Modeling, state estimation, and optimal control for the US COVID-19 outbreak

Optimal social distancing in epidemic control: cost prioritization, adherence and insights into preparedness principles

The COVID-19 pandemic experience has highlighted the importance of developing general control principles to inform future pandemic preparedness based on the tension between the different control options, ranging from elimination to mitigation, and related costs. Similarly, during the COVID-19 pandemic, social distancing has been confirmed to be the critical response tool until vaccines become available. Open-loop optimal control of a transmission model for COVID-19 in one of its most aggressive outbreaks is used to identify the best social distancing policies aimed at balancing the direct epidemiological costs of a threatening epidemic with its indirect (i.e., societal level) costs arising from enduring control measures. In particular, we analyse how optimal social distancing varies according to three key policy factors, namely, the degree of prioritization of indirect costs, the adherence to control measures, and the timeliness of intervention. As the prioritization of indirect costs increases, (i) the corresponding optimal distancing policy suddenly switches from elimination to suppression and, finally, to mitigation; (ii) the "effective" mitigation region-where hospitals' overwhelming is prevented-is dramatically narrow and shows multiple control waves; and (iii) a delicate balance emerges, whereby low adherence and lack of timeliness inevitably force ineffective mitigation as the only accessible policy option. The present results show the importance of open-loop optimal control, which is traditionally absent in public health preparedness, for studying the suppression-mitigation trade-off and supplying robust preparedness guidelines.

Coevolutionary stability of host-symbiont systems with mixed-mode transmission

The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduced a conceptual model to study the stable coexistence and coevolution of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. Using an age-structured Leslie model for the host, we demonstrated how the obligate symbiont could modify the host's life history traits (survival and fecundity) and the long-term growth rate of the infected lineage. When the symbiont is vertically transmitted, we found that the host and its symbiont could maximize the infected lineage's evolutionary success (multi-level selection). Our model showed that symbionts' effect on host longevity and reproduction might differ, even be opposing, and their net effect might often be counterintuitive. The evolutionary stability of the ecologically stable coexistence was analyzed in the framework of coevolutionary dynamics. Moreover, we found conditions for the ecological and evolutionary stability of the resident host-symbiont pair, which does not allow invasion by rare mutants (each mutant dies out by ecological selection). We concluded that, within the context of our simplified model conditions, a host-symbiont system with mixed-mode transmission is evolutionarily stable unconditionally only if the host can maximize the Malthusian parameters of the infected and non-infected lineages using the same strategy. Finally, we performed a game-theoretical analysis of our selection situation and compared two stability definitions.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.

An updated estimation approach for SEIR models with stochastic perturbations: Application to COVID-19 data in Bogotá

This paper studies the updated estimation method for estimating the transmission rate changes over time. The models for the population dynamics under SEIR epidemic models with stochastic perturbations are analysed the dynamics of the COVID-19 pandemic in Bogotá, Colombia. We performed computational experiments to interpret COVID-19 dynamics using actual data for the proposed models. We estimate the model parameters and updated their estimates for reported infected and recovered data.

Inverse problem for parameters identification in a modified SIRD epidemic model using ensemble neural networks

In this paper, we propose a parameter identification methodology of the SIRD model, an extension of the classical SIR model, that considers the deceased as a separate category. In addition, our model includes one parameter which is the ratio between the real total number of infected and the number of infected that were documented in the official statistics. Due to many factors, like governmental decisions, several variants circulating, opening and closing of schools, the typical assumption that the parameters of the model stay constant for long periods of time is not realistic. Thus our objective is to create a method which works for short periods of time. In this scope, we approach the estimation relying on the previous 7 days of data and then use the identified parameters to make predictions. To perform the estimation of the parameters we propose the average of an ensemble of neural networks. Each neural network is constructed based on a database built by solving the SIRD for 7 days, with random parameters. In this way, the networks learn the parameters from the solution of the SIRD model. Lastly we use the ensemble to get estimates of the parameters from the real data of Covid19 in Romania and then we illustrate the predictions for different periods of time, from 10 up to 45 days, for the number of deaths. The main goal was to apply this approach on the analysis of COVID-19 evolution in Romania, but this was also exemplified on other countries like Hungary, Czech Republic and Poland with similar results. The results are backed by a theorem which guarantees that we can recover the parameters of the model from the reported data. We believe this methodology can be used as a general tool for dealing with short term predictions of infectious diseases or in other compartmental models.

Stability analysis and optimal control of a fractional-order generalized SEIR model for the COVID-19 pandemic

In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R 0 , the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann-Liouville (R-L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed.

Optimal strategies for coordinating infection control and socio-economic activities

It becomes challenging to identify feasible control strategies for simultaneously relaxing the countermeasures and containing the Covid-19 pandemic, given China's huge population size, high susceptibility, persist vaccination waning, and relatively weak strength of health systems. We propose a novel mathematical model with waning of immunity and solve the optimal control problem, in order to provide an insight on how much detecting and social distancing are required to coordinate socio-economic activities and epidemic control. We obtain the optimal intensity of countermeasures, i.e., the dynamic nucleic acid screening and social distancing, under which the health system is functioning normally and people can engage in a certain level of socio-economic activities. We find that it is the isolation capacity or the restriction of the case fatality rate (CFR) rather than the hospital capacity that mainly determines the optimal strategies. And the solved optimal controls under quarterly CFR restrictions exhibit oscillations. It is worth noticing that, if without considering booster or very low booster rate, the optimal strategy is a "on-off" mode, alternating between lock down and opening with certain social distancing, which reflects the importance and necessity of China's static management on a certain area during Covid-19 outbreak. The findings suggest some feasible paths to smoothly transit from the Covid-19 pandemic to an endemic phase.

Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States

The rapid spread of the numerous outbreaks of the coronavirus disease 2019 (COVID-19) pandemic has fueled interest in mathematical models designed to understand and predict infectious disease spread, with the ultimate goal of contributing to the decision making of public health authorities. Here, we propose a computational pipeline that dynamically parameterizes a modified SEIRD (susceptible-exposed-infected-recovered-deceased) model using standard daily series of COVID-19 cases and deaths, along with isolated estimates of population-level seroprevalence. We test our pipeline in five heavily impacted states of the US (New York, California, Florida, Illinois, and Texas) between March and August 2020, considering two scenarios with different calibration time horizons to assess the update in model performance as new epidemiologic data become available. Our results show a median normalized root mean squared error (NRMSE) of 2.38% and 4.28% in calibrating cumulative cases and deaths in the first scenario, and 2.41% and 2.30% when new data are assimilated in the second scenario, respectively. Then, 2-week (4-week) forecasts of the calibrated model resulted in median NRMSE of cumulative cases and deaths of 5.85% and 4.68% (8.60% and 17.94%) in the first scenario, and 1.86% and 1.93% (2.21% and 1.45%) in the second. Additionally, we show that our method provides significantly more accurate predictions of cases and deaths than a constant parameterization in the second scenario (p < 0.05). Thus, we posit that our methodology is a promising approach to analyze the dynamics of infectious disease outbreaks, and that our forecasts could contribute to designing effective pandemic-arresting public health policies.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00366-023-01816-9.

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.

Effectiveness of feedback control and the trade-off between death by COVID-19 and costs of countermeasures

We provided a framework of a mathematical epidemic modeling and a countermeasure against the novel coronavirus disease (COVID-19) under no vaccines and specific medicines. The fact that even asymptomatic cases are infectious plays an important role for disease transmission and control. Some patients recover without developing the disease; therefore, the actual number of infected persons is expected to be greater than the number of confirmed cases of infection. Our study distinguished between cases of confirmed infection and infected persons in public places to investigate the effect of isolation. An epidemic model was established by utilizing a modified extended Susceptible-Exposed-Infectious-Recovered model incorporating three types of infectious and isolated compartments, abbreviated as SEIIIHHHR. Assuming that the intensity of behavioral restrictions can be controlled and be divided into multiple levels, we proposed the feedback controller approach to implement behavioral restrictions based on the active number of hospitalized persons. Numerical simulations were conducted using different detection rates and symptomatic ratios of infected persons. We investigated the appropriate timing for changing the degree of behavioral restrictions and confirmed that early initiating behavioral restrictions is a reasonable measure to reduce the burden on the health care system. We also examined the trade-off between reducing the cumulative number of deaths by the COVID-19 and saving the cost to prevent the spread of the virus. We concluded that a bang-bang control of the behavioral restriction can reduce the socio-economic cost, while a control of the restrictions with multiple levels can reduce the cumulative number of deaths by infection.

Incorporating variant frequencies data into short-term forecasting for COVID-19 cases and deaths in the USA: a deep learning approach

BACKGROUND

Since the US reported its first COVID-19 case on January 21, 2020, the science community has been applying various techniques to forecast incident cases and deaths. To date, providing an accurate and robust forecast at a high spatial resolution has proved challenging, even in the short term.

METHOD

Here we present a novel multi-stage deep learning model to forecast the number of COVID-19 cases and deaths for each US state at a weekly level for a forecast horizon of 1-4 weeks. The model is heavily data driven, and relies on epidemiological, mobility, survey, climate, demographic, and SARS-CoV-2 variant frequencies data. We implement a rigorous and robust evaluation of our model-specifically we report on weekly performance over a one-year period based on multiple error metrics, and explicitly assess how our model performance varies over space, chronological time, and different outbreak phases.

FINDINGS

The proposed model is shown to consistently outperform the CDC ensemble model for all evaluation metrics in multiple spatiotemporal settings, especially for the longer-term (3 and 4 weeks ahead) forecast horizon. Our case study also highlights the potential value of variant frequencies data for use in short-term forecasting to identify forthcoming surges driven by new variants.

INTERPRETATION

Based on our findings, the proposed forecasting framework improves upon the available state-of-the-art forecasting tools currently used to support public health decision making with respect to COVID-19 risk.

FUNDING

This work was funded the NSF Rapid Response Research (RAPID) grant Award ID 2108526 and the CDC Contract #75D30120C09570.

A stochastic inventory model of COVID-19 and robust, real-time identification of carriers at large and infection rate via asymptotic laws

A critical operations management problem in the ongoing COVID-19 pandemic is cognizance of (a) the number of all carriers at large (CaL) conveying the SARS-CoV-2, including asymptomatic ones and (b) the infection rate (IR). Both are random and unobservable, affecting the spread of the disease, patient arrivals to health care units (HCUs) and the number of deaths. A novel, inventory perspective of COVID-19 is proposed, with random inflow, random losses and retrials (recurrent cases) and delayed/distributed exit, with randomly varying fractions of the exit distribution. A minimal construal, it enables representation of COVID-19 evolution with close fit of national incidence profiles, including single and multiple pattern outbreaks, oscillatory, periodic or non-periodic evolution, followed by retraction, leveling off, or strong resurgence. Furthermore, based on asymptotic laws, the minimum number of variables that must be monitored for identifying CaL and IR is determined and a real-time identification method is presented. The method is data-driven, utilizing the entry rate to HCUs and scaled, or dimensionless variables, including the mean residence time of symptomatic carriers in CaL and the mean residence time in CaL of patients entering HCUs. As manifested by several robust case studies of national COVID-19 incidence profiles, it provides efficient identification in real-time under unbiased monitoring error, without relying on any model. The propagation factor, a stochastic process, is reconstructed from the identified trajectories of CaL and IR, enabling evaluation of control measures. The results are useful towards the design of policies restricting COVID-19 and encumbrance to HCUs and mitigating economic contraction.

A Mathematical Evaluation of the Cost-Effectiveness of Self-Protection, Vaccination, and Disinfectant Spraying for COVID-19 Control

The world is on its path from the post-COVID period, but a fresh wave of the coronavirus infection engulfing most European countries makes the pandemic catastrophic. Mathematical models are of significant importance in unveiling strategies that could stem the spread of the disease. In this paper, a deterministic mathematical model of COVID-19 is studied to characterize a range of feasible control strategies to mitigate the disease. We carried out an analytical investigation of the model’s dynamic behaviour at its equilibria and observed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number, ${\mathcal{R}}_0$ is less than unity. The endemic equilibrium is also shown to be globally asymptotically stable when ${\mathcal{R}}_0>1$ . Further, we showed that the model exhibits forward bifurcation around ${\mathcal{R}}_0=1$ . Sensitivity analysis was carried out to determine the impact of various factors on the basic reproduction number ${\mathcal{R}}_0$ and consequently, the spread of the disease. An optimal control problem was formulated from the sensitivity analysis. Cost-effectiveness analysis is conducted to determine the most cost-effective strategy that can be adopted to control the spread of COVID-19. The investigation revealed that combining self-protection and environmental control is the most cost-effective control strategy among the enlisted strategies.

Nonlinear dynamic epidemiological analysis of effects of vaccination and dynamic transmission on COVID-19

This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic. We are especially interested in two current topics: effect of vaccination and the universally observed oscillations in infections. We use a nonlinear Susceptible, Infected, & Immune model incorporating a dynamic transmission rate and vaccination policy. The US data provides a starting point for analyzing stability, bifurcations and dynamics in general. Further parametric analysis reveals a saddle-node bifurcation under imperfect vaccination leading to the occurrence of sustained epidemic equilibria. This work points to the tremendous value of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of vaccination, and frequency, phase, and amplitude of transmission rate on the persistent dynamic behavior of the disease.

Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic

We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes.

Optimal control for a SIR epidemic model with limited quarantine

Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs, and they can be maintained only for a short period of time. Here we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model with a limitation on the total duration of the quarantine. The control is done by means of the reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma (t)$$\end{document}σ(t), i.e., the number of secondary infections produced by a primary infection, which can be arbitrarily varied in time over a quarantine period T to account for external interventions. We also assume that the most strict quarantine (lower bound of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}σ) cannot last for a period longer than a value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ. The aim is to minimize the cumulative number of ever-infected individuals (recovered) and the socioeconomic cost of interventions in the long term, by finding the optimal way to vary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma (t)$$\end{document}σ(t). We show that the optimal solution is a single bang-bang, i.e., the strict quarantine is turned on only once, and is turned off after the maximum allowed time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.

Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain

Omicron, a mutant strain of COVID-19, has been sweeping the world since November 2021. A major characteristic of Omicron transmission is that it is less harmful to healthy adults, but more dangerous for people with underlying disease, the elderly, or children. To simulate the spread of Omicron in the population, we developed a new 9-dimensional mathematical model with high-risk and low-risk exposures. Then we analyzed its dynamic properties and obtain the basic reproduction number R 0 . With the data of confirmed cases from March 1, 2022 published on the official website of Shanghai, China, we used the weighted nonlinear least square estimation method to estimate the parameters, and get the basic reproduction number R 0 ≈ 1 . 5118 . Finally, we considered three control measures (isolation, detection and treatment), and studied the optimal control strategy and cost-effectiveness analysis of the model. The control strategy G is determined to be the optimal control strategy from the purpose of making fewer people infected. In strategy G, the three human control measures contain six control variables, and the control strength of these variables needs to be varied according to the pattern shown in Figure 11, so that the number of infections can be minimized and the percentage of reduction of infections can reach more than 95%.

Modeling COVID-19 Transmission Dynamics: A Bibliometric Review

A good amount of research has evolved just in three years in COVID-19 transmission, mortality, vaccination, and some socioeconomic studies. A few bibliometric reviews have already been performed in the literature, especially on the broad theme of COVID-19, without any particular area such as transmission, mortality, or vaccination. This paper fills this gap by conducting a bibliometric review on COVID-19 transmission as the first of its kind. The main aim of this study is to conduct a bibliometric review of the literature in the area of COVID-19 transmission dynamics. We have conducted bibliometric analysis using descriptive and network analysis methods to review the literature in this area using RStudio, Openrefine, VOSviewer, and Tableau. We reviewed 1103 articles published in 2020-2022. The result identified the top authors, top disciplines, research patterns, and hotspots and gave us clear directions for classifying research topics in this area. New research areas are rapidly emerging in this area, which needs constant observation by researchers to combat this global epidemic.

Efficient Mobile Ad Hoc Route Maintenance Against Social Distances Using Attacker Detection Automation

In MANET, routing plays a vital role in packet interaction and data transmission. It is always easy to manage the data transmission over the MANET because of uncentralized control on the MANET nodes. Since the efficient route on MANET controls the packets and does not simplify the route between the source and destination. Hence the maintenance of route interaction becomes a crucial process. Methods: It is critical to enhance the route and decrease the attacker to sustain successful data transfers via the MANET Network. MANET, on the other hand, permits route interaction with security threads. The four processing schema are proposed in this study work to retain the security safeguards against Routing Protocols. The Rushing Attacker has significantly influenced MANET packet-based data transfer, particularly node communication. The Attacker Detection Automation of Bee Colony Optimization (ADABCP) Method is proposed in this article. Results: Existing ESCT, ZRDM-LFPM, and ENM-LAC techniques were compared to the suggested outcome. Consequently, routing and data transfer have enhanced the proposed illustration (SIRT-ADABCP-HRLD). Compared to the recommended approach, the end-to-end latency, communication overhead, packet delivery ratio, network lifetime, and energy usage are all improved. Discussion: The performance evaluation results of SIRT–ADABCP-HRLD with existing methods in terms of low End to End Delay (ms) of 49.8361% compared to existing methods ESCT, ENM-LAC, and ZRDM-LFPM. In terms of low Communication Overhead, an 81.4462% decrease compared to existing methods. However, it improves packet delivery by 56.9775%, more than ESCT, ENM-LAC, and ZRDM-LFPM. The energy consumption decreased by 36.31% less value than the existing process.

Feedback control of social distancing for COVID-19 via elementary formulae

Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields elementary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the number of uninfected people may be taken into account. Those formulae might therefore be useful to decision makers. A feedback loop stemming from model-free control leads to a remarkable robustness with respect to severe uncertainties and mismatches. Although an identification procedure is presented, a good knowledge of the recovery rate is not necessary for our control strategy.

Recursive state and parameter estimation of COVID-19 circulating variants dynamics

COVID-19 pandemic response with non-pharmaceutical interventions is an intrinsic control problem. Governments weigh social distancing policies to avoid overload in the health system without significant economic impact. The mutability of the SARS-CoV-2 virus, vaccination coverage, and mobility restriction measures change epidemic dynamics over time. A model-based control strategy requires reliable predictions to be efficient on a long-term basis. In this paper, a SEIR-based model is proposed considering dynamic feedback estimation. State and parameter estimations are performed on state estimators using augmented states. Three methods were implemented: constrained extended Kalman filter (CEKF), CEKF and smoother (CEKF & S), and moving horizon estimator (MHE). The parameters estimation was based on vaccine efficacy studies regarding transmissibility, severity of the disease, and lethality. Social distancing was assumed as a measured disturbance calculated using Google mobility data. Data from six federative units from Brazil were used to evaluate the proposed strategy. State and parameter estimations were performed from 1 October 2020 to 1 July 2021, during which Zeta and Gamma variants emerged. Simulation results showed that lethality increased between 11 and 30% for Zeta mutations and between 44 and 107% for Gamma mutations. In addition, transmissibility increased between 10 and 37% for the Zeta variant and between 43 and 119% for the Gamma variant. Furthermore, parameter estimation indicated temporal underreporting changes in hospitalized and deceased individuals. Overall, the estimation strategy showed to be suitable for dynamic feedback as simulation results presented an efficient detection and dynamic characterization of circulating variants.

Modeling the transmission of second-wave COVID-19 caused by imported cases: A case study

As the first-wave COVID-19 has passed in 2020, people's awareness of self-protection began to decline gradually. How to prevent and control the second-wave COVID-19 has become an important issue in many countries and regions. By analyzing the transmission of the second-wave COVID-19 caused by an imported case in Tonghua City, Jilin Province, China, in January 2021, we establish a new mathematical COVID-19 model to simulate the transmission characteristics of the second-wave COVID-19. First, we analyze the basic properties of the model, prove the existence of the equilibrium point, and obtain the expression of the basic reproduction number with important biological significance. Secondly, we use the weighted nonlinear least square estimation method to fit the cases in Tonghua City of Jilin Province in January 2021, and get the estimated value of the parameters. The basic reproduction number of the second-wave COVID-19 in Tonghua City is R 0 = 1 . 0695 , which is much smaller than that of the first-wave COVID-19 in Wuhan in 2020. Finally, in the optimal control part, we consider two control methods (keeping social distance and nucleic acid detection of all people in the city) to simulate the control of the disease. The results show that the control intensity of the two control methods needs to be dynamically changed and adjusted, so that the cost can be minimized with the least infection. The results of this paper can not only provide suggestions for health management departments, but also provide a reference for the analysis of the second-wave COVID-19 in other countries or regions.

A regime switch analysis on Covid-19 in Romania

In this paper we propose a three stages analysis of the evolution of Covid19 in Romania. There are two main issues when it comes to pandemic prediction. The first one is the fact that the numbers reported of infected and recovered are unreliable, however the number of deaths is more accurate. The second issue is that there were many factors which affected the evolution of the pandemic. In this paper we propose an analysis in three stages. The first stage is based on the classical SIR model which we do using a neural network. This provides a first set of daily parameters. In the second stage we propose a refinement of the SIR model in which we separate the deceased into a distinct category. By using the first estimate and a grid search, we give a daily estimation of the parameters. The third stage is used to define a notion of turning points (local extremes) for the parameters. We call a regime the time between these points. We outline a general way based on time varying parameters of SIRD to make predictions.

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

The realistic assessments of public health intervention strategies are of great significance to effectively combat the COVID-19 epidemic and the formation of intervention policy. In this paper, an extended COVID-19 epidemic model is devised to assess the severity of the pandemic and explore effective control strategies. The model is characterized by ordinary differential equations with seven-state variables, and it incorporates some parameters associated with the interventions (i.e., media publicity, home isolation, vaccination and face-mask wearing) to investigate the impacts of these interventions on the spread of the COVID-19 epidemic. Some dynamic behaviors of the model, such as forward and backward bifurcation, are analyzed. Specifically, we calibrate the model parameters using actual COVID-19 infected data in Brazil by Markov Chain Monte Carlo algorithm such that we can study the effects of interventions on a practical case. Through a comprehensive exploration of model design and analysis, model calibration, sensitivity analysis, implementation of optimal control problems and cost-effectiveness analysis, the rationality of our model is verified, and the effective strategies to combat the epidemic in Brazil are revealed. The results show that the asymptomatic infected individuals are the main drivers of COVID-19 transmission, and rapid detection of asymptomatic infections is critical to combat the COVID-19 epidemic in Brazil. Interestingly, the effect of the vaccination rate associated with pharmaceutical intervention on the basic reproduction number is much lower than that of non-pharmaceutical interventions (NPIs). Our study also highlights the importance of media publicity. To reduce the infected individuals, the multi-pronged NPIs have considerable positive effects on controlling the outbreak of COVID-19. The infections are significantly decreased by the early implementation of media publicity complemented with home isolation and face-mask wearing strategy. When the cost of implementation is taken into account, the early implementation of media publicity complemented with a face-mask wearing strategy can significantly mitigate the second wave of the epidemic in Brazil. These results provide some management implications for controlling COVID-19.

EKF-SIRD model algorithm for predicting the coronavirus (COVID-19) spreading dynamics

In this paper, we study the Covid 19 disease profile in the Algerian territory since February 25, 2020 to February 13, 2021. The idea is to develop a decision support system allowing public health decision and policy-makers to have future statistics (the daily prediction of parameters) of the pandemic; and also encourage citizens for conducting health protocols. Many studies applied traditional epidemic models or machine learning models to forecast the evolution of coronavirus epidemic, but the use of such models alone to make the prediction will be less precise. For this purpose, we assume that the spread of the coronavirus is a moving target described by an epidemic model. On the basis of a SIRD model (Susceptible-Infection-Recovery- Death), we applied the EKF algorithm to predict daily all parameters. These predicted parameters will be much beneficial to hospital managers for updating the available means of hospitalization (beds, oxygen concentrator, etc.) in order to reduce the mortality rate and the infected. Simulations carried out reveal that the EKF seems to be more efficient according to the obtained results.

Optimal health and economic impact of non-pharmaceutical intervention measures prior and post vaccination in England: a mathematical modelling study

Background. Even with good progress on vaccination, SARS-CoV-2 infections in the UK may continue to impose a high burden of disease and therefore pose substantial challenges for health policy decision makers. Stringent government-mandated physical distancing measures (lockdown) have been demonstrated to be epidemiologically effective, but can have both positive and negative economic consequences. The duration and frequency of any intervention policy could, in theory, be optimized to maximize economic benefits while achieving substantial reductions in disease. Methods. Here, we use a pre-existing SARS-CoV-2 transmission model to assess the health and economic implications of different strengths of control through time in order to identify optimal approaches to non-pharmaceutical intervention stringency in the UK, considering the role of vaccination in reducing the need for future physical distancing measures. The model is calibrated to the COVID-19 epidemic in England and we carry out retrospective analysis of the optimal timing of precautionary breaks in 2020 and the optimal relaxation policy from the January 2021 lockdown, considering the willingness to pay (WTP) for health improvement. Results. We find that the precise timing and intensity of interventions is highly dependent upon the objective of control. As intervention measures are relaxed, we predict a resurgence in cases, but the optimal intervention policy can be established dependent upon the WTP per quality adjusted life year loss avoided. Our results show that establishing an optimal level of control can result in a reduction in net monetary loss of billions of pounds, dependent upon the precise WTP value. Conclusion. It is vital, as the UK emerges from lockdown, but continues to face an on-going pandemic, to accurately establish the overall health and economic costs when making policy decisions. We demonstrate how some of these can be quantified, employing mechanistic infectious disease transmission models to establish optimal levels of control for the ongoing COVID-19 pandemic.

Optimal policies for mitigating pandemic costs: a minimal model

There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Of the various non-pharmaceutical interventions that were proposed and implemented to control the spread of the COVID-19 pandemic partial and complete lockdowns were used repeatedly in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model to understand the costs and benefits of these strategies that mitigate pandemic costs subject to constraints, we adopt the language of optimal control theory. This allows us to determine top-down policies for the nature and dynamics of social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, to partial lockdown to ensure not over-running hospitals, to alternating-shifts with significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening {and entail high socioeconomic costs}. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.

Parameter estimation of the COVID-19 transmission model using an improved quantum-behaved particle swarm optimization algorithm

The outbreak of coronavirus disease (COVID-19) and its accompanying pandemic have created an unprecedented challenge worldwide. Parametric modeling and analyses of the COVID-19 play a critical role in providing vital information about the character and relevant guidance for controlling the pandemic. However, the epidemiological utility of the results obtained from the COVID-19 transmission model largely depends on accurately identifying parameters. This paper extends the susceptible-exposed-infectious-recovered (SEIR) model and proposes an improved quantum-behaved particle swarm optimization (QPSO) algorithm to estimate its parameters. A new strategy is developed to update the weighting factor of the mean best position by the reciprocal of multiplying the fitness of each best particle with the average fitness of all best particles, which can enhance the global search capacity. To increase the particle diversity, a probability function is designed to generate new particles in the updating iteration. When compared to the state-of-the-art estimation algorithms on the epidemic datasets of China, Italy and the US, the proposed method achieves good accuracy and convergence at a comparable computational complexity. The developed framework would be beneficial for experts to understand the characteristics of epidemic development and formulate epidemic prevention and control measures.

Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection

Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.

Designing social distancing policies for the COVID-19 pandemic: A probabilistic model predictive control approach

The effective control of the COVID-19 pandemic is one the most challenging issues of recent years. The design of optimal control policies is challenging due to a variety of social, political, economical and epidemiological factors. Here, based on epidemiological data reported in recent studies for the Italian region of Lombardy, which experienced one of the largest and most devastating outbreaks in Europe during the first wave of the pandemic, we present a probabilistic model predictive control (PMPC) approach for the systematic study of what if scenarios of social distancing in a retrospective analysis for the first wave of the pandemic in Lombardy. The performance of the proposed PMPC was assessed based on simulations of a compartmental model that was developed to quantify the uncertainty in the level of the asymptomatic cases in the population, and the synergistic effect of social distancing during various activities, and public awareness campaign prompting people to adopt cautious behaviors to reduce the risk of disease transmission. The PMPC takes into account the social mixing effect, i.e. the effect of the various activities in the potential transmission of the disease. The proposed approach demonstrates the utility of a PMPC approach in addressing COVID-19 transmission and implementing public relaxation policies.

COVID-19 waves: variant dynamics and control

The waves of COVID-19 infections driven by its variants continue to nullify the success we achieved through efficacious vaccines, social restrictions, testing and quarantine policies. This paper models the two major variants-driven waves by two sets of susceptible-infected-quarantined-recovered-vaccinated-deceased coupled dynamics that are modulated by the three main interventions: vaccination, quarantine and restrictions. This \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SI^2Q^2R^2VD$$\end{document}SI2Q2R2VD system is used to demonstrate that the second major novel coronavirus wave in the US is caused by the delta variant and the corresponding rapid surge in infectious cases is driven by the unvaccinated pool of the populace. Next, a feedback control based planned vaccination strategy is derived and is shown to be able to suppress the surge in infections effectively.

Fractional-order backstepping strategy for fractional-order model of COVID-19 outbreak

The coronavirus disease (COVID-19) pandemic has impacted many nations around the world. Recently, new variant of this virus has been identified that have a much higher rate of transmission. Although vaccine production and distribution are currently underway, non-pharmacological interventions are still being implemented as an important and fundamental strategy to control the spread of the virus in countries around the world. To realize and forecast the transmission dynamics of this disease, mathematical models can be very effective. Various mathematical modeling methods have been proposed to investigate the transmission patterns of this new infection. In this paper, we utilized the fractional-order dynamics of COVID-19. The goal is to control the prevalence of the disease using non-pharmacological interventions. In this paper, a novel fractional-order backstepping sliding mode control (FOBSMC) is proposed for non-pharmacological decisions. Recently, new variant of this virus have been identified that have a much higher rate of transmission, so finally the effectiveness of the proposed controller in the presence of new variant of COVID-19 is investigated.

Controlling epidemic diseases based only on social distancing level: General case

The COVID-19 outbreak is an epidemic disease caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). When a new virus emerges, generally, little is known about it, and no vaccines or other pharmaceutical interventions are available. In the case of a person-to-person transmission virus with no vaccines or other pharmaceutical interventions, the only way to control the virus outbreak is by keeping a sustained physical distancing between the individuals. However, to adjust the level of the physical distancing accurately can be so complicated. Any level above the necessary can compromise the economic activity, and any level below can collapse the health care system. This work proposes a controller to keep the number of hospitalized individuals below a limit, and a new group-structured model to describe the COVID-19 outbreak. The proposed controller is robust to the uncertainties in the parameters of the model and keeps the number of infected individuals controlled only by adjusting the social distancing level. Numerical simulations, to show the behavior of the proposed controller and model, are done.

Optimal intervention strategies to mitigate the COVID-19 pandemic effects

Governments across the world are currently facing the task of selecting suitable intervention strategies to cope with the effects of the COVID-19 pandemic. This is a highly challenging task, since harsh measures may result in economic collapse while a relaxed strategy might lead to a high death toll. Motivated by this, we consider the problem of forming intervention strategies to mitigate the impact of the COVID-19 pandemic that optimize the trade-off between the number of deceases and the socio-economic costs. We demonstrate that the healthcare capacity and the testing rate highly affect the optimal intervention strategies. Moreover, we propose an approach that enables practical strategies, with a small number of policies and policy changes, that are close to optimal. In particular, we provide tools to decide which policies should be implemented and when should a government change to a different policy. Finally, we consider how the presented results are affected by uncertainty in the initial reproduction number and infection fatality rate and demonstrate that parametric uncertainty has a more substantial effect when stricter strategies are adopted.

COVID-19 and Chikungunya: an optimal control model with consideration of social and environmental factors

Chikungunya is one of the Aedes aegypti diseases that mosquito transmits to humans and that are common in tropical countries like Yemen. In this work, we formulated a novel dynamic mathematical model framework, which integrates COVID-19 and Chikungunya outbreaks. The proposed model is governed by a system of dynamic ordinary differential equations (ODEs). Particle swarm optimization was employed to solve the parameters estimation problem of the outbreaks of COVID-19 and Chikungunya in Yemen (March 1, 2020, to May 30, 2020). Besides, a bi-objective optimal control model was formulated, which minimizes the number of affected individuals and minimizes the total cost associated with the intervention strategies. The bi-objective optimal control was also solved using PSO. Five preventive measures were considered to curb the environmental and social factors that trigger the emergence of these viruses. Several strategies were simulated to evaluate the best possible strategy under the conditions and available resources in Yemen. The results obtained confirm that the strategy, which provides resources to prevent the transmission of Chikungunya and provides sufficient resources for testing, applying average social distancing, and quarrying the affected individuals, has a significant effect on flattening the epidemic curves and is the most suitable strategy in Yemen.

SARS-CoV-2 active infection prevalence and seroprevalence in the adult population of St. Louis County

BACKGROUND

The true prevalence of COVID-19 is difficult to estimate due to the absence of random population-based testing. To estimate current and past COVID-19 infection prevalence in a large urban area, we conducted a population-based survey in St. Louis County, Missouri.

METHODS

The population-based survey of active infection (PCR) and seroprevalence (IgG antibodies) of adults (≥ 18 years) was conducted through random-digit dialing and targeted sampling of St. Louis County residents with oversampling of Black residents. Infection prevalence of residents was estimated using design-based and raking weighting.

RESULTS

Between August 17 and October 24, 2020, 1,245 residents completed a survey and underwent PCR testing; 1,073 residents completed a survey and underwent PCR and IgG testing or self-reported results. Weighted prevalence estimates of residents with active infection was 1.9% (95% CI, 0.4% to 3.3%) and 5.6% were ever infected (95% CI, 3.3% to 8.0%). Overall infection hospitalization and fatality ratios were 4.9% and 1.4%, respectively.

CONCLUSIONS

Through October 2020, the percentage of residents that had ever been infected was relatively low. A markedly higher percentage of Black and other minorities compared to White residents were infected with COVID-19. The St. Louis region remained highly vulnerable to widespread infection in late 2020.

Comparative study of a mathematical epidemic model, statistical modeling, and deep learning for COVID-19 forecasting and management

The COVID-19 pandemic has caused a global crisis with 47,209,305 confirmed cases and 1,209,505 confirmed deaths worldwide as of November 2, 2020. Forecasting confirmed cases and understanding the virus dynamics is necessary to provide valuable insights into the growth of the outbreak and facilitate policy-making regarding virus containment and utilization of medical resources. In this study, we applied a mathematical epidemic model (MEM), statistical model, and recurrent neural network (RNN) variants to forecast the cumulative confirmed cases. We proposed a reproducible framework for RNN variants that addressed the stochastic nature of RNN variants leveraging z-score outlier detection. We incorporated heterogeneity in susceptibility into the MEM considering lockdowns and the dynamic dependency of the transmission and identification rates which were estimated using Poisson likelihood fitting. While the experimental results demonstrated the superiority of RNN variants in forecasting accuracy, the MEM presented comprehensive insights into the virus spread and potential control strategies.

Reconstruction of the transmission dynamics of the first COVID-19 epidemic wave in Thailand

Thailand was the first country reporting the first Coronavirus disease 2019 (COVID-19) infected individual outside mainland China. Here we delineated the course of the COVID-19 outbreak together with the timeline of the control measures and public health policies employed by the Thai government during the first wave of the COVID-19 outbreak in Thailand. Based on the comprehensive epidemiological data, we reconstructed the dynamics of COVID-19 transmission in Thailand using a stochastic modeling approach. Our stochastic model incorporated the effects of individual heterogeneity in infectiousness on disease transmission, which allows us to capture relevant features of superspreading events. We found that our model could accurately capture the transmission dynamics of the first COVID-19 epidemic wave in Thailand. The model predicted that at the end of the first wave, the number of cumulative confirmed cases was 3091 (95%CI: 2782-3400). We also estimated the time-varying reproduction number (R_t) during the first epidemic wave. We found that after implementing the nationwide interventions, the R_t in Thailand decreased from the peak value of 5.67 to a value below one in less than one month, indicating that the control measures employed by the Thai government during the first COVID-19 epidemic wave were effective. Finally, the effects of transmission heterogeneity and control measures on the likelihood of outbreak extinction were also investigated.

Transmission dynamics model and the coronavirus disease 2019 epidemic: applications and challenges

Since late 2019, the beginning of coronavirus disease 2019 (COVID-19) pandemic, transmission dynamics models have achieved great development and were widely used in predicting and policy making. Here, we provided an introduction to the history of disease transmission, summarized transmission dynamics models into three main types: compartment extension, parameter extension and population-stratified extension models, highlight the key contribution of transmission dynamics models in COVID-19 pandemic: estimating epidemiological parameters, predicting the future trend, evaluating the effectiveness of control measures and exploring different possibilities/scenarios. Finally, we pointed out the limitations and challenges lie ahead of transmission dynamics models.

Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

SUPPLEMENTARY INFORMATION

The online version supplementary material available at 10.1007/s11071-022-07235-7.

Optimal control analysis of COVID-19 vaccine epidemic model: a case study

The purpose of this research is to explore the complex dynamics and impact of vaccination in controlling COVID-19 outbreak. We formulate the classical epidemic compartmental model by introducing vaccination class. Initially, the proposed mathematical model is analyzed qualitatively. The basic reproductive number is computed and its numerical value is estimated using actual reported data of COVID-19 for Pakistan. The sensitivity analysis is performed to analyze the contribution of model embedded parameters in transmission of the disease. Further, we compute the equilibrium points and discussed its local and global stability. In order to investigate the influence of model key parameters on the transmission and controlling of the disease, we perform numerical simulations describing the impact of various scenarios of vaccine efficacy rate and other controlling measures. Further, on the basis of sensitivity analysis, the proposed model is restructured to obtained optimal control model by introducing time-dependent control variablesu 1 ( t ) for isolation,u 2 ( t ) for vaccine efficacy andu 3 ( t ) for treatment enhancement. Using optimal control theory and Pontryagin's maximum principle, the model is optimized and important optimality conditions are derived. In order to explore the impact of various control measures on the disease dynamics, we considered three different scenarios, i.e., single and couple and threefold controlling interventions. Finally, the graphical interpretation of each case is depicted and discussed in detail. The simulation results revealed that although single and couple scenarios can be implemented for the disease minimization but, the effective case to curtail the disease incidence is the threefold scenario which implements all controlling measures at the same time.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Functional observability and target state estimation in large-scale networks

Observing the states of a network is fundamental to our ability to explore and control the dynamics of complex natural, social, and technological systems. The problem of determining whether the system is observable has been addressed by network control researchers over the past decade. Progress on the further problem of actually designing and implementing efficient algorithms to infer the states from limited measurements has been hampered by the high dimensionality of large-scale networks. Noting that often only a small number of state variables in a network are essential for control, intervention, and monitoring purposes, this work develops a graph-based theory and highly scalable methods that achieve accurate estimation of target variables of network systems with minimal sensing and computational resources.

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

Ethics of U.S. government policy responses to the COVID‐19 pandemic: A utilitarianism perspective

COVID‐19 hit the United States in January 2020, quickly resulting in stay‐at‐home orders that sent the U.S. economy into a major recession. The federal government leveraged fiscal, regulatory, and monetary policies to provide relief. Decisions had to be made in a complex environment wrought with difficult choices, complicated by the federalist governing system in the United States. Myers (2016, p. 202) asserted, “If an event like the [1918 influenza] pandemic were to occur in the United States, it is important that the government be prepared, not only in terms of material, but ethically.” We analyze the ethical choices of the initial responses by reviewing early U.S. government responses and the impact of culture, federalism, and justice. We conclude that utilitarian analyses of balancing infection rates and economic impacts must be supplemented with Kantian principles of not treating people as means to an end, balancing the protection of individual freedoms with the good of society, and protecting vulnerable groups. As governments prepare for future crises, ethical considerations should be built into those plans as guardrails to guide decision‐makers.

Effect of an antiviral drug control and its variable order fractional network in host COVID-19 kinetics

In December 2019, a novel coronavirus disease (COVID-19) appeared in Wuhan, China. After that, it spread rapidly all over the world. Novel coronavirus belongs to the family of Coronaviridae and this new strain is called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epithelial cells of our throat and lungs are the main target area of the SARS-CoV-2 virus which leads to COVID-19 disease. In this article, we propose a mathematical model for examining the effects of antiviral treatment over viral mutation to control disease transmission. We have considered here three populations namely uninfected epithelial cells, infected epithelial cells, and SARS-CoV-2 virus. To explore the model in light of the optimal control-theoretic strategy, we use Pontryagin's maximum principle. We also illustrate the existence of the optimal control and the effectiveness of the optimal control is studied here. Cost-effectiveness and efficiency analysis confirms that time-dependent antiviral controlled drug therapy can reduce the viral load and infection process at a low cost. Numerical simulations have been done to illustrate our analytical findings. In addition, a new variable-order fractional model is proposed to investigate the effect of antiviral treatment over viral mutation to control disease transmission. Considering the superiority of fractional order calculus in the modeling of systems and processes, the proposed variable-order fractional model can provide more accurate insight for the modeling of the disease. Then through the genetic algorithm, optimal treatment is presented, and its numerical simulations are illustrated.

The Effect of Local and Global Interventions on Epidemic Spreading

Epidemic spreading causes severe challenges to the global public health system, and global and local interventions are considered an effective way to contain such spreading, including school closures (local), border control (global), etc. However, there is little study on comparing the efficiency of global and local interventions on epidemic spreading. Here, we develop a new model based on the Susceptible-Exposed-Infectious-Recovered (SEIR) model with an additional compartment called “quarantine status”. We simulate various kinds of outbreaks and interventions. Firstly, we predict, consistent with previous studies, interventions reduce epidemic spreading to 16% of its normal level. Moreover, we compare the effect of global and local interventions and find that local interventions are more effective than global ones. We then study the relationships between incubation period and interventions, finding that early implementation of rigorous intervention significantly reduced the scale of the epidemic. Strikingly, we suggest a Pareto optimal in the intervention when resources were limited. Finally, we show that combining global and local interventions is the most effective way to contain the pandemic spreading if initially infected individuals are concentrated in localized regions. Our work deepens our understandings of the role of interventions on the pandemic, and informs an actionable strategy to contain it.

Exploring senior managers' perceptions of the COVID-19 Crisis in Iran: a qualitative content analysis study

BACKGROUND

Identification of the experience of senior managers in tackling biological crises can be a roadmap for future crisis management planning. The aim of the present study was to investigate the experiences of senior managers during the COVID-19 crisis.

METHODS

This is a descriptive qualitative research. Data were collected using in-depth and semi-structured individual interviews. Accordingly, 20 senior managers of medical universities with experience in managing the COVID-19 crisis were enrolled in the study using purposive sampling. Data were collected from February 2020 to May 2021. For data analysis, qualitative content analytical approach was used.

RESULTS

According to the results, 4 main themes and 10 sub-themes were obtained; they included dealing with issues and challenges in the face of COVID-19 disease (Structural challenges, Cultural challenges, Educational challenges, COVID-19 complexity); individual and managerial competencies (Individual competencies, Managerial competencies); comprehensive, accountable, and efficient management (Comprehensive and accountable management, efficient management); and professional and organizational self-efficacy (Professional self-efficacy, organizational self-efficacy) were obtained.

CONCLUSIONS

In the present study, a number of senior managers' experiences in the COVID-19 crisis management were identified. Managers and policymakers of the health system are suggested to use the results of the present study to effectively manage the crisis and improve crisis management in various health-related areas by providing an effective cultural and organizational context.

Optimization strategies of human mobility during the COVID-19 pandemic: A review

The impact of the ongoing COVID-19 pandemic is being felt in all spheres of our lives - cutting across the boundaries of nation, wealth, religions or race. From the time of the first detection of infection among the public, the virus spread though almost all the countries in the world in a short period of time. With humans as the carrier of the virus, the spreading process necessarily depends on the their mobility after being infected. Not only in the primary spreading process, but also in the subsequent spreading of the mutant variants, human mobility plays a central role in the dynamics. Therefore, on one hand travel restrictions of varying degree were imposed and are still being imposed, by various countries both nationally and internationally. On the other hand, these restrictions have severe fall outs in businesses and livelihood in general. Therefore, it is an optimization process, exercised on a global scale, with multiple changing variables. Here we review the techniques and their effects on optimization or proposed optimizations of human mobility in different scales, carried out by data driven, machine learning and model approaches.