Rational evaluation of various epidemic models based on the COVID-19 data of China

Model-informed health and socio-economic benefits of enhancing global equity and access to Covid-19 vaccines

We take a model-informed approach to the view that a global equitable access (GEA) to Covid-19 vaccines is the key to bring this pandemic to an end. We show that the equitable redistribution (proportional to population size) of the currently available vaccines is not sufficient to stop the pandemic, whereas a 60% increase in vaccine access (the global share of vaccinated people) would have allowed the current distribution to stop the pandemic in about a year of vaccination, saving millions of people in poor countries. We then investigate the interplay between access to vaccines and their distribution among rich and poor countries, showing that the access increase to stop the pandemic gets minimized at + 32% by the equitable distribution (- 36% in rich countries and + 60% in poor ones). To estimate the socio-economic benefits of a vaccination campaign with enhanced global equity and access (eGEA), we compare calibrated simulations of the current scenario with a hypothetical, vaccination-intensive scenario that assumes high rollouts (shown however by many rich and poor countries during the 2021-2022 vaccination campaign) and an improved equity from the current 2.5:1 to a 2:1 rich/poor-ratio of the population fractions vaccinated per day. Assuming that the corresponding + 130% of vaccine production is made possible by an Intellectual Property waiver, we show that the money saved on vaccines globally by the selected eGEA scenario overcomes the 5-year profit of the rights holders in the current situation. This justifies compensation mechanisms in exchange for the necessary licensing agreements. The good news is that the benefits of this eGEA scenario are still relevant, were we ready to implement it now.

Effect of sojourn time distributions on the early dynamics of COVID-19 outbreak

Compartmental models are commonly used in practice to investigate the dynamical response of infectious diseases such as the COVID-19 outbreak. Such models generally assume exponentially distributed latency and infectiousness periods. However, the exponential distribution assumption fails when the sojourn times are expected to distribute around their means. This study aims to derive a novel S (Susceptible)-E (Exposed)-P (Presymptomatic)-A (Asymptomatic)-D (Symptomatic)-C (Reported) model with arbitrarily distributed latency, presymptomatic infectiousness, asymptomatic infectiousness, and symptomatic infectiousness periods. The SEPADC model is represented by nonlinear Volterra integral equations that generalize ordinary differential equation-based models. Our primary aim is the derivation of a general relation between intrinsic growth rate r and basic reproduction number R 0 with the help of the well-known Lotka-Euler equation. The resulting r - R 0 equation includes separate roles of various stages of the infection and their sojourn time distributions. We show that R 0 estimates are considerably affected by the choice of the sojourn time distributions for relatively higher values of r. The well-known exponential distribution assumption has led to the underestimation of R 0 values for most of the countries. Exponential and delta-distributed sojourn times have been shown to yield lower and upper bounds of the R 0 values depending on the r values. In quantitative experiments, R 0 values of 152 countries around the world were estimated through our novel formulae utilizing the parameter values and sojourn time distributions of the COVID-19 pandemic. The global convergence, R 0 = 4.58 , has been estimated through our novel formulation. Additionally, we have shown that increasing the shape parameter of the Erlang distributed sojourn times increases the skewness of the epidemic curves in entire dynamics.

The COVID-19 pandemic in various restriction policy scenarios based on the dynamic social contact rate

The social contact rate has influenced the transmission of COVID-19, with more social contact resulting in more contagion cases. We chose 18 countries with the most confirmed cases in the first 200 days after the Wuhan lockdown. This was the first study using the dynamic social contact rate to simulate the epidemic under diverse restriction policies over 500 days since the COVID-19 outbreak. The developed General Dynamic Model suggested that the probability of contagion ranged from 12.52% to 39.39% in the epidemic. The geometric mean of the social contact rates differed from 18.21% to 96.00% between countries. The restriction policies in developed economies were 3.5 times more efficient than in developing economies. We compare the effectiveness of different policies for disease prevention and discuss the influence of policy adjustment frequency for each country. Maintaining the tightest restriction or alternate tightening and loosening restrictions was recommended, with each having an average 72.45% and 79.78% reduction in maximum active cases, respectively.

Bounding pandemic spread by heat spread

The beginning of a pandemic is a crucial stage for policymakers. Proper management at this stage can reduce overall health and economical damage. However, knowledge about the pandemic is insufficient. Thus, the use of complex and sophisticated models is challenging. In this study, we propose analytical and stochastic heat spread-based boundaries for the pandemic spread as indicated by the Susceptible-Infected-Recovered (SIR) model. We study the spread of a pandemic on an interaction (social) graph as a diffusion and compared it with the stochastic SIR model. The proposed boundaries are not requiring accurate biological knowledge such as the SIR model does.

A probabilistic epidemiological model for infectious diseases: The case of COVID-19 at global-level

This study has developed a probabilistic epidemiological model a few weeks after the World Health Organization declared COVID-19 a pandemic (based on the little data available at that time). The aim was to assess relative risks for future scenarios and evaluate the effectiveness of different management actions for 1 year ahead. We quantified, categorized, and ranked the risks for scenarios such as business as usual, and moderate and strong mitigation. We estimated that, in the absence of interventions, COVID-19 would have a 100% risk of explosion (i.e., more than 25% infections in the world population) and 34% (2.6 billion) of the world population would have been infected until the end of simulation. We analyzed the suitability of model scenarios by comparing actual values against estimated values for the first 6 weeks of the simulation period. The results proved to be more suitable with a business-as-usual scenario in Asia and moderate mitigation in the other continents. If everything went on like this, we would have 55% risk of explosion and 22% (1.7 billion) of the world population would have been infected. Strong mitigation actions in all continents could reduce these numbers to, 7% and 3% (223 million), respectively. Although the results were based on the data available in March 2020, both the model and probabilistic approach proved to be practicable and could be a basis for risk assessment in future pandemic episodes with unknown virus, especially in the early stages, when data and literature are scarce.

Quantifying Social Interventions for Combating COVID-19 via a Symmetry-Based Model

The COVID-19 pandemic has revealed new features in terms of substantial changes in rates of infection, cure, and death as a result of social interventions, which significantly challenges traditional SEIR-type models. In this paper we developed a symmetry-based model for quantifying social interventions for combating COVID-19. We found that three key order parameters, separating degree (S) for susceptible populations, healing degree (H) for mild cases, and rescuing degree (R) for severe cases, all display logistic dynamics, establishing a novel dynamic model named SHR. Furthermore, we discovered two evolutionary patterns of healing degree with a universal power law in 23 areas in the first wave. Remarkably, the model yielded a quantitative evaluation of the dynamic back-to-zero policy in the third wave in Beijing using 12 datasets of different sizes. In conclusion, the SHR model constitutes a rational basis by which we can understand this complex epidemic and policymakers can carry out sustainable anti-epidemic measures to minimize its impact.

Analysis of COVID-19 in India using a vaccine epidemic model incorporating vaccine effectiveness and herd immunity

COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated population taking into account the rate of vaccination and vaccine waning. The dynamics of the model has been investigated, and the condition for a disease-free endemic equilibrium state is obtained. Further, the analysis is extended to study the COVID-19 spread in India by considering the availability of vaccines and the related critical parameters such as vaccination rate, vaccine efficacy and waning of vaccine's impact on deciding the emerging fate of this epidemic. We have also discussed the conditions for herd immunity due to vaccinated individuals among the people. Our results highlight the importance of vaccines, the effectiveness of booster vaccination in protecting people from infection, and their importance in epidemic and pandemic modeling.

An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration

BACKGROUND AND OBJECTIVE

In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical model considers various mechanisms of interaction between the sub-populations in addition to population migration.

METHODS

The steady-state solutions for the disease-free and endemic scenarios are calculated, and the local stability of the equilibium solutions is determined using linear analysis, Descartes' rule of signs and the Routh-Hurwitz criterion. We demonstrate rigorously the existence and uniqueness of non-negative solutions for the mathematical model, and we prove that the system has no periodic solutions using Dulac's criterion. To solve this system, a nonstandard finite-difference method is proposed.

RESULTS

As the main results, we show that the computer method presented in this work is uniquely solvable, and that it preserves the non-negativity of initial approximations. Moreover, the steady-state solutions of the continuous model are also constant solutions of the numerical scheme, and the stability properties of those solutions are likewise preserved in the discrete scenario. Furthermore, we establish the consistency of the scheme and, using a discrete form of Gronwall's inequality, we prove theoretically the stability and the convergence properties of the scheme. For convenience, a Matlab program of our method is provided in the appendix.

CONCLUSIONS

The computer method presented in this work is a nonstandard scheme with multiple dynamical and numerical properties. Most of those properties are thoroughly confirmed using computer simulations. Its easy implementation make this numerical approach a useful tool in the investigation on the propagation of infectious diseases. From the theoretical point of view, the present work is one of the few papers in which a nonstandard scheme is fully and rigorously analyzed not only for the dynamical properties, but also for consistently, stability and convergence.

Qualitative and quantitative analysis of the COVID-19 pandemic by a two-side fractional-order compartmental model

Global efforts are focused on discussing effective measures for minimizing the impact of COVID-19 on global community. It is clear that the ongoing pandemic of this virus caused an immense threat to public health and economic development. Mathematical models with real data simulations are powerful tools that can identify key factors of pandemic and improve control or mitigation strategies. Compared with integer-order and left-hand side fractional models, two-side fractional models can better capture the state of pandemic spreading. In this paper, two-side fractional models are first proposed to qualitative and quantitative analysis of the COVID-19 pandemic. A basic framework are given for the prediction and analysis of infectious diseases by these types of models. By means of asymptotic stability analysis of disease-free and endemic equilibrium points, basic reproduction number R₀ can be obtained, which is helpful for estimating the severity of an outbreak qualitatively. Sensitivity analysis of R₀ is performed to identify and rank key epidemiological parameters. Based on the real data of the United States, numerical tests reveal that the model with both left-hand side fractional derivative and right-hand side fractional integral terms has a better forecast ability for the epidemic trend in the next ten days. Our extensive computational results also quantitatively reveal that non-pharmaceutical interventions, such as isolation, stay at home, strict control of social distancing, and rapid testing can play an important role in preventing the pandemic of the disease. Thus, the two-side fractional models are proposed in this paper can successfully capture the change rule of COVID-19, which provide a strong tool for understanding and analyzing the trend of the outbreak.

On mobility trends analysis of COVID-19 dissemination in Mexico City

This work presents a tool for forecasting the spread of the new coronavirus in Mexico City, which is based on a mathematical model with a metapopulation structure that uses Bayesian statistics and is inspired by a data-driven approach. The daily mobility of people in Mexico City is mathematically represented by an origin-destination matrix using the open mobility data from Google and the Transportation Mexican Survey. This matrix is incorporated in a compartmental model. We calibrate the model against borough-level incidence data collected between 27 February 2020 and 27 October 2020, while using Bayesian inference to estimate critical epidemiological characteristics associated with the coronavirus spread. Given that working with metapopulation models leads to rather high computational time consumption, and parameter estimation of these models may lead to high memory RAM consumption, we do a clustering analysis that is based on mobility trends to work on these clusters of borough separately instead of taken all of the boroughs together at once. This clustering analysis can be implemented in smaller or larger scales in different parts of the world. In addition, this clustering analysis is divided into the phases that the government of Mexico City has set up to restrict individual movement in the city. We also calculate the reproductive number in Mexico City using the next generation operator method and the inferred model parameters obtaining that this threshold is in the interval (1.2713, 1.3054). Our analysis of mobility trends can be helpful when making public health decisions.

Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View

In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ1,σ2 and β1,β2, and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19.

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.

Where Do We Go From Here? A Framework for Using Susceptible-Infectious-Recovered Models for Policy Making in Emerging Infectious Diseases

OBJECTIVES

Throughout the coronavirus disease 2019 pandemic, susceptible-infectious-recovered (SIR) modeling has been the preeminent modeling method to inform policy making worldwide. Nevertheless, the usefulness of such models has been subject to controversy. An evolution in the epidemiological modeling field is urgently needed, beginning with an agreed-upon set of modeling standards for policy recommendations. The objective of this article is to propose a set of modeling standards to support policy decision making.

METHODS

We identify and describe 5 broad standards: transparency, heterogeneity, calibration and validation, cost-benefit analysis, and model obsolescence and recalibration. We give methodological recommendations and provide examples in the literature that employ these standards well. We also develop and demonstrate a modeling practices checklist using existing coronavirus disease 2019 literature that can be employed by readers, authors, and reviewers to evaluate and compare policy modeling literature along our formulated standards.

RESULTS

We graded 16 articles using our checklist. On average, the articles met 6.81 of our 19 categories (36.7%). No articles contained any cost-benefit analyses and few were adequately transparent.

CONCLUSIONS

There is significant room for improvement in modeling pandemic policy. Issues often arise from a lack of transparency, poor modeling assumptions, lack of a system-wide perspective in modeling, and lack of flexibility in the academic system to rapidly iterate modeling as new information becomes available. In anticipation of future challenges, we encourage the modeling community at large to contribute toward the refinement and consensus of a shared set of standards for infectious disease policy modeling.