Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control

In this paper, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. While Markov Decision Processes (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spreading according to the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost. [ FROM AUTHOR] Copyright of IISE Transactions is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Using the SIR Model to Analyze the Epidemiological Situation in Kazakhstan and Neighboring Countries

In this paper, we study the epidemic situation in Kazakhstan and neighboring countries, taking into account territorial features in emergency situations. As you know, the excessive concentration of the population in large cities and the transition to a world without borders created ideal conditions for a global pandemic. The article also provides the results of a detailed analysis of the solution approaches to modeling the development of epidemics by types of models (basic SIR model, modified SEIR models) and the practical application of the SIR model using an example (Kazakhstan, Russia, Kyrgyzstan, Uzbekistan and other neighboring countries). The obtained processing results are based on statistical data from open sources on the development of the COVID-19 epidemic. The result obtained is a general solution of the SIR-model of the spread of the epidemic according to the fourth-order Runge-Kutta method. The parameters β, γ, which are indicators of infection, recovery, respectively, were calculated using data at the initial phase of the Covid 2019 epidemic. An analysis of anti-epidemic measures in neighboring countries is given. © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

Dynamic Properties for a Second-Order Stochastic SEIR Model with Infectivity in Incubation Period and Homestead-Isolation of the Susceptible Population

In this article, we analyze a second-order stochastic SEIR epidemic model with latent infectious and susceptible populations isolated at home. Firstly, by putting forward a novel inequality, we provide a criterion for the presence of an ergodic stationary distribution of the model. Secondly, we establish sufficient conditions for extinction. Thirdly, by solving the corresponding Fokker–Plank equation, we derive the probability density function around the quasi-endemic equilibrium of the stochastic model. Finally, by using the epidemic data of the corresponding deterministic model, two numerical tests are presented to illustrate the validity of the theoretical results. Our conclusions demonstrate that nations should persevere in their quarantine policies to curb viral transmission when the COVID-19 pandemic proceeds to spread internationally. © 2023 by the authors.

Can ship travel contain COVID-19 outbreak after re-opening: a Bayesian meta-analysis.

Large gatherings of people on cruise ships and warships are often at high risk of COVID-19 infections. To assess the transmissibility of SARS-CoV-2 on warships and cruise ships and to quantify the effectiveness of the containment measures, the transmission coefficient (ß), basic reproductive number (R0), and time to deploy containment measures were estimated by the Bayesian Susceptible-Exposed-Infected-Recovered model. A meta-analysis was conducted to predict vaccine protection with or without non-pharmaceutical interventions (NPIs). The analysis showed that implementing NPIs during voyages could reduce the transmission coefficients of SARS-CoV-2 by 50%. Two weeks into the voyage of a cruise that begins with 1 infected passenger out of a total of 3,711 passengers, we estimate there would be 45 (95% CI:25-71), 33 (95% CI:20-52), 18 (95% CI:11-26), 9 (95% CI:6-12), 4 (95% CI:3-5), and 2 (95% CI:2-2) final cases under 0%, 10%, 30%, 50%, 70%, and 90% vaccine protection, respectively, without NPIs. The timeliness of strict NPIs along with implementing strict quarantine and isolation measures is imperative to contain COVID-19 cases in cruise ships. The spread of COVID-19 on ships was predicted to be limited in scenarios corresponding to at least 70% protection from prior vaccination, across all passengers and crew.

Stability analysis of an epidemic model with vaccination and time delay

This paper presents an epidemic model with varying population, incorporating a new vaccination strategy and time delay. It investigates the impact of vaccination with respect to vaccine efficacy and the time required to see the effects, followed by determining how to control the spread of the disease according to the basic reproduction ratio of the disease. Some numerical simulations are provided to illustrate the theoretical results.

The lockdown and vaccination distribution in Thailand's COVID-19 epidemic: A model study.

Background: Several countries used varied degrees of social isolation measures in response to the COVID-19 outbreak. In 2021, the lockdown in Thailand began on July 20 and lasted for the following six weeks. The lockdown has extremely detrimental effects on the economy and society, even though it may reduce the number of COVID-19 instances. Our goals are to assess the impact of the lockdown policy, the commencement time of lockdown, and the vaccination rate on the number of COVID-19 cases in Thailand in 2021. Methods: We modeled the dynamics of COVID-19 in Thailand throughout 2021 using the SEIR model. The Google Mobility Index, vaccine distribution rate, and lockdown were added to the model. The Google Mobility Index represents the movement of individuals during a pandemic and shows how people react to lockdown. The model also examines the effect of vaccination rate on the incidence of COVID-19. Results: The modeling approach demonstrates that a 6-week lockdown decreases the incidence number of COVID-19 by approximately 15.49-18.17%, depending on the timing of the lockdown compared to a non-lockdown scenario. An increasing vaccination rate potentially reduce the incidence number of COVID-19 by 5.12-18.35% without launching a lockdown. Conclusion: Lockdowns can be an effective method to slow down the spread of COVID-19 when the vaccination program is not fully functional. When the vaccines are easily accessible on a large scale, the lockdown may terminated.

Fast track to differential equations: Applications-Oriented-Comprehensible-Compact

The second edition of this successful textbook includes a significantly extended chapter on Climate Change with an analysis of the CO2 budget. It also contains a completely new part on Epidemiology, treating the SEIR-model which describes the behavior and dynamics of epidemics. In particular, COVID-19 with actual data is discussed. This compact introduction to ordinary differential equations and their applications is aimed at anyone who in their studies is confronted voluntarily or involuntarily with this versatile subject. Numerous applications from physics, technology, biomathematics, cosmology, economy and optimization theory are given. proofs and unnecessary formalism are avoided as far as possible. The focus is on modelling ordinary differential equations of the first and second orders as well as their analytical and numerical solution methods, in which the theory is dealt with briefly before moving on to application examples. In addition, program codes show exemplarily how even more challenging questions can be tackled and represented meaningfully with the help of a computer algebra system. The first chapter deals with the necessary prior knowledge of integral and differential calculus. 103 motivating exercises together with their solutions round off the work. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021. All rights reserved.

Real human close contact-based analysis on COVID-19 combined interventions

COVID-19 has threatened human lives. However, the efficiency of combined interventions on COVID-19 has not been accurately analyzed. In this study, an improved SEIR model considering both real human indoor close contact behaviors and personal susceptibility to COVID-19 was established. Taking Hong Kong as an example, a quantitative efficiency assessment of combined interventions (i.e. close contact reduction, vaccination, mask-wearing, school closures, workplace closures, and body temperature screening in public places) was carried out. The results showed that the infection risk of COVID-19 of students, workers, and non-workers/students were 3.1%, 8.7%, and 13.6%, respectively. The basic reproduction number R0 was equal to 1 when the close contact reduction rate was 59.9% or the vaccination rate reached 89.5%. The results could provide scientific support for interventions on COVID-19 prevention and control. © 2022 17th International Conference on Indoor Air Quality and Climate, INDOOR AIR 2022. All rights reserved.

Asymptotic and transient dynamics of SEIR epidemic models on weighted networks

We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.

Modelling and Analysis of Hospital Inventory Policies during COVID-19 Pandemic

The global coronavirus pandemic (COVID-19) started in 2020 and is still ongoing today. Among the numerous insights the community has learned from the COVID-19 pandemic is the value of robust healthcare inventory management. The main cause of many casualties around the world is the lack of medical resources for those who need them. To inhibit the spread of COVID-19, it is therefore imperative to simulate the demand for desirable medical goods at the proper time. The estimation of the incidence of infections using the right epidemiological criteria has a significant impact on the number of medical supplies required. Modeling susceptibility, exposure, infection, hospitalization, isolation, and recovery in relation to the COVID-19 pandemic is indeed crucial for the management of healthcare inventories. The goal of this research is to examine the various inventory policies such as reorder point, periodic order, and just-in-time in order to minimize the inventory management cost for medical commodities. To accomplish this, a SEIHIsRS model has been employed to comprehend the dynamics of COVID-19 and determine the hospitalized percentage of infected people. Based on this information, various situations are developed, considering the lockdown, social awareness, etc., and an appropriate inventory policy is recommended to reduce inventory management costs. It is observed that the just-in-time inventory policy is found to be the most cost-effective when there is no lockdown or only a partial lockdown. When there is a complete lockdown, the periodic order policy is the best inventory policy. The periodic order and reorder policies are cost-effective strategies to apply when social awareness is high. It has also been noticed that periodic order and reorder policies are the best inventory strategies for uncertain vaccination efficacy. This effort will assist in developing the best healthcare inventory management strategies to ensure that the right healthcare requirements are available at a minimal cost. © 2023 by the authors.

Evaluating vaccine allocation strategies using simulation-assisted causal modeling.

We develop a model to retrospectively evaluate age-dependent counterfactual vaccine allocation strategies against the coronavirus disease 2019 (COVID-19) pandemic. To estimate the effect of allocation on the expected severe-case incidence, we employ a simulation-assisted causal modeling approach that combines a compartmental infection-dynamics simulation, a coarse-grained causal model, and literature estimates for immunity waning. We compare Israel's strategy, implemented in 2021, with counterfactual strategies such as no prioritization, prioritization of younger age groups, or a strict risk-ranked approach; we find that Israel's implemented strategy was indeed highly effective. We also study the impact of increasing vaccine uptake for given age groups. Because of its modular structure, our model can easily be adapted to study future pandemics. We demonstrate this by simulating a pandemic with characteristics of the Spanish flu. Our approach helps evaluate vaccination strategies under the complex interplay of core epidemic factors, including age-dependent risk profiles, immunity waning, vaccine availability, and spreading rates.

Simulation Analysis of Infectious Disease Trend Based on Improved SEIR Model

Scholars have carried out a lot of research in the field of using data processing methods to analyze the evolution characteristics and development trends of infectious diseases. The research on data model method is more in-depth, that is, according to the specific characteristics of infectious diseases, suitable data models are designed and combined with different parameters to analyze infectious diseases, mainly including infectious disease data models based on statistical theory or dynamic theory. The former is mostly used in the case of insufficient initial data. Local analysis is carried out by means of a priori or assumptions to achieve global prediction. The latter mainly includes SIR model, complex network model, and cellular automata model. SIR model is the most in-depth research. Scholars have constructed or optimized Si model, SIS model, SEIR model, IR model, and other derivative models based on SIR model in combination with the characteristics of viruses. In this paper, the data source is Wuhan epidemic information released by Health Commission of Hubei Province. Combined with the specific characteristics of COVID-19, the traditional dynamic propagation model is optimized, and an improved SEIR model is constructed. The results of the improved SEIR model are in good agreement with the actual epidemic trend in Wuhan. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Improved SEIR Model Based on Recovery Rate Optimization to Predict COVID-19

When using the traditional SEIR infectious disease model to predict the trend of novel coronavirus pneumonia epidemic, numerous initial parameters need to be tuned, and the parameters cannot change over time during the prediction process, which reduces the accuracy of the model. Firstly, thesis used a logistic model to preprocess the SEIR model parameters and proposed a SEIR model based on time series recovery rate optimization with a new parameter of effective immunity rate. Secondly, the model was trained with epidemic data from domestic and foreign provinces and cities, and the usability of the model was demonstrated experimentally, and the mean absolute percentage error (MAPE) and goodness of fit (R2) were used to compare with other models, which proved the superiority of the model prediction and indicated further research directions. © 2022 IEEE.

Prediction and Analysis of COVID-19 Epidemic Based on Improved GEP Algorithm to Optimize SEIR Mode

In 2019, COVID-19 (CoronaVirus Disease 2019) broke out all over the world. COVID-19 is an infectious disease, which has a huge impact on the global economy. It is very difficult to prevent and control the epidemic situation of this infectious disease. At present, many SEIR(Susceptible Exposed Infected Recovered)models are used to predict the number of infectious diseases, which has the shortcomings of low prediction accuracy and inaccurate inflection point prediction. Therefore, this paper proposes that the prediction and analysis of COVID-19 based on improved GEP algorithm and optimized SEIR model can improve the prediction accuracy and inflection point prediction accuracy, and provide a theoretical basis for epidemic prevention of large-scale infectious diseases in the future. The algorithm. First, establish SEIR (Susceptible Exposed Infected Recovered) model to analyze the epidemic trend, and then use improved GEP (Gene Expression Programming) algorithm to analyze the infection coefficient of SEIR model beta And coefficient of restitution y, perform parameter estimation to optimize the initial value I and recovery coefficient of the infected population y and so on to improve the accuracy of model prediction. The experimental data take the number of COVID-19 infected people in the United States, China, the United Kingdom and Italy as examples. The results show that the SEIR model optimized based on the improved GEP algorithm conforms to the inflection point of the actual data, and the average error value is 1.32%. The algorithm provides a theoretical basis for the future epidemic prevention. © 2022 IEEE.

The analysis of a time delay fractional COVID-19 model via Caputo type fractional derivative.

Novel coronavirus (COVID-19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID-19 SEIR epidemic model via Caputo fractional derivatives using a predictor-corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag-Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs.

Mathematical Modeling Evaluates How Vaccinations Affected the Course of COVID-19 Disease Progression.

The regulation policies implemented, the characteristics of vaccines, and the evolution of the virus continue to play a significant role in the progression of the SARS-CoV-2 pandemic. Numerous research articles have proposed using mathematical models to predict the outcomes of different scenarios, with the aim of improving awareness and informing policy-making. In this work, we propose an expansion to the classical SEIR epidemiological model that is designed to fit the complex epidemiological data of COVID-19. The model includes compartments for vaccinated, asymptomatic, hospitalized, and deceased individuals, splitting the population into two branches based on the severity of progression. In order to investigate the impact of the vaccination program on the spread of COVID-19 in Greece, this study takes into account the realistic vaccination program implemented in Greece, which includes various vaccination rates, different dosages, and the administration of booster shots. It also examines for the first time policy scenarios at crucial time-intervention points for Greece. In particular, we explore how alterations in the vaccination rate, immunity loss, and relaxation of measures regarding the vaccinated individuals affect the dynamics of COVID-19 spread. The modeling parameters revealed an alarming increase in the death rate during the dominance of the delta variant and before the initiation of the booster shot program in Greece. The existing probability of vaccinated people becoming infected and transmitting the virus sets them as catalytic players in COVID-19 progression. Overall, the modeling observations showcase how the criticism of different intervention measures, the vaccination program, and the virus evolution has been present throughout the various stages of the pandemic. As long as immunity declines, new variants emerge, and vaccine protection in reducing transmission remains incompetent; monitoring the complex vaccine and virus evolution is critical to respond proactively in the future.

Modelling the roles of visitor flows and returning migrants in the spatial diffusion of COVID-19 from Wuhan city in China.

COVID-19 has spread to many cities and countries in the world since the major outbreak in Wuhan city in later 2019. Population flow is the main channel of COVID-19 transmission between different cities and countries. This study recognizes that the flows of different population groups such as visitors and migrants returning to hometown are different in nature due to different length of stay and exposure to infection risks, contributing to the spatial diffusion of COVID-19 differently. To model population flows and the spatial diffusion of COVID-19 more accurately, a population group based SEIR (susceptible-exposed-infectious-recovered) metapopulation model is developed consisting of 32 regions including Wuhan, the rest of Hubei and other 30 provinces in Mainland China. The paper found that, in terms of the total export, Wuhan residents as visitors and Wuhan migrants returned to hometown were the first and second largest contributors in the simulation period. In terms of the net export, Wuhan migrants returned to hometown were the largest contributor, followed by Wuhan residents as visitors.

Age-specific transmission dynamics under suppression control measures during SARS-CoV-2 Omicron BA.2 epidemic.

BACKGROUND: From March to June 2022, an Omicron BA.2 epidemic occurred in Shanghai. We aimed to better understand the transmission dynamics and identify age-specific transmission characteristics for the epidemic. METHODS: Data on COVID-19 cases were collected from the Shanghai Municipal Health Commission during the period from 20th February to 1st June. The effective reproductive number (Rt) and transmission distance between cases were calculated. An age-structured SEIR model with social contact patterns was developed to reconstruct the transmission dynamics and evaluate age-specific transmission characteristics. Least square method was used to calibrate the model. Basic reproduction number (R0) was estimated with next generation matrix. RESULTS: R0 of Omicron variant was 7.9 (95% CI: 7.4 to 8.4). With strict interventions, Rt had dropped quickly from 3.6 (95% CI: 2.7 to 4.7) on 4th March to below 1 on 18th April. The mean transmission distance of the Omicron epidemic in Shanghai was 13.4 km (95% CI: 11.1 to 15.8 km), which was threefold longer compared with that of epidemic caused by the wild-type virus in Wuhan, China. The model estimated that there would have been a total 870,845 (95% CI: 815,400 to 926,289) cases for the epidemic from 20th February to 15th June, and 27.7% (95% CI: 24.4% to 30.9%) cases would have been unascertained. People aged 50-59 years had the highest transmission risk 0.216 (95% CI: 0.210 to 0.222), and the highest secondary attack rate (47.62%, 95% CI: 38.71% to 56.53%). CONCLUSIONS: The Omicron variant spread more quickly and widely than other variants and resulted in about one third cases unascertained for the recent outbreak in Shanghai. Prioritizing isolation and screening of people aged 40-59 might suppress the epidemic more effectively. Routine surveillance among people aged 40-59 years could also provide insight into the stage of the epidemic and the timely detection of new variants. TRIAL REGISTRATION: We did not involve clinical trial.

Analysis of the COVID-19 pandemic using a compartmental model with time-varying parameters fitted by a genetic algorithm.

Analyzing the COVID-19 pandemic is a critical factor in developing effective policies to deal with similar challenges in the future. However, many parameters (e.g., the actual number of infected people, the effectiveness of vaccination) are still subject to considerable debate because they are unobservable. To model a pandemic and estimate unobserved parameters, researchers use compartmental models. Most often, in such models, the transition rates are considered as constants, which allows simulating only one epidemiological wave. However, multiple waves have been reported for COVID-19 caused by different strains of the virus. This paper presents an approach based on the reconstruction of real distributions of transition rates using genetic algorithms, which makes it possible to create a model that describes several pandemic peaks. The model is fitted on registered COVID-19 cases in four countries with different pandemic control strategies (Germany, Sweden, UK, and US). Mean absolute percentage error (MAPE) was chosen as the objective function, the MAPE values of 2.168%, 2.096%, 1.208% and 1.703% were achieved for the listed countries, respectively. Simulation results are consistent with the empirical statistics of medical studies, which confirms the quality of the model. In addition to observables such as registered infected, the output of the model contains variables that cannot be measured directly. Among them are the proportion of the population protected by vaccines, the size of the exposed compartment, and the number of unregistered cases of COVID-19. According to the results, at the peak of the pandemic, between 14% (Sweden) and 25% (the UK) of the population were infected. At the same time, the number of unregistered cases exceeds the number of registered cases by 17 and 3.4 times, respectively. The average duration of the vaccine induced immune period is shorter than claimed by vaccine manufacturers, and the effectiveness of vaccination has declined sharply since the appearance of the Delta and Omicron strains. However, on average, vaccination reduces the risk of infection by about 65-70%.

ANALYSIS AND PREDICTION OF COVID-19 USING SIR AND SEIR MODELS IN ALBANIA

The SARS-CoV-2 (COVID-19), has drastically changed our human lifestyle, affecting it badly. This virus has spread quickly to 223 countries and territories worldwide, leading to more than 279 million confirmed cases and about 5.4 million victims as of December 2021. Having a tool for analyzing and predicting the future of this disease it is very important for governments, medical systems, and economic sectors. Thus, the modeling of the spread and the prediction of the total number of cases has been analyzed extensively in many countries by several researchers. Some papers are published on mathematical modeling on the spread of COVID-19 in Albania. The aim of this paper is to study the spreading of COVID-19 in Albania. This research was based on official data available since October 31, 2021. We use the susceptible-infected-removed model (SIR) model and the susceptible-expected-infected-removed (SEIR) model to analyze and predict COVID-19 spread in Albania. Both models are mathematical models used in epidemic outbreaks. The analysis includes confirmed and recovered cases, deaths and the growth rate in Albania. The authors have attempted to analyze and predict the disease along with its related issues to determine the maximum number of infected people, the speed of spread, and most importantly, its evaluation using a model-based parameter estimation method. Calculations are done using adaptive SIR and SEIR models featuring dynamical recuperation and propagation rates. The official data of COVID-19 spread in Albania, reported by the Ministry of public health, has been used to verify the current model results. Initially was shown that the two models, the SIR and SEIR models, had a good fit with the daily reported data. Overall, the SEIR model was able to predict disease trends better, but both models fail to fully capture the impact of other factors, such as social distance and vaccination. The two most important parameters of the SIR model, β varies between 0.024 and 0.283 and γ varies between 0.007 and 0.247. The basic reproduction number (R0) and reproduction number (R) fluctuates in interval [1.26, 3.826] and [0.536, 3.064], respectively. The reproduction rate fluctuates between 0.61 and 1.87 and has a very small coefficient R2 (in linear regression). SEIR model produced the average basic reproduction number R0 = 1.183, the average rate of infection β = 0.121 and the average rate of recovery γ = 0.105. Both models fit well with the data, but their predictions are not so well, which means that other factors must be taken into account for more accurate predictions. © 2023, Consulting and Training Center - KEY. All rights reserved.