupled climate models spanning the years 1850 through 2300. They enable us to investigate how extremes will change depending on the geographic location not only in terms of the magnitude, but also in terms of the timing of the changes. We find that in general, changes in extremes are stronger and more rapid over land masses than over oceans. In addition, our statistical models allow for changes in the different parameters of the fitted generalized extreme value distributions (a location, a scale and a shape parameter) to take place independently and at varying time periods. Different statistical models are presented and the Bayesian Information Criterion is used for model selection. It turns out that in most regions, changes in mean and variance take place simultaneously while the shape parameter of the distribution is predicted to stay constant. In the Arctic region, however, a different picture emerges: There, climate variability is predicted to increase rather quickly in the second half of the twenty-first century, probably due to the melting of ice, whereas changes in the mean values take longer and come into effect later.

Temporal dynamic characteristics of human monkeypox epidemic in 2022 around the world under the COVID-19 pandemic background

Background

The reemergence of the monkeypox epidemic has aroused great concern internationally. Concurrently, the COVID-19 epidemic is still ongoing. It is essential to understand the temporal dynamics of the monkeypox epidemic in 2022 and its relationship with the dynamics of the COVID-19 epidemic. In this study, we aimed to explore the temporal dynamic characteristics of the human monkeypox epidemic in 2022 and its relationship with those of the COVID-19 epidemic.

Methods

We used publicly available data of cumulative monkeypox cases and COVID-19 in 2022 and COVID-19 at the beginning of 2020 for model validation and further analyses. The time series data were fitted with a descriptive model using the sigmoid function. Two important indices (logistic growth rate and semi-saturation period) could be obtained from the model to evaluate the temporal characteristics of the epidemic.

Results

As for the monkeypox epidemic, the growth rate of infection and semi-saturation period showed a negative correlation (r = 0.47, p = 0.034). The growth rate also showed a significant relationship with the locations of the country in which it occurs [latitude (r = -0.45, p = 0.038)]. The development of the monkeypox epidemic did not show significant correlation compared with the that of COVID-19 in 2020 and 2022. When comparing the COVID-19 epidemic with that of monkeypox, a significantly longer semi-saturation period was observed for monkeypox, while a significant larger growth rate was found in COVID-19 in 2020.

Conclusions

This novel study investigates the temporal dynamics of the human monkeypox epidemic and its relationship with the ongoing COVID-19 epidemic, which could provide more appropriate guidance for local governments to plan and implement further fit-for-purpose epidemic prevention policies.

Modeling the positive testing rate of COVID-19 in South Africa using a semi-parametric smoother for binomial data

Identification and isolation of COVID-19 infected persons plays a significant role in the control of COVID-19 pandemic. A country's COVID-19 positive testing rate is useful in understanding and monitoring the disease transmission and spread for the planning of intervention policy. Using publicly available data collected between March 5th, 2020 and May 31st, 2021, we proposed to estimate both the positive testing rate and its daily rate of change in South Africa with a flexible semi-parametric smoothing model for discrete data. There was a gradual increase in the positive testing rate up to a first peak rate in July, 2020, then a decrease before another peak around mid-December 2020 to mid-January 2021. The proposed semi-parametric smoothing model provides a data driven estimates for both the positive testing rate and its change. We provide an online R dashboard that can be used to estimate the positive rate in any country of interest based on publicly available data. We believe this is a useful tool for both researchers and policymakers for planning intervention and understanding the COVID-19 spread.

How do the smart travel ban policy and intercity travel pattern affect COVID-19 trends? Lessons learned from Iran

COVID-19, as the most significant epidemic of the century, infected 467 million people and took the lives of more than 6 million individuals as of March 19, 2022. Due to the rapid transmission of the disease and the lack of definitive treatment, countries have employed nonpharmaceutical interventions. This study aimed to investigate the effectiveness of the smart travel ban policy, which has been implemented for non-commercial vehicles in the intercity highways of Iran since November 21, 2020. The other goal was to suggest efficient COVID-19 forecasting tools and to examine the association of intercity travel patterns and COVID-19 trends in Iran. To this end, weekly confirmed cases and deaths due to COVID-19 and the intercity traffic flow reported by loop detectors were aggregated at the country's level. The Box-Jenkins methodology was employed to evaluate the policy's effectiveness, using the interrupted time series analysis. The results indicated that the autoregressive integrated moving average with explanatory variable (ARIMAX) model outperformed the univariate ARIMA model in predicting the disease trends based on the MAPE criterion. The weekly intercity traffic and its lagged variables were entered as covariates in both models of the disease cases and deaths. The results indicated that the weekly intercity traffic increases the new weekly COVID-19 cases and deaths with a time lag of two and five weeks, respectively. Besides, the interrupted time series analysis indicated that the smart travel ban policy had decreased intercity travel by around 29%. Nonetheless, it had no significant direct effect on COVID-19 trends. This study suggests that the travel ban policy would not be efficient lonely unless it is coupled with active measures and adherence to health protocols by the people.

P. On computational analysis of nonlinear regression models addressing heteroscedasticity and autocorrelation issues: An application to COVID-19 data

This paper develops a method for nonlinear regression models estimation that is robust to heteroscedasticity and autocorrelation of errors. Using nonlinear least squares estimation, four popular growth models (Exponential, Gompertz, Verhulst, and Weibull) were computed. Some assumptions on the errors of these models (independence, normality, and homoscedasticity) being violated, the estimates are improved by modeling the residuals using the ETS method. For an application purpose, this approach has been used to predict the daily cumulative number of novel coronavirus (COVID-19) cases in Africa for the study period, from March 13, 2020, to June 26, 2021. The comparison of the proposed model to the competitors was done using statistical metrics such as MAPE, MAE, RMSE, AIC, BIC, and AICc. The findings revealed that the modified Gompertz model is the most accurate in forecasting the total number of COVID-19 cases in Africa. Moreover, the developed approach will be useful for researchers and policymakers for predicting purpose and for better decision making in different fields of its applications.

A phenomenological model for COVID-19 data taking into account neighboring-provinces effect and random noise

We model the incidence of the COVID-19 disease during the first wave of the epidemic in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infections through a density-independent parameter that entails positive spatial correlation. Pointwise values of the input parameters are fitted by an optimization procedure. To accommodate the significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a random noise is incorporated into the model, whose parameters are calibrated by maximum likelihood estimation. The calculated paths of the stochastic response and the probabilistic regions are in good agreement with the data.

A novel approach for COVID-19 Infection forecasting based on multi-source deep transfer learning

COVID-19 is a contagious disease; so, predicting its future infections in a provincial region requires the consideration of the related data (i.e., rates of infection, mortality and recovery, etc.) over a period of time. Clearly, the COVID-19 data of a particular provincial region can be easily modelled as a time-series. However, predicting the future COVID-19 infections in a particular region is quite challenging when the availability of COVID-19 dataset of the province is of little quantity. Accordingly, ML models when deployed for such tasks usually results in low infection prediction accuracy. To overcome such issues of low variance and high bias in a model due to data scarcity, multi-source transfer learning (MSTL) along with deep learning may be quite useful and effective. Therefore, this paper proposes a novel technique based on multi-source deep transfer learning (MSDTL) to efficiently forecast the future COVID-19 infections in the provinces with insufficient COVID-19 data. The proposed approach is a novel contribution as it considers the fact that future COVID-19 transmission in a region also depends on its population density and economic conditions (GDP) for accurate forecasting of the infections to tackle the pandemic efficiently. The importance of this feature selection is experimentally proved in this paper. Our proposed approach employs the well-known recurrent neural network architecture, the Long-short term memory (LSTM), a popular deep-learning model for history-dependent tasks. A comparative analysis has been performed with existing state-of-art algorithms to portray the efficiency of LSTM. Thus, formation of MSDTL approach enhances the predictive precision capability of the LSTM. We evaluate the proposed methodology over the COVID-19 dataset from sixty-two provinces belonging to different nations. We then empirically evaluate the performance of the proposed approach using two different evaluation metrics, viz. The mean absolute percentage error and the coefficient of determination. We show that our proposed MSDTL based approach is better in terms of the accuracy of the future infection prediction, and produces improvements up to 96% over its without-TL counterpart.

Convex-Concave fitting to successively updated data and its application to covid-19 analysis

Let n measurements of a process be provided sequentially, where the process follows a sigmoid shape, but the data have lost sigmoidicity due to measuring errors. If we smooth the data by making least the sum of squares of errors subject to one sign change in the second divided differences, then we obtain a sigmoid approximation. It is known that the optimal fit of this calculation is composed of two separate sections, one best convex and one best concave. We propose a method that starts at the beginning of the data and proceeds systematically to construct the two sections of the fit for the current data, step by step as n is increased. Although the minimization calculation at each step may have many local minima, it can be solved in about O ( n 2 ) operations, because of properties of the join between the convex and the concave section. We apply this method to data of daily Covid-19 cases and deaths of Greece, the United States of America and the United Kingdom. These data provide substantial differences in the final approximations. Thus, we evaluate the performance of the method in terms of its capabilities as both constructing a sigmoid-type approximant to the data and a trend detector. Our results clarify the optimization calculation both in a systematic manner and to a good extent. At the same time, they reveal some features of the method to be considered in scenaria that may involve predictions, and as a tool to support policy-making. The results also expose some limitations of the method that may be useful to future research on convex-concave data fitting.

Modeling and Preliminary Analysis of the Impact of Meteorological Conditions on the COVID-19 Epidemic

Since the COVID-19 epidemic outbreak at the end of 2019, many studies regarding the impact of meteorological factors on the attack have been carried out, and inconsistent conclusions have been reached, indicating the issue's complexity. To more accurately identify the effects and patterns of meteorological factors on the epidemic, we used a combination of logistic regression (LgR) and partial least squares regression (PLSR) modeling to investigate the possible effects of common meteorological factors, including air temperature, relative humidity, wind speed, and surface pressure, on the transmission of the COVID-19 epidemic. Our analysis shows that: (1) Different countries and regions show spatial heterogeneity in the number of diagnosed patients of the epidemic, but this can be roughly classified into three types: "continuous growth", "staged shock", and "finished"; (2) Air temperature is the most significant meteorological factor influencing the transmission of the COVID-19 epidemic. Except for a few areas, regional air temperature changes and the transmission of the epidemic show a significant positive correlation, i.e., an increase in air temperature is conducive to the spread of the epidemic; (3) In different countries and regions studied, wind speed, relative humidity, and surface pressure show inconsistent correlation (and significance) with the number of diagnosed cases but show some regularity.

A method for forecasting the number of hospitalized and deceased based on the number of newly infected during a pandemic

In this paper we propose a phenomenological model for forecasting the numbers of deaths and of hospitalized persons in a pandemic wave, assuming that these numbers linearly depend, with certain delays [Formula: see text] for deaths and [Formula: see text] for hospitalized, on the number of new cases. We illustrate the application of our method using data from the third wave of the COVID-19 pandemic in Croatia, but the method can be applied to any new wave of the COVID-19 pandemic, as well as to any other possible pandemic. We also supply freely available Mathematica modules to implement the method.

An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

Introduction

Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models.

Methods

We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R2 to compare and analyze the goodness-of-fit of LDE and GLDE models.

Results

Both models fitted the epidemic curves well, and all results were statistically significant. The R2 test value of COVID-19 was 0.924 (p < 0.001) fitted by the GLDE model and 0.916 (p < 0.001) fitted by the LDE model. The R2 test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R2 test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks.

Conclusion

The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

Towards predicting COVID-19 infection waves: A random-walk Monte Carlo simulation approach

Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In light of the present COVID-19 pandemic, there is a pressing need to better understand observed epidemic growth with multiple peak structures, preferably using first-principles methods. Along the lines of our previous work  [Physica A 574, 126014 (2021)], here we apply 2D random-walk Monte Carlo calculations to better understand COVID-19 spread through contact interactions. Lockdown scenarios and all other control interventions are imposed through mobility restrictions and a regulation of the infection rate within the stochastically interacting population. The susceptible, infected and recovered populations are tracked over time, with daily infection rates obtained without recourse to the solution of differential equations. The simulations were carried out for population densities corresponding to four countries, India, Serbia, South Africa and USA. In all cases our results capture the observed infection growth rates. More importantly, the simulation model is shown to predict secondary and tertiary waves of infections with reasonable accuracy. This predictive nature of multiple wave structures provides a simple and effective tool that may be useful in planning mitigation strategies during the present pandemic.

Comparison of various epidemic models on the COVID-19 outbreak in Indonesia

This paper compares four mathematical models to describe Indonesia's current coronavirus disease 2019 (COVID-19) pandemic. The daily confirmed case data are used to develop the four models: Logistic, Richards, SIR, and SEIR. A least-square fitting computes each parameter to the available confirmed cases data. We conducted parameterization and sensitivity experiments by varying the length of the data from 60 until 300 days of transmission. All models are susceptible to the epidemic data. Though the correlations between the models and the data are pretty good (>90%), all models still show a poor performance (RMSE>18%). In this study case, Richards model is superior to other models from the highest projection of the positive cases of COVID-19 in Indonesia. At the same time, others underestimate the outbreak and estimate too early decreasing phase. Richards model predicts that the pandemic remains high for a long time, while others project the pandemic will finish much earlier.

Identifying the cycles in COVID-19 infection: the case of Turkey

The new coronavirus disease, called COVID-19, has spread extremely quickly to more than 200 countries since its detection in December 2019 in China. COVID-19 marks the return of a very old and familiar enemy. Throughout human history, disasters such as earthquakes, volcanic eruptions and even wars have not caused more human losses than lethal diseases, which are caused by viruses, bacteria and parasites. The first COVID-19 case was detected in Turkey on 12 March 2020 and researchers have since then attempted to examine periodicity in the number of daily new cases. One of the most curious questions in the pandemic process that affects the whole world is whether there will be a second wave. Such questions can be answered by examining any periodicities in the series of daily cases. Periodic series are frequently seen in many disciplines. An important method based on harmonic regression is the focus of the study. The main aim of this study is to identify the hidden periodic structure of the daily infected cases. Infected case of Turkey is analyzed by using periodogram-based methodology. Our results revealed that there are 4, 5 and 62 days cycles in the daily new cases of Turkey.

Modeling Performance of Microservices Systems with Growth Theory

CONTEXT

The microservices architectural style is gaining momentum in the IT industry. This style does not guarantee that a target system can continuously meet acceptable performance levels. The ability to study the violations of performance requirements and eventually predict them would help practitioners to tune techniques like dynamic load balancing or horizontal scaling to achieve the resilience property.

OBJECTIVE

The goal of this work is to study the violations of performance requirements of microservices through time series analysis and provide practical instruments that can detect resilient and non-resilient microservices and possibly predict their performance behavior.

METHOD

We introduce a new method based on growth theory to model the occurrences of violations of performance requirements as a stochastic process. We applied our method to an in-vitro e-commerce benchmark and an in-production real-world telecommunication system. We interpreted the resulting growth models to characterize the microservices in terms of their transient performance behavior.

RESULTS

Our empirical evaluation shows that, in most of the cases, the non-linear S-shaped growth models capture the occurrences of performance violations of resilient microservices with high accuracy. The bounded nature associated with this models tell that the performance degradation is limited and thus the microservice is able to come back to an acceptable performance level even under changes in the nominal number of concurrent users. We also detect cases where linear models represent a better description. These microservices are not resilient and exhibit constant growth and unbounded performance violations over time. The application of our methodology to a real in-production system identified additional resilience profiles that were not observed in the in-vitro experiments. These profiles show the ability of services to react differently to the same solicitation. We found that when a service is resilient it can either decrease the rate of the violations occurrences in a continuous manner or with repeated attempts (periodical or not).

CONCLUSIONS

We showed that growth theory can be successfully applied to study the occurences of performance violations of in-vitro and in-production real-world systems. Furthermore, the cost of our model calibration heuristics, based on the mathematical expression of the selected non-linear growth models, is limited. We discussed how the resulting models can shed some light on the trend of performance violations and help engineers to spot problematic microservice operations that exhibit performance issues. Thus, meaningful insights from the application of growth theory have been derived to characterize the behavior of (non) resilient microservices operations.

Hospital preparedness during epidemics using simulation: the case of COVID-19

This paper presents a discrete event simulation model to support decision-making for the short-term planning of hospital resource needs, especially Intensive Care Unit (ICU) beds, to cope with outbreaks, such as the COVID-19 pandemic. Given its purpose as a short-term forecasting tool, the simulation model requires an accurate representation of the current system state and high fidelity in mimicking the system dynamics from that state. The two main components of the simulation model are the stochastic modeling of patient admission and patient flow processes. The patient arrival process is modelled using a Gompertz growth model, which enables the representation of the exponential growth caused by the initial spread of the virus, followed by a period of maximum arrival rate and then a decreasing phase until the wave subsides. We conducted an empirical study concluding that the Gompertz model provides a better fit to pandemic-related data (positive cases and hospitalization numbers) and has superior prediction capacity than other sigmoid models based on Richards, Logistic, and Stannard functions. Patient flow modelling considers different pathways and dynamic length of stay estimation in several healthcare stages using patient-level data. We report on the application of the simulation model in two Autonomous Regions of Spain (Navarre and La Rioja) during the two COVID-19 waves experienced in 2020. The simulation model was employed on a daily basis to inform the regional logistic health care planning team, who programmed the ward and ICU beds based on the resulting predictions.

A new logistic growth model applied to COVID-19 fatality data

BACKGROUND

Recent work showed that the temporal growth of the novel coronavirus disease (COVID-19) follows a sub-exponential power-law scaling whenever effective control interventions are in place. Taking this into consideration, we present a new phenomenological logistic model that is well-suited for such power-law epidemic growth.

METHODS

We empirically develop the logistic growth model using simple scaling arguments, known boundary conditions and a comparison with available data from four countries, Belgium, China, Denmark and Germany, where (arguably) effective containment measures were put in place during the first wave of the pandemic. A non-linear least-squares minimization algorithm is used to map the parameter space and make optimal predictions.

RESULTS

Unlike other logistic growth models, our presented model is shown to consistently make accurate predictions of peak heights, peak locations and cumulative saturation values for incomplete epidemic growth curves. We further show that the power-law growth model also works reasonably well when containment and lock down strategies are not as stringent as they were during the first wave of infections in 2020. On the basis of this agreement, the model was used to forecast COVID-19 fatalities for the third wave in South Africa, which was in progress during the time of this work.

CONCLUSION

We anticipate that our presented model will be useful for a similar forecasting of COVID-19 induced infections/deaths in other regions as well as other cases of infectious disease outbreaks, particularly when power-law scaling is observed.

A Spatial Analysis of COVID-19 in African Countries: Evaluating the Effects of Socio-Economic Vulnerabilities and Neighbouring

The ongoing highly contagious coronavirus disease 2019 (COVID-19) pandemic, which started in Wuhan, China, in December 2019, has now become a global public health problem. Using publicly available data from the COVID-19 data repository of Our World in Data, we aimed to investigate the influences of spatial socio-economic vulnerabilities and neighbourliness on the COVID-19 burden in African countries. We analyzed the first wave (January-September 2020) and second wave (October 2020 to May 2021) of the COVID-19 pandemic using spatial statistics regression models. As of 31 May 2021, there was a total of 4,748,948 confirmed COVID-19 cases, with an average, median, and range per country of 101,041, 26,963, and 2191 to 1,665,617, respectively. We found that COVID-19 prevalence in an Africa country was highly dependent on those of neighbouring Africa countries as well as its economic wealth, transparency, and proportion of the population aged 65 or older (p-value < 0.05). Our finding regarding the high COVID-19 burden in countries with better transparency and higher economic wealth is surprising and counterintuitive. We believe this is a reflection on the differences in COVID-19 testing capacity, which is mostly higher in more developed countries, or data modification by less transparent governments. Country-wide integrated COVID suppression strategies such as limiting human mobility from more urbanized to less urbanized countries, as well as an understanding of a county's social-economic characteristics, could prepare a country to promptly and effectively respond to future outbreaks of highly contagious viral infections such as COVID-19.

A hybrid approach to forecast the COVID-19 epidemic trend

Studying the progress and trend of the novel coronavirus pneumonia (COVID-19) transmission mode will help effectively curb its spread. Some commonly used infectious disease prediction models are introduced. The hybrid model is proposed, which overcomes the disadvantages of the logistic model's inability to predict the number of confirmed diagnoses and the drawbacks of too many tuning parameters of the SEIR (Susceptible, Exposed, Infectious, Recovered) model. The realization and superiority of the prediction of the proposed model are proven through experiments. At the same time, the influence of different initial values of the parameters that need to be debugged on the hybrid model is further studied, and the mean error is used to quantify the prediction effect. By forecasting epidemic size and peak time and simulating the effects of public health interventions, this paper aims to clarify the transmission dynamics of COVID-19 and recommend operation suggestions to slow down the epidemic. It is suggested that the quick detection of cases, sufficient implementation of quarantine and public self-protection behaviours are critical to slow down the epidemic.

Emergence of universality in the transmission dynamics of COVID-19

The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model-the Blue Sky model-and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.

A differential equations model-fitting analysis of COVID-19 epidemiological data to explain multi-wave dynamics

Compartmental epidemiological models are, by far, the most popular in the study of dynamics related with infectious diseases. It is, therefore, not surprising that they are frequently used to study the current COVID-19 pandemic. Taking advantage of the real-time availability of COVID-19 related data, we perform a compartmental model fitting analysis of the portuguese case, using an online open-access platform with the integrated capability of solving systems of differential equations. This analysis enabled the data-driven validation of the used model and was the basis for robust projections of different future scenarios, namely, increasing the detected infected population, reopening schools at different moments, allowing Easter celebrations to take place and population vaccination. The method presented in this work can easily be used to perform the non-trivial task of simultaneously fitting differential equation solutions to different epidemiological data sets, regardless of the model or country that might be considered in the analysis.

Performance management of OECD countries on Covid-19 pandemic: a criticism using data envelopment analysis models

Purpose

The Covid-19 pandemic spread rapidly around the world and required strict restriction plans and policies. In most countries around the world, the outbreak of the disease has been serious and has greatly affected the health system and the economy. The factors such as the number of patients with chronic diseases, the number of people over 65 years old, hospital facilities, the number of confirmed Covid-19 cases, the recovering Covid-19 cases and the number of deaths affect the rate of spread of Covid-19. This study aims to evaluate the performances of 21 Organisation for Economic Co-operation and Development (OECD) countries against the Covid-19 outbreak using three data envelopment analysis (DEA) models.

Design/methodology/approach

In this study, the performance of 21 OECD countries to manage the Covid-19 process has been analysed weekly via DEA which is widely used in various practical problems and provides a general framework for efficiency evaluation problems using the inputs and outputs of decision-making units.

Findings

The analysis showed that 11 countries out of 21 countries were efficient for selected weeks. According to the DEA results from the 20-week review (09 April 2020–20 August 2020), information about the course of the epidemic prevention and the normalization process for any country can be obtained.

Originality/value

In this study, due to the problem of the discrimination power of DEA, the cross-efficiency model and the super-efficiency model also used. In addition, the output-oriented model was preferred in this study for Covid-19 management efficiency.

Forecasting the Long-Term Trends of Coronavirus Disease 2019 (COVID-19) Epidemic Using the Susceptible-Infectious-Recovered (SIR) Model

A simple model for predicting Coronavirus Disease 2019 (COVID-19) epidemic is presented in this study. The prediction model is presented based on the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to describe the epidemic time evolution of infectious diseases. The original version of the Kermack and McKendrick model is used in this study. This included the daily rates of infection spread by infected individuals when these individuals interact with a susceptible population, which is denoted by the parameter β, while the recovery rates to determine the number of recovered individuals is expressed by the parameter γ. The parameters estimation of the three-compartment SIR model is determined through using a mathematical sequential reduction process from the logistic growth model equation. As the parameters are the basic characteristics of epidemic time evolution, the model is always tested and applied to the latest actual data of confirmed COVID-19 cases. It seems that this simple model is still reliable enough to describe the dynamics of the COVID-19 epidemic, not only qualitatively but also quantitatively with a high degree of correlation between actual data and prediction results. Therefore, it is possible to apply this model to predict cases of COVID-19 in several countries. In addition, the parameter characteristics of the classic SIR model can provide information on how these parameters reflect the efforts by each country to prevent the spread of the COVID-19 outbreak. This is clearly seen from the changes of the parameters shown by the classic SIR model.

Behavioral response of population on transmissibility and saturation incidence of deadly pandemic through fractional order dynamical system

The world entered in another wave of the SARS-CoV-2 due to non-compliance of standard operating procedures appropriately, initiated by respective governments. Apparently, measures like using face masks and social distancing were not observed by populace that ultimately worsens the situation. The behavioral response of the population induces a change in the dynamical outcomes of the pandemic, which is documented in this paper for all intents and purposes. The innovative perception is executed through a compartmental model with the incorporation of fractional calculus and saturation incident rate. In the first instance, the epidemiological model is designed with proportional fractional definition considering the compartmental individuals of susceptible, social distancing, exposed, quarantined, infected, isolated and recovered populations. By virtue of proportional fractional derivative, effective dynamical outcomes of equilibrium states and basic reproduction number are successfully elaborated with memory effect. The expansion of this derivative greatly simplifies the model to integer order while remaining in the fractional context. Subsequently, the memory effects on the asymptotic profiles are demonstrated through various graphical plots and tabulated values. In addition, the inclusion of saturation incident rate further explains the transmissibility of infection for different behavior of susceptible individuals. Mathematically, the results are also validated through comparative analysis of values with the solutions attained from fractional fourth order Runge-Kutta method (FRK4).

An improved SIR model describing the epidemic dynamics of the COVID-19 in China

In this letter, an improved SIR (ISIR) model is proposed, to analyze the spread of COVID-19 during the time window 21/01/2020-08/02/2021. The parameters can be extracted from an inverse problem of the ISIR to assess the risk of COVID-19. This study identifies that the cure rate is 0.05 and the reproduction number is 0.4490 during the time interval. The prediction values demonstrates high similarity to the reported data. The results indicate that the disease had been under control in China.

Predicting of the Coronavirus Disease 2019 (COVID-19) Epidemic Using Estimation of Parameters in the Logistic Growth Model

The COVID-19 pandemic was impacting the health and economy around the world. All countries have taken measures to control the spread of the epidemic. Because it is not known when the epidemic will end in several countries, then the prediction of the COVID-19 pandemic is a very important challenge. This study has predicted the temporal evolution of the COVID-19 pandemic in several countries using the logistic growth model. This model has analyzed several countries to describe the epidemic situation of these countries. The time interval of the actual data used as a comparison with the prediction results of this model was starting in the firstly confirmed COVID-19 cases to December 2020. This study examined an approach to the complexity spread of the COVID-19 pandemic using the logistic growth model formed from an ordinary differential equation. This model described the time-dependent population growth rate characterized by the three parameters of the analytical solution. The non-linear least-squares method was used to estimate the three parameters. These parameters described the rate growth constant of infected cases and the total number of confirmed cases in the final phase of the epidemic. This model is applied to the spread of the COVID-19 pandemic in several countries. The prediction results show the spread dynamics of COVID-19 infected cases which are characterized by time-dependent dynamics. In this study, the proposed model provides estimates for the model parameters that are good for predicting the COVID-19 pandemic because they correspond to actual data for all analyzed countries. It is based on the coefficient of determination, R², and the R² value of more than 95% which is obtained from the non-linear curves for all analyzed countries. It shows that this model has the potential to contribute to better public health policy-making in the prevention of the COVID-19 pandemic.

Bertalanffy-Pütter models for the first wave of the COVID-19 outbreak

The COVID-19 pandemics challenges governments across the world. To develop adequate responses, they need accurate models for the spread of the disease. Using least squares, we fitted Bertalanffy-Pütter (BP) trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed. BP-models achieved excellent fits (R-squared above 99%) to all data. Using them to smoothen the data, in the median one could forecast that the final count (asymptotic limit) of infections and fatalities would be 2.48 times (95% confidence limits 2.42-2.6) and 2.67 times (2.39-2.765) the total count at the respective peak (inflection point). By comparison, using logistic growth would evaluate this ratio as 2.00 for all data. The case fatality rate, defined as the quotient of the asymptotic limits of fatalities and confirmed infections, was in the median 4.85% (confidence limits 4.4%-6.5%). Our result supports the strategies of governments that kept the epidemic peak low, as then in the median fewer infections and fewer fatalities could be expected.

Predict Mortality in Patients Infected with COVID-19 Virus Based on Observed Characteristics of the Patient using Logistic Regression

The spread of COVID-19 has made the world a mess. Up to this day, 5,235,452 cases confirmed worldwide with 338,612 death. One of the methods to predict mortality risk is machine learning algorithm using medical features, which means it takes time. Therefore, in this study, Logistic Regression is modeled by training 114 data and used to create a prediction over the patient’s mortality using nonmedical features. The model can help hospitals and doctors to prioritize who has a high probability of death and triage patients especially when the hospital is overrun by patients. The model can accurately predict with more than 90% accuracy achieved. Further analysis found that age is the most important predictor in the patient’s mortality rate. Using this model, the death rate caused by COVID-19 could be reduced.

Mid-Epidemic Forecasts of COVID-19 Cases and Deaths: A Bivariate Model Applied to the UK

BACKGROUND

The evolution of the COVID-19 epidemic has been accompanied by efforts to provide comparable international data on new cases and deaths. There is also accumulating evidence on the epidemiological parameters underlying COVID-19. Hence, there is potential for epidemic models providing mid-term forecasts of the epidemic trajectory using such information. The effectiveness of lockdown or lockdown relaxation can also be assessed by modelling later epidemic stages, possibly using a multiphase epidemic model.

METHODS

Commonly applied methods to analyse epidemic trajectories or make forecasts include phenomenological growth models (e.g., the Richards family of densities) and variants of the susceptible-infected-recovered (SIR) compartment model. Here, we focus on a practical forecasting approach, applied to interim UK COVID data, using a bivariate Reynolds model (for cases and deaths), with implementation based on Bayesian inference. We show the utility of informative priors in developing and estimating the model and compare error densities (Poisson-gamma, Poisson-lognormal, and Poisson-log-Student) for overdispersed data on new cases and deaths. We use cross validation to assess medium-term forecasts. We also consider the longer-term postlockdown epidemic profile to assess epidemic containment, using a two-phase model.

RESULTS

Fit to interim mid-epidemic data show better fit to training data and better cross-validation performance for a Poisson-log-Student model. Estimation of longer-term epidemic data after lockdown relaxation, characterised by protracted slow downturn and then upturn in cases, casts doubt on effective containment.

CONCLUSIONS

Many applications of phenomenological models have been to complete epidemics. However, evaluation of such models based simply on their fit to observed data may give only a partial picture, and cross validation against actual trends is also valuable. Similarly, it may be preferable to model incidence rather than cumulative data, although this raises questions about suitable error densities for modelling often erratic fluctuations. Hence, there may be utility in evaluating alternative error assumptions.

Regional forecasting of COVID-19 caseload by non-parametric regression: a VAR epidemiological model

OBJECTIVES

The COVID-19 pandemic (caused by SARS-CoV-2) has introduced significant challenges for accurate prediction of population morbidity and mortality by traditional variable-based methods of estimation. Challenges to modelling include inadequate viral physiology comprehension and fluctuating definitions of positivity between national-to-international data. This paper proposes that accurate forecasting of COVID-19 caseload may be best preformed non-parametrically, by vector autoregression (VAR) of verifiable data regionally.

METHODS

A non-linear VAR model across 7 major demographically representative New York City (NYC) metropolitan region counties was constructed using verifiable daily COVID-19 caseload data March 12-July 23, 2020. Through association of observed case trends with a series of (county-specific) data-driven dynamic interdependencies (lagged values), a systematically non-assumptive approximation of VAR representation for COVID-19 patterns to-date and prospective upcoming trends was produced.

RESULTS

Modified VAR regression of NYC area COVID-19 caseload trends proves highly significant modelling capacity of observed patterns in longitudinal disease incidence (county R2 range: 0.9221-0.9751, all p < 0.001). Predictively, VAR regression of daily caseload results at a county-wide level demonstrates considerable short-term forecasting fidelity (p < 0.001 at one-step ahead) with concurrent capacity for longer-term (tested 11-week period) inferences of consistent, reasonable upcoming patterns from latest (model data update) disease epidemiology.

CONCLUSIONS

In contrast to macroscopic variable-assumption projections, regionally-founded VAR modelling may substantially improve projection of short-term community disease burden, reduce potential for biostatistical error, as well as better model epidemiological effects resultant from intervention. Predictive VAR extrapolation of existing public health data at an interdependent regional scale may improve accuracy of current pandemic burden prognoses.

Rapid review of COVID-19 epidemic estimation studies for Iran

BACKGROUND

To inform researchers about the methodology and results of epidemic estimation studies performed for COVID-19 epidemic in Iran, we aimed to perform a rapid review.

METHODS

We searched for and included published articles, preprint manuscripts and reports that estimated numbers of cumulative or daily deaths or cases of COVID-19 in Iran. We found 131 studies and included 29 of them.

RESULTS

The included studies provided outputs for a total of 84 study-model/scenario combinations. Sixteen studies used 3-4 compartmental disease models. At the end of month two of the epidemic (2020-04-19), the lowest (and highest) values of predictions were 1,777 (388,951) for cumulative deaths, 20,588 (2,310,161) for cumulative cases, and at the end of month four (2020-06-20), were 3,590 (1,819,392) for cumulative deaths, and 144,305 (4,266,964) for cumulative cases. Highest estimates of cumulative deaths (and cases) for latest date available in 2020 were 418,834 on 2020-12-19 (and 41,475,792 on 2020-12-31). Model estimates predict an ominous course of epidemic progress in Iran. Increase in percent population using masks from the current situation to 95% might prevent 26,790 additional deaths (95% confidence interval 19,925-35,208) by the end of year 2020.

CONCLUSIONS

Meticulousness and degree of details reported for disease modeling and statistical methods used in the included studies varied widely. Greater heterogeneity was observed regarding the results of predicted outcomes. Consideration of minimum and preferred reporting items in epidemic estimation studies might better inform future revisions of the available models and new models to be developed. Not accounting for under-reporting drives the models' results misleading.

Short-term real-time prediction of total number of reported COVID-19 cases and deaths in South Africa: a data driven approach

BACKGROUND

The rising burden of the ongoing COVID-19 epidemic in South Africa has motivated the application of modeling strategies to predict the COVID-19 cases and deaths. Reliable and accurate short and long-term forecasts of COVID-19 cases and deaths, both at the national and provincial level, are a key aspect of the strategy to handle the COVID-19 epidemic in the country.

METHODS

In this paper we apply the previously validated approach of phenomenological models, fitting several non-linear growth curves (Richards, 3 and 4 parameter logistic, Weibull and Gompertz), to produce short term forecasts of COVID-19 cases and deaths at the national level as well as the provincial level. Using publicly available daily reported cumulative case and death data up until 22 June 2020, we report 5, 10, 15, 20, 25 and 30-day ahead forecasts of cumulative cases and deaths. All predictions are compared to the actual observed values in the forecasting period.

RESULTS

We observed that all models for cases provided accurate and similar short-term forecasts for a period of 5 days ahead at the national level, and that the three and four parameter logistic growth models provided more accurate forecasts than that obtained from the Richards model 10 days ahead. However, beyond 10 days all models underestimated the cumulative cases. Our forecasts across the models predict an additional 23,551-26,702 cases in 5 days and an additional 47,449-57,358 cases in 10 days. While the three parameter logistic growth model provided the most accurate forecasts of cumulative deaths within the 10 day period, the Gompertz model was able to better capture the changes in cumulative deaths beyond this period. Our forecasts across the models predict an additional 145-437 COVID-19 deaths in 5 days and an additional 243-947 deaths in 10 days.

CONCLUSIONS

By comparing both the predictions of deaths and cases to the observed data in the forecasting period, we found that this modeling approach provides reliable and accurate forecasts for a maximum period of 10 days ahead.

Mechanisms of recurrent outbreak of COVID-19: a model-based study

Recurrent outbreaks of the coronavirus disease 2019 (COVID-19) have occurred in many countries around the world. We developed a twofold framework in this study, which is composed by one novel descriptive model to depict the recurrent global outbreaks of COVID-19 and one dynamic model to understand the intrinsic mechanisms of recurrent outbreaks. We used publicly available data of cumulative infected cases from 1 January 2020 to 2 January 2021 in 30 provinces in China and 43 other countries around the world for model validation and further analyses. These time series data could be well fitted by the new descriptive model. Through this quantitative approach, we discovered two main mechanisms that strongly correlate with the extent of the recurrent outbreak: the sudden increase in cases imported from overseas and the relaxation of local government epidemic prevention policies. The compartmental dynamical model (Susceptible, Exposed, Infectious, Dead and Recovered (SEIDR) Model) could reproduce the obvious recurrent outbreak of the epidemics and showed that both imported infected cases and the relaxation of government policies have a causal effect on the emergence of a new wave of outbreak, along with variations in the temperature index. Meanwhile, recurrent outbreaks affect consumer confidence and have a significant influence on GDP. These results support the necessity of policies such as travel bans, testing of people upon entry, and consistency of government prevention and control policies in avoiding future waves of epidemics and protecting economy.

Modeling and forecasting the spread of COVID-19 pandemic in India and significance of lockdown: A mathematical outlook

A very special type of pneumonic disease that generated the COVID-19 was first identified in Wuhan, China in December 2019 and is spreading all over the world. The ongoing outbreak presents a challenge for data scientists to model COVID-19, when the epidemiological characteristics of the COVID-19 are yet to be fully explained. The uncertainty around the COVID-19 with no vaccine and effective medicine available till today create additional pressure on the epidemiologists and policy makers. In such a crucial situation, it is very important to predict infected cases to support prevention of the disease and aid in the preparation of healthcare service. India is fighting efficiently against COVID-19 and facing greater challenges because of its large population and high population density. Though the government of India is taking all needful steps to prevent its spread but it is not enough to control and stop spread of the disease so far, perhaps due to defiant nature of people living in India. Effective measure to control this disease, medical professionals needs to know the estimated size of this pandemic and pace. In this study, an attempt has been made to understand the spreading capability of COVID-19 in India through some simple models. Findings suggest that the lockdown strategies implemented in India are not successfully reducing the pace of the pandemic significantly after first lockdown.

Generalized Richards model for predicting COVID-19 dynamics in Saudi Arabia based on particle swarm optimization Algorithm

COVID-19 pandemic is spreading around the world becoming thus a serious concern for health, economic and social systems worldwide. In such situation, predicting as accurately as possible the future dynamics of the virus is a challenging problem for scientists and decision-makers. In this paper, four phenomenological epidemic models as well as Suspected-Infected-Recovered (SIR) model are investigated for predicting the cumulative number of infected cases in Saudi Arabia in addition to the probable end-date of the outbreak. The prediction problem is formulated as an optimization framework and solved using a Particle Swarm Optimization (PSO) algorithm. The Generalized Richards Model (GRM) has been found to be the best one in achieving two objectives: first, fitting the collected data (covering 223 days between March 2^nd and October 10, 2020) with the lowest mean absolute percentage error (MAPE = 3.2889%), the highest coefficient of determination (R² = 0.9953) and the lowest root mean squared error (RMSE = 8827); and second, predicting a probable end date found to be around the end of December 2020 with a projected number of 378,299 at the end of the outbreak. The obtained results may help the decision-makers to take suitable decisions related to the pandemic mitigation and containment and provide clear understanding of the virus dynamics in Saudi Arabia.

COVID-19 in India: Statewise Analysis and Prediction

BACKGROUND

The highly infectious coronavirus disease (COVID-19) was first detected in Wuhan, China in December 2019 and subsequently spread to 212 countries and territories around the world, infecting millions of people. In India, a large country of about 1.3 billion people, the disease was first detected on January 30, 2020, in a student returning from Wuhan. The total number of confirmed infections in India as of May 3, 2020, is more than 37,000 and is currently growing fast.

OBJECTIVE

Most of the prior research and media coverage focused on the number of infections in the entire country. However, given the size and diversity of India, it is important to look at the spread of the disease in each state separately, wherein the situations are quite different. In this paper, we aim to analyze data on the number of infected people in each Indian state (restricted to only those states with enough data for prediction) and predict the number of infections for that state in the next 30 days. We hope that such statewise predictions would help the state governments better channelize their limited health care resources.

METHODS

Since predictions from any one model can potentially be misleading, we considered three growth models, namely, the logistic, the exponential, and the susceptible-infectious-susceptible models, and finally developed a data-driven ensemble of predictions from the logistic and the exponential models using functions of the model-free maximum daily infection rate (DIR) over the last 2 weeks (a measure of recent trend) as weights. The DIR is used to measure the success of the nationwide lockdown. We jointly interpreted the results from all models along with the recent DIR values for each state and categorized the states as severe, moderate, or controlled.

RESULTS

We found that 7 states, namely, Maharashtra, Delhi, Gujarat, Madhya Pradesh, Andhra Pradesh, Uttar Pradesh, and West Bengal are in the severe category. Among the remaining states, Tamil Nadu, Rajasthan, Punjab, and Bihar are in the moderate category, whereas Kerala, Haryana, Jammu and Kashmir, Karnataka, and Telangana are in the controlled category. We also tabulated actual predicted numbers from various models for each state. All the R2 values corresponding to the logistic and the exponential models are above 0.90, indicating a reasonable goodness of fit. We also provide a web application to see the forecast based on recent data that is updated regularly.

CONCLUSIONS

States with nondecreasing DIR values need to immediately ramp up the preventive measures to combat the COVID-19 pandemic. On the other hand, the states with decreasing DIR can maintain the same status to see the DIR slowly become zero or negative for a consecutive 14 days to be able to declare the end of the pandemic.