Progress and Perspective of Transmission Dynamics Models in Prevention and Control of Infectious Diseases

The current respiratory infectious disease has expanded over the world, posing a serious threat to people's physical and mental health, as well as their lives. Science and technology immediately united to fight against such deadly infectious disease in the past 100 years. Mathematical models have proved invaluable to understand and help control infectious disease epidemics. By simplifying real world phenomena, these models describe, analyze, and predict disease transmission patterns, producing tractable solutions in the face of quickly changing situations. In this Chapter, we firstly summarized the history and development of the mathematical models in infectious diseases. Afterwards, the specific transmission dynamics models with different model structures used in fitting and forecasting the situation of the current respiratory infectious disease were introduced, aiming different analytical objectives including but not limited to parameter estimation, trend prediction and early warning, prevention and control measures effectiveness evaluation, and transmission uncertainty exploration. Summary in values of transmission dynamics models is followed to illustrate their contribution in understanding and combating infectious disease outbreaks. Despite their utility, however, mathematical models are facing several important challenges which, if ignored, would result in biased estimation of the crucial epidemiological parameters, bad fitting of the data, or misinterpretation of the results. In conclusion, mathematical modeling should be one of the most valuable tools to reflect such huge uncertainties or, on the other hand, warn of the worst situation. An appreciation of models' shortcomings not only clarifies why they cannot do but helps anticipate what they can. © People's Medical Publishing House, PR of China 2022.

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.)

RANDOMIZED FRACTIONAL SEIR-VQHP MODEL WITH APPLICATIONS IN COVID-19 DATA PREDICTION

This paper is to investigate the extent and speed of the spread of the coronavirus disease 2019 (COVID-19) pandemic in the United States (US). For this purpose, the fractional form of the susceptible-exposed-infected-recovered-vaccinated-quarantined-hospitalized-social distancing (SEIR-VQHP) model is initially developed, considering the effects of social distancing, quarantine, hospitalization, and vaccination. Then, a Monte Carlo-based back analysis method is proposed by defining the model parameters, viz. the effects of social distancing rate (α), infection rate (β), vaccination rate (ρ), average latency period (γ), infection-to-quarantine rate (δ), time-dependent recovery rate (λ), time-dependent mortality rate (κ), hospitalization rate (ξ), hospitalization-to-recovery rate (ψ), hospitalization-to-mortality rate (ϕ), and the fractional degree of differential equations as random variables, to obtain the optimal parameters and provide the best combination of fractional order so as to give the best possible fit to the data selected between January 20, 2020 and February 10, 2021. The results demonstrate that the number of infected, recovered, and dead cases by the end of 2021 will reach 1.0, 49.8, and 0.7 million, respectively. Moreover, the histograms of the fractional order acquired from back analysis are provided that can be utilized in similar fractional analyses as an informed initial suggestion. Furthermore, a sensitivity analysis is provided to investigate the effect of vaccination and social distancing on the number of infected cases. The results show that if the social distancing increases by 25% and the vaccination rate doubles, the number of infected cases will drop to 0.13 million by early 2022, indicating relative pandemic control in the US. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company 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).

Long-term prediction of the COVID-19 epidemics induced by Omicron-virus in China based on a novel non-autonomous delayed SIR model

Since the outbreak of COVID-19, the severe acute respiratory syndrome coronavirus 2 genome is still mutating. Omicron, a recently emerging virus with a shorter incubation period, faster transmission speed, and stronger immune escape ability, is soaring worldwide and becoming the mainstream virus in the COVID-19 pandemic. It is especially critical for the governments, healthcare systems, and economic sectors to have an accurate estimate of the trend of this disaster. By using different mathematical approaches, including the classical susceptible-infected-recovered (SIR) model and its extensions, many investigators have tried to predict the outbreaks of COVID-19. In this study, we employed a novel model which is based upon the well-known susceptible-infected-removed (SIR) model with the time-delay and time-varying coefficients in our previous works. We aim to predict the evolution of the epidemics effectively in nine cities and provinces of China, including A City, B City, C City, D City, E City, F City, G City, H City and I Province. The results show it is effective to model the spread of the large-scale and sporadic COVID-19 induced by Omicron virus by the novel non-autonomous delayed SIR compartment model. The significance of this study is that it can provide the management department of epidemic control with theoretical references and subsequent evaluation of the prevention, control measures, and effects.

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.

Quantifying the spatial spillover effects of non-pharmaceutical interventions on pandemic risk.

BACKGROUND: Non-pharmaceutical interventions (NPIs) implemented in one place can affect neighboring regions by influencing people's behavior. However, existing epidemic models for NPIs evaluation rarely consider such spatial spillover effects, which may lead to a biased assessment of policy effects. METHODS: Using the US state-level mobility and policy data from January 6 to August 2, 2020, we develop a quantitative framework that includes both a panel spatial econometric model and an S-SEIR (Spillover-Susceptible-Exposed-Infected-Recovered) model to quantify the spatial spillover effects of NPIs on human mobility and COVID-19 transmission. RESULTS: The spatial spillover effects of NPIs explain [Formula: see text] [[Formula: see text] credible interval: 52.8-[Formula: see text]] of national cumulative confirmed cases, suggesting that the presence of the spillover effect significantly enhances the NPI influence. Simulations based on the S-SEIR model further show that increasing interventions in only a few states with larger intrastate human mobility intensity significantly reduce the cases nationwide. These region-based interventions also can carry over to interstate lockdowns. CONCLUSIONS: Our study provides a framework for evaluating and comparing the effectiveness of different intervention strategies conditional on NPI spillovers, and calls for collaboration from different regions.

Multivariate time series short term forecasting using cumulative data of coronavirus.

Coronavirus emerged as a highly contagious, pathogenic virus that severely affects the respiratory system of humans. The epidemic-related data is collected regularly, which machine learning algorithms can employ to comprehend and estimate valuable information. The analysis of the gathered data through time series approaches may assist in developing more accurate forecasting models and strategies to combat the disease. This paper focuses on short-term forecasting of cumulative reported incidences and mortality. Forecasting is conducted utilizing state-of-the-art mathematical and deep learning models for multivariate time series forecasting, including extended susceptible-exposed-infected-recovered (SEIR), long-short-term memory (LSTM), and vector autoregression (VAR). The SEIR model has been extended by integrating additional information such as hospitalization, mortality, vaccination, and quarantine incidences. Extensive experiments have been conducted to compare deep learning and mathematical models that enable us to estimate fatalities and incidences more precisely based on mortality in the eight most affected nations during the time of this research. The metrics like mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) are employed to gauge the model's effectiveness. The deep learning model LSTM outperformed all others in terms of forecasting accuracy. Additionally, the study explores the impact of vaccination on reported epidemics and deaths worldwide. Furthermore, the detrimental effects of ambient temperature and relative humidity on pathogenic virus dissemination have been analyzed.

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.

Advanced Nonlinear Robust Approach for Controlling COVID-19 System Based on Vaccination Campaign

This study proposes a new approach for controlling COVID-19 through vaccination, where an adequately descriptive mathematical model is created for COVID-19 using the susceptible exposed infectious recovered (SEIR) model of epidemic diseases. The presented control approach is synthesized using a combination of feedback linearization and H∞ control, and incorporates model reference control to achieve optimal time responses with the aid of the black hole optimization (BHO) algorithm. The effectiveness of the designed control law is evaluated using data from the lombardy region of Italy. The results of the simulation show that the proposed control approach is able to effectively control the COVID-19 outbreak by accurately implementing the desirable vaccination, while effectively addressing nonlinearity and uncertainty in the COVID-19 system with a desirable control action. The control method has achieved the required immunity of 6.6 million individuals after approximately 25 days with a transmission rate reduced to zero in a short time, and a vaccination rate of 170 thousand people per day © 2023, International Journal of Intelligent Engineering and Systems.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.

A model for the SARS-CoV-2 dynamics in a population lacking herd immunity

We introduced the S-HI model, a generalized SEIR model to describe the dynamics of the SARS-CoV-2 virus in a community without herd immunity and performed simulations for six months. The S- HI model consists of eight equations corresponding to susceptible individuals, exposed, asymptomatic infected, asymptomatic recovered, symptomatic infected, quarantined, symptomatic recovered and dead. We study the dynamics of the infected, asymptomatic. Dead classes in 4 different networks: households, workplaces, agglomeration places and the general community, showing that the dynamics of the three compartments have the exact nature in each layer and that the speed of the disease considerably increases in the networks with the highest weight of contacts. The reproduction number, R0, is greater than 1 in all networks conforming to the theory. The variants of the SARS-Cov-2 virus are not taken into account, so the S-HI model would fit a situation similar to the first wave of contagion after the mandatory lockdown. Copyright: © 2022 by the authors.

Erlang-Distributed SEIR Epidemic Models with Cross-Diffusion

We explore the effects of cross-diffusion dynamics in epidemiological models. Using reaction–diffusion models of infectious disease, we explicitly consider situations where an individual in a category will move according to the concentration of individuals in other categories. Namely, we model susceptible individuals moving away from infected and infectious individuals. Here, we show that including these cross-diffusion dynamics results in a delay in the onset of an epidemic and an increase in the total number of infectious individuals. This representation provides more realistic spatiotemporal dynamics of the disease classes in an Erlang SEIR model and allows us to study how spatial mobility, due to social behavior, can affect the spread of an epidemic. We found that tailored control measures, such as targeted testing, contact tracing, and isolation of infected individuals, can be more effective in mitigating the spread of infectious diseases while minimizing the negative impact on society and the economy.

Segregated mobility patterns amplify neighborhood disparities in the spread of COVID-19

The global and uneven spread of COVID-19, mirrored at the local scale, reveals stark differences along racial and ethnic lines. We respond to the pressing need to understand these divergent outcomes via neighborhood level analysis of mobility and case count information. Using data from Chicago over 2020, we leverage a metapopulation Susceptible-Exposed-Infectious-Removed model to reconstruct and simulate the spread of SARS-CoV-2 at the ZIP Code level. We demonstrate that exposures are mostly contained within one's own ZIP Code and demographic group. Building on this observation, we illustrate that we can understand epidemic progression using a composite metric combining the volume of mobility and the risk that each trip represents, while separately these factors fail to explain the observed heterogeneity in neighborhood level outcomes. Having established this result, we next uncover how group level differences in these factors give rise to disparities in case rates along racial and ethnic lines. Following this, we ask what-if questions to quantify how segregation impacts COVID-19 case rates via altering mobility patterns. We find that segregation in the mobility network has contributed to inequality in case rates across demographic groups.

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.