Selection of forecasting models for infectious diseases in large warships.

As important combat platforms, large warships have the characteristics of compact internal space and dense personnel. Once infectious diseases occur, they are very easy to spread. Therefore, it is very important to select suitable forecasting models for infectious diseases in this environment. This paper introduces 4 classic dynamics models of infectious diseases, summarizes various kinds of compartmental models and their key characteristics, and discusses several common practical simulation requirements, helping relevant health personnel to cope with the challenges in health and epidemic prevention such as the prevention and control of coronavirus disease 2019.Copyright © 2022, Second Military Medical University Press. All rights reserved.

Epidemic Management via Imperfect Testing: A Multi-criterial Perspective.

Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.

Evaluation of the main parameters of the compartmental model of the epidemic development based on the example of the spread of the COVID-19 pandemic in Chernivtsi region

The paper considers the application of the theoretical model of epidemiological development of COVID-19 disease among the regional population based on the statistical data in Chernivtsi region of Ukraine for the period from March 2020 to June 2021. Using these data, a mathematical assessment of the values of the main parameters of the compartmental model (SIR) beta and gamma was performed and the analysis of the relationship between the values of beta and gamma and antiepidemiological measures was carried out for the region. Determining the parameters beta and gamma based on available statistics allows us to predict the duration of precautionary measures such as quarantine, lockdown, border closure and predict the effectiveness of their implementation as well. The analysis of statistical data showed the moderate effectiveness of quarantine and lockdown in changing the daily rates of infected and recovered people, while the dynamics of the epidemic development during these periods changed from negative to positive. The introduction of vaccination has shown the significant reduction in the daily rate of infected people and the substantial increase in the daily rate of the recovered people.

Selection of forecasting models for infectious diseases in large warships

As important combat platforms, large warships have the characteristics of compact internal space and dense personnel. Once infectious diseases occur, they are very easy to spread. Therefore, it is very important to select suitable forecasting models for infectious diseases in this environment. This paper introduces 4 classic dynamics models of infectious diseases, summarizes various kinds of compartmental models and their key characteristics, and discusses several common practical simulation requirements, helping relevant health personnel to cope with the challenges in health and epidemic prevention such as the prevention and control of coronavirus disease 2019.Copyright © 2022, Second Military Medical University Press. All rights reserved.

A Theoretical Linguistic Fuzzy Rule-Based Compartmental Modeling for the COVID-19 Pandemic

The COVID-19 pandemic has affected the whole world quite seriously. The number of new infectious cases and death cases are rapidly increasing over time. In this study, a theoretical linguistic fuzzy rule-based susceptible-exposed-infectious-isolated-recovered (SEIIsR) compartmental model has been proposed to predict the dynamics of the transmission of COVID-19 over time considering population immunity and infectiousness heterogeneity based on viral load in the model. The model's equilibrium points have been calculated, and stability analysis of the model's equilibrium points has been conducted. Consequently, the fuzzy basic reproduction number, R0f, of the fuzzy model has been formulated. Finally, the temporal dynamics of different compartmental populations with immunity and infectiousness heterogeneity using the fuzzy Mamdani model are delineated, and some disease control policies have been suggested to get over the infection in no time. Copyright © 2022, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

SIRSi-vaccine dynamical model for the Covid-19 pandemic.

Covid-19, caused by severe acute respiratory syndrome coronavirus 2, broke out as a pandemic during the beginning of 2020. The rapid spread of the disease prompted an unprecedented global response involving academic institutions, regulatory agencies, and industries. Vaccination and nonpharmaceutical interventions including social distancing have proven to be the most effective strategies to combat the pandemic. In this context, it is crucial to understand the dynamic behavior of the Covid-19 spread together with possible vaccination strategies. In this study, a susceptible-infected-removed-sick model with vaccination (SIRSi-vaccine) was proposed, accounting for the unreported yet infectious. The model considered the possibility of temporary immunity following infection or vaccination. Both situations contribute toward the spread of diseases. The transcritical bifurcation diagram of alternating and mutually exclusive stabilities for both disease-free and endemic equilibria were determined in the parameter space of vaccination rate and isolation index. The existing equilibrium conditions for both points were determined in terms of the epidemiological parameters of the model. The bifurcation diagram allowed us to estimate the maximum number of confirmed cases expected for each set of parameters. The model was fitted with data from São Paulo, the state capital of SP, Brazil, which describes the number of confirmed infected cases and the isolation index for the considered data window. Furthermore, simulation results demonstrate the possibility of periodic undamped oscillatory behavior of the susceptible population and the number of confirmed cases forced by the periodic small-amplitude oscillations in the isolation index. The main contributions of the proposed model are as follows: A minimum effort was required when vaccination was combined with social isolation, while additionally ensuring the existence of equilibrium points. The model could provide valuable information for policymakers, helping define disease prevention mitigation strategies that combine vaccination and non-pharmaceutical interventions, such as social distancing and the use of masks. In addition, the SIRSi-vaccine model facilitated the qualitative assessment of information regarding the unreported infected yet infectious cases, while considering temporary immunity, vaccination, and social isolation index.

Competitive Epidemic Spreading Over Networks

In this letter, we consider an epidemic model for two competitive viruses spreading over a metapopulation network, termed the 'bivirus model' for convenience. The dynamics are described by a networked continuous-time dynamical system, with each node representing a population and edges representing infection pathways for the viruses. We survey existing results on the bivirus model beginning with the nature of the equilibria, including whether they are isolated, and where they exist within the state space with the corresponding interpretation in the context of epidemics. We identify key convergence results, including the conclusion that for generic system parameters, global convergence occurs for almost all initial conditions. Conditions relating to the stability properties of various equilibria are also presented. In presenting these results, we also recall some of the key tools and theories used to secure them. We conclude by discussing the various open problems, ranging from control and network optimization, to further characterization of equilibria, and finally extensions such as modeling three or more viruses.

Assessing the Impact of Vaccination on the Dynamics of COVID-19 in Africa: A Mathematical Modeling Study.

Several effective COVID-19 vaccines are administered to combat the COVID-19 pandemic globally. In most African countries, there is a comparatively limited deployment of vaccination programs. In this work, we develop a mathematical compartmental model to assess the impact of vaccination programs on curtailing the burden of COVID-19 in eight African countries considering SARS-CoV-2 cumulative case data for each country for the third wave of the COVID-19 pandemic. The model stratifies the total population into two subgroups based on individual vaccination status. We use the detection and death rates ratios between vaccinated and unvaccinated individuals to quantify the vaccine's effectiveness in reducing new COVID-19 infections and death, respectively. Additionally, we perform a numerical sensitivity analysis to assess the combined impact of vaccination and reduction in the SARS-CoV-2 transmission due to control measures on the control reproduction number (Rc). Our results reveal that on average, at least 60% of the population in each considered African country should be vaccinated to curtail the pandemic (lower the Rc below one). Moreover, lower values of Rc are possible even when there is a low (10%) or moderate (30%) reduction in the SARS-CoV-2 transmission rate due to NPIs. Combining vaccination programs with various levels of reduction in the transmission rate due to NPI aids in curtailing the pandemic. Additionally, this study shows that vaccination significantly reduces the severity of the disease and death rates despite low efficacy against COVID-19 infections. The African governments need to design vaccination strategies that increase vaccine uptake, such as an incentive-based approach.

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

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

N-Step-Ahead Optimal Control of a Compartmental Model of COVID-19

This paper uses a compartmental model that accounts for some of the main features of the COVID-19 pandemic. Assuming a control that represents the aggregated intensity of non pharmaceutical interventions, such as lockdown in varying degrees and the use of masks and social distancing, this text proposes an N-step-ahead optimal control (NSAOC) method that is easy to calculate and provides a guideline for implementation. The compartmental model is extended to account for vaccination, and the N-step-ahead optimal control is calculated for this case as well. The proposed control is robust to parameter variation in all model parameters, when they are assumed to be normally distributed about nominal values. In addition, the proposed NSAOC is shown to compare favorably with a recently proposed PID-like controller. © 2023, Brazilian Society for Automatics--SBA.

Well-posedness for a diffusion–reaction compartmental model simulating the spread of COVID-19

This paper is concerned with the well-posedness of a diffusion–reaction system for a susceptible-exposed-infected-recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with nonlinear diffusions, depending on the total amount of the SEIR populations. The model aims at describing the spatio-temporal spread of the COVID-19 pandemic and is a variation of the one recently introduced, discussed, and tested in a paper by Viguerie et al (2020). Here, we deal with the mathematical analysis of the resulting Cauchy–Neumann problem: The existence of solutions is proved in a rather general setting, and a suitable time discretization procedure is employed. It is worth mentioning that the uniform boundedness of the discrete solution is shown by carefully exploiting the structure of the system. Uniform estimates and passage to the limit with respect to the time step allow to complete the existence proof. Then, two uniqueness theorems are offered, one in the case of a constant diffusion coefficient and the other for more regular data, in combination with a regularity result for the solutions. © 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.

Existence for Fractional SEIR Compartmental Model Involving Hilfer Fractional Derivative

In this paper, we research a type of newfashioned fractional models for COVID-19 outbreak, further improve it to Hilfer fractional mathematical models be called as SEIR compartmental models of order α(0,1) and type β[0,1] on an unbounded domain [0,+f). The existence for the nonlinear Hilfer fractional differential equations are proved via Schauder's fixed point theorem based on appropriate growth conditions in suitable Banach spaces. We conclude that the Hilfer fractional differential system has at least one solution in specified Banach space. © 2022 IEEE.

Integrative modelling of reported case numbers and seroprevalence reveals time-dependent test efficiency and infectious contacts.

Mathematical models have been widely used during the ongoing SARS-CoV-2 pandemic for data interpretation, forecasting, and policy making. However, most models are based on officially reported case numbers, which depend on test availability and test strategies. The time dependence of these factors renders interpretation difficult and might even result in estimation biases. Here, we present a computational modelling framework that allows for the integration of reported case numbers with seroprevalence estimates obtained from representative population cohorts. To account for the time dependence of infection and testing rates, we embed flexible splines in an epidemiological model. The parameters of these splines are estimated, along with the other parameters, from the available data using a Bayesian approach. The application of this approach to the official case numbers reported for Munich (Germany) and the seroprevalence reported by the prospective COVID-19 Cohort Munich (KoCo19) provides first estimates for the time dependence of the under-reporting factor. Furthermore, we estimate how the effectiveness of non-pharmaceutical interventions and of the testing strategy evolves over time. Overall, our results show that the integration of temporally highly resolved and representative data is beneficial for accurate epidemiological analyses.

Evaluating a SARS-CoV-2 screening strategy based on serological tests.

BACKGROUND: facing the SARS-CoV-2 epidemic requires intensive testing on the population to early identify and isolate infected subjects. Although RT-PCR is the most reliable technique to detect ongoing infections, serological tests are frequently proposed as tools in heterogeneous screening strategies. OBJECTIVES: to analyse the performance of a screening strategy proposed by the local government of Tuscany (Central Italy), which first uses qualitative rapid tests for antibody detection, and then RT-PCR tests on the positive subjects. METHODS: a simulation study is conducted to investigate the number of RT-PCR tests required by the screening strategy and the undetected ongoing infections in a pseudo-population of 500,000 subjects, under different prevalence scenarios and assuming a sensitivity of the serological test ranging from 0.50 to 0.80 (specificity 0.98). A compartmental model is used to predict the number of new infections generated by the false negatives two months after the screening, under different values of the infection reproduction number. RESULTS: assuming a sensitivity equal to 0.80 and a prevalence of 0.3%, the screening procedure would require on average 11,167 RT-PCR tests and would produce 300 false negatives, responsible after two months of a number of contagions ranging from 526 to 1,132, under the optimistic scenario of a reproduction number between 0.5 to 1. Resources and false negatives increase with the prevalence. CONCLUSIONS: the analysed screening procedure should be avoided unless the prevalence and the rate of contagion are very low. The cost and effectiveness of the screening strategies should be evaluated in the actual context of the epidemic, accounting for the fact that it may change over time.

Euler iteration augmented physics-informed neural networks for time-varying parameter estimation of the epidemic compartmental model

Introduction: Differential equations governed compartmental models are known for their ability to simulate epidemiological dynamics and provide highly accurate descriptive and predictive results. However, identifying the corresponding parameters of flow from one compartment to another in these models remains a challenging task. These parameters change over time due to the effect of interventions, virus variation and so on, thus time-varying compartmental models are required to reflect the dynamics of the epidemic and provide plausible results.Methods: In this paper, we propose an Euler iteration augmented physics-informed neural networks(called Euler-PINNs) to optimally integrates real-world reported data, epidemic laws and deep neural networks to capture the dynamics of COVID-19. The proposed Euler-PINNs method integrates the differential equations into deep neural networks by discretizing the compartmental model with suitable time-step and expressing the desired parameters as neural networks. We then define a robust and concise loss of the predicted data and the observed data for the epidemic in question and try to minimize it. In addition, a novel activation function based on Fourier theory is introduced for the Euler-PINNs method, which can deal with the inherently stochastic and noisy real-world data, leading to enhanced model performance.Results and Discussion: Furthermore, we verify the effectiveness of the Euler-PINNs method on 2020 COVID-19-related data in Minnesota, the United States, both qualitative and quantitative analyses of the simulation results demonstrate its accuracy and efficiency. Finally, we also perform predictions based on data from the early stages of the outbreak, and the experimental results demonstrate that the Euler-PINNs method remains robust on small dataset.

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology.

We propose a novel use of generative adversarial networks (GANs) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. We apply these methods to a compartmental model in epidemiology that is able to model space and time variations, and that mimics the spread of COVID-19 in an idealised town. To do this, the GAN is set within a reduced-order model, which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters.

Compartmental modeling for SARS-CoV-2 pandemic simulation

In this article, we briefly explored the historical origin and applications of popular SIR-based compartmental models, especially on the modelling of the on-going SARS-CoV-2 epidemic. We discussed the emergence of the early compartmental models as well as the derivation of SIR-variants from specific studies. Specifically, we discussed the advantages of the addition of specialized compartments in SIR-variants like the SEIR and SVIR model in the modelling of disease latency and effect of vaccination, as well as the application and expansion of these models using published peer-reviewed studies on the SARS-CoV-2 epidemic as instances. Lastly, we briefly went over the limitations of compartmental models and potential substitution approaches. © 2022 Author(s).

Modeling variants of the COVID-19 virus in Hawai‘i and the responses to forecasting

In this paper we introduce a model for the spread of COVID-19 which takes into account competing SARS-CoV-2 mutations as well as the possibility of reinfection due to fading of vaccine protection. Our primary focus is to describe the impact of the B.1.617.2 (Delta) and B.1.1.529 (Omicron) variants on the state of Hawai‘i and to illustrate how the model performed during the pandemic, both in terms of accuracy, and as a resource for the government and media. Studying the effect of the pandemic on the Hawaiian archipelago is of notable interest because, as an isolated environment, its unique geography affords partially controlled travel to and from the state. We highlight the modeling efforts of the Hawai‘i Pandemic Applied Modeling Work Group (HiPAM) which used the model presented here, and we detail the model fitting and forecasting for the periods from July 2021 to October 2021 (Delta surge) and from November 2021 to April 2022 (Omicron surge). Our results illustrate that the model was both accurate when the forecasts were built on assumptions that held true, and was inaccurate when the public response to the forecasts was to enforce safety measures that invalidated the assumptions in the model. © 2023 the Author(s), licensee AIMS Press.

Mitigating Epidemics Through Vaccination, Treatment, and Awareness Programs

We modify the standard susceptible-infected-recovered-dead epidemic model to include three mitigation strategies, vaccination, treatment, and awareness programs;and compute its epidemic threshold. Further, we formulate an optimization problem to calculate the optimum rates of the mitigation strategies. The optimization problem minimizes a cost function that takes into account: (i) The deaths caused by the epidemic. (ii) Indirect costs incurred due to loss in health of the population (e.g. temporary loss of productivity due to absence from work caused by infection). (iii) Costs of employing the mitigation strategies (costs of vaccination, treatment, and running awareness programs). We have tuned the epidemic model for COVID-19 pandemic and computed the optimal strategies. Results show that the epidemic peak reduces when optimal strategy is employed, leading to a better epidemic management. Further, importance of the vaccination strategy increases with the increasing spreading rate (virulence) of the epidemic. © 2022 ACM.

Susceptibility to Resurgent COVID-19 Outbreaks Following Vaccine Rollouts: A Modeling Study.

Using the recently proposed Susceptible-Asymptomatic-Infected-Vaccinated-Removed (SAIVR) model, we study the impact of key factors affecting COVID-19 vaccine rollout effectiveness and the susceptibility to resurgent epidemics. The SAIVR model expands the widely used Susceptible-Infectious-Removed (SIR) model for describing epidemics by adding compartments to include the asymptomatic infected (A) and the vaccinated (V) populations. We solve the model numerically to make predictions on the susceptibility to resurgent COVID-19 epidemics depending on initial vaccination coverage, importation loads, continuing vaccination, and more contagious SARS-CoV-2 variants, under persistent immunity and immunity waning conditions. The parameters of the model represent reported epidemiological characteristics of the SARS-CoV-2 virus such as the disease spread in countries with high levels of vaccination coverage. Our findings help explain how the combined effects of different vaccination coverage levels and waning immunity lead to distinct patterns of resurgent COVID-19 epidemics (either surges or endemic), which are observed in countries that implemented different COVID-19 health policies and achieved different vaccinated population plateaus after the vaccine rollouts in the first half of 2021.