Bayesian computational methods for state-space models with application to SIR model

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ FROM AUTHOR] Copyright of Journal of Statistical Computation & Simulation is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Hybrid discrete-time-continuous-time models and a SARS CoV-2 mystery: Sub-Saharan Africa's low SARS CoV-2 disease burden.

Worldwide, the recent SARS-CoV-2 virus has infected more than 670 million people and killed nearly 67.0 million. In Africa, the number of confirmed COVID-19 cases was approximately 12.7 million as of January 11, 2023, that is about 2% of the infections around the world. Many theories and modeling techniques have been used to explain this lower-than-expected number of reported COVID-19 cases in Africa relative to the high disease burden in most developed countries. We noted that most epidemiological mathematical models are formulated in continuous-time interval, and taking Cameroon in Sub-Saharan Africa, and New York State in the USA as case studies, in this paper we developed parameterized hybrid discrete-time-continuous-time models of COVID-19 in Cameroon and New York State. We used these hybrid models to study the lower-than-expected COVID-19 infections in developing countries. We then used error analysis to show that a time scale for a data-driven mathematical model should match that of the actual data reporting.

Optimal interventional policy based on discrete-time fuzzy rules equivalent model utilizing with COVID-19 pandemic data.

In this paper, a mathematical model of the COVID-19 pandemic is formulated by fitting it to actual data collected during the fifth wave of the COVID-19 pandemic in Coahuila, Mexico, from June 2022 to October 2022. The data sets used are recorded on a daily basis and presented in a discrete-time sequence. To obtain the equivalent data model, fuzzy rules emulated networks are utilized to derive a class of discrete-time systems based on the daily hospitalized individuals' data. The aim of this study is to investigate the optimal control problem to determine the most effective interventional policy including precautionary and awareness measures, the detection of asymptomatic and symptomatic individuals, and vaccination. A main theorem is developed to guarantee the closed-loop system performance by utilizing approximate functions of the equivalent model. The numerical results indicate that the proposed interventional policy can eradicate the pandemic within 1-8 weeks. Additionally, the results show that if the policy is implemented within the first 3 weeks, the number of hospitalized individuals remains below the hospital's capacity.

Mathematical analysis of COVID-19 pandemic by using the concept of SIR model.

The health organizations around the world are currently facing one of the greatest challenges, to overcome the current global pandemic, COVID-19. It erupted in December 2019, in Wuhan City, China. It spreads rapidly throughout the world within couple of months. In this paper, the data of the COVID-19 have been collected, organized, analyzed and interpreted using the discrete-time model of SIR epidemic model. Moreover, results for several countries from different regions of the world have been obtained. Furthermore, comparative study has been carried out for the countries under consideration. The comparison was performed for the data of different countries on same dates of each month. However, the calculations are carried out for thirteen consecutive weeks, to investigate the rate of spread and the control of the disease in these countries. This guides us to some important concepts like factors favoring the spread of virus and those resisting the spread. Different regions are studied and their data have been evaluated to know which regions are the most effected. This study helps to know the important factors about the behavior of the coronavirus in different environments, such as lockdowns, temperatures, humidity and other restrictions. The proposed concepts and equations can be used to project the upcoming behavior of the pandemic.

An Application of SEIR Model to the COVID-19 Spread

The Susceptible-Exposed-Infectious-Recovered (SEIR) model is applied in several countries to ascertain the spread of the coronavirus disease 2019 (COVID-19). We consider discrete-time SEIR epidemic model in a closed system which does not account for births or deaths, total population size under consideration is constant. This dynamical system is generated by a non-linear evolution operator depending on four parameters. Under some conditions on parameters we reduce the evolution operator to a quadratic stochastic operator (QSO) which maps 3-dimensional simplex to itself. We show that the QSO has uncountable set of fixed points (all laying on the boundary of the simplex). It is shown that all trajectories of the dynamical system (generated by the QSO) of the SEIR model are convergent (i.e. the QSO is regular). Moreover, we discuss the efficiency of the model for Uzbekistan © 2023 L&H Scientific Publishing, LLC. All rights reserved

A Discrete Model for the Evolution of Infection Prior to Symptom Onset

We consider a between-host model for a single epidemic outbreak of an infectious disease. According to the progression of the disease, hosts are classified in regard to the pathogen load. Specifically, we are assuming four phases: non-infectious asymptomatic phase, infectious asymptomatic phase (key-feature of the model where individuals show up mild or no symptoms), infectious symptomatic phase and finally an immune phase. The system takes the form of a non-linear Markov chain in discrete time where linear transitions are based on geometric (main model) or negative-binomial (enhanced model) probability distributions. The whole system is reduced to a single non-linear renewal equation. Moreover, after linearization, at least two meaningful definitions of the basic reproduction number arise: firstly as the expected secondary asymptomatic cases produced by an asymptomatic primary case, and secondly as the expected number of symptomatic individuals that a symptomatic individual will produce. We study the evolution of infection transmission before and after symptom onset. Provided that individuals can develop symptoms and die from the disease, we take disease-induced mortality as a measure of virulence and it is assumed to be positively correlated with a weighted average transmission rate. According to our findings, transmission rate of the infection is always higher in the symptomatic phase yet under a suitable condition, most of the infections take place prior to symptom onset.

FORECASTING the COVID-19 USING the DISCRETE GENERALIZED LOGISTIC MODEL

Using mathematical models to describe the dynamics of infectious-diseases transmission in large communities can help epidemiological scientists to understand different factors affecting epidemics as well as health authorities to decide measures effective for infection prevention. In this study, we use a discrete version of the Generalized Logistic Model (GLM) to describe the spread of the coronavirus disease 2019 (COVID-19) pandemic in Saudi Arabia. We assume that we are operating in discrete time so that the model is represented by a first-order difference equation, unlike time-continuous models, which employ differential equations. Using this model, we forecast COVID-19 spread in Saudi Arabia and we show that the short-term predicted number of cumulative cases is in agreement with the confirmed reports. © 2022

Data-driven model prediction and optimal control for interventional policy of a class of susceptible-infectious-removed dynamics with COVID-19 data

Adaptive optimal-control and model prediction are proposed for a class of susceptible-infectious-removed dynamics according to the COVID-19 data. From the practical point of view, data sets of COVID-19 pandemics are daily collected and presented in a discrete-time sequence. Therefore, the discrete-time mathematical model of COVID-19 pandemics is formulated in this work. By developing the time-varying transmission rate, the model's accuracy is significantly contributed to the actual data of the COVID-19 pandemic. Furthermore, the interventional policy is derived by the proposed optimal controller when the closed-loop performance is guaranteed by theoretical aspects and numerical results. © 2022 John Wiley & Sons Ltd.

Model Dynamics and Optimal Control for Intervention Policy of COVID-19 Epidemic with Quarantine and Immigrating Disturbances.

A dynamic model called SqEAIIR for the COVID-19 epidemic is investigated with the effects of vaccination, quarantine and precaution promotion when the traveling and immigrating individuals are considered as unknown disturbances. By utilizing only daily sampling data of isolated symptomatic individuals collected by Mexican government agents, an equivalent model is established by an adaptive fuzzy-rules network with the proposed learning law to guarantee the convergence of the model's error. Thereafter, the optimal controller is developed to determine the adequate intervention policy. The main theorem is conducted to demonstrate the setting of all designed parameters regarding the closed-loop performance. The numerical systems validate the efficiency of the proposed scheme to control the epidemic and prevent the overflow of requiring healthcare facilities. Moreover, the sufficient performance of the proposed scheme is achieved with the effect of traveling and immigrating individuals.

A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals.

Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.

Dynamic group testing to control and monitor disease progression in a population

In this paper, we introduce a "discrete-time SIR stochastic block model"that also allows for group testing and interventions on a daily basis. Our model can be regarded as a discrete version of the well-known continuous-time SIR stochastic network model [1] and relies on a specific type of weighted graph to capture the underlying community spread. Given that infection model, we then formulate a dynamic group-testing problem by asking: (a) what is the minimum number of tests needed everyday to identify all infections? and (b) are there nonadaptive group testing strategies that achieve this with vanishing error probability? Our results show that one can leverage the knowledge of the community infection model to compute a lower bound on the number of tests and also inform nonadaptive group testing algorithms, so that they can achieve (almost) the same performance as complete individual testing with a much smaller number of tests. Moreover, these algorithms are order-optimal, under specific conditions. © 2022 IEEE.

A MATHEMATICAL SIR MODEL ON THE SPREAD OF INFECTIOUS DISEASES CONSIDERING HUMAN IMMUNITY

In this paper, we propose a mathematical model of infection by infectious diseases, taking into account the division of the population according to the criteria of immunity. Our objective is to demonstrate the positive effect of this idea against the different epidemics. We have proposed two strategies to reduce the great human and material losses caused by these diseases, respectively awareness programs on the importance of the exercise of sport and a healthy food to increase human immunity, treatment and health care for people with low immunity. The Pontryagin maximum principle is applied to characterize the optimal controls, and the optimality system is solved using an iterative approach. Finally, numerical simulations are performed to verify the theoretical analysis using MATLAB. © 2022 the author(s).

Chaotic control of the dynamical behavior of COVID-19 through the electromagnetic fields

Investigating the dynamical behavior of a system is an effective method to predict and control its future behavior. Studying the dynamic behavior of a virus can prevent the pathogenicity of a virus and save human lives during the disease epidemic. If the transmission of information from the virus genome to the environment is locked, the pathogenicity of the virus stops. Information transmission can be checked via the investigation of the spin information transport. In the current study, we have characterized the dynamical behavior of the virus by studying the spin transport through its RNA chain to estimate the information transfer path in the system. A voltage generator with adjustable frequency as a control system has been designed using the control theory of chaotic systems. Our aim is disturbing and reduces the transmitted information from viruses to the environment. The external stimuli can propel the system to the locked information transfer situation. Applying an external field noise with a specific frequency range (200-500 GHz) controlled through the external controller system can destroy the information transmitted by the virus to the environment. Disturbance intensity as a control parameter adjusts the external field frequency to push the system to the chaotic behavior which will be able to lock the information transfer and then prevent the spread of the epidemic.

OPTIMAL CONTROL FOR A DISCRETE TIME EPIDEMIC MODEL WITH ZONES EVOLUTION

In this paper, we present a new mathematical model to describe the evolution of an infectious disease in regions and between individuals. For this purpose we considered two systems, the first one for humans Si Ii Ri, where Si represents the number of susceptible, Ii of infected and Ri of cured. The second system ZiSZIiZRi represents the different types of regions, where Zis is the number of susceptible regions, where there are only susceptible people, after visiting an infected person, a susceptible region is likely to be infected, which we will note ZiI, the last compartment ZiR denotes the infected regions, which are restored after the recovery of all infected people. In addition, we considered three control strategies u, v and w to control the spread of the virus within regions and between individuals. Numerical examples are provided to illustrate the effectiveness of our proposed control strategy. © 2022 the author(s).

Application of Optimal Stopping Theory to Pandemic Lockdown Policies

During the COVID-19 pandemic, governments are facing challenges in determining the optimal time to exit the lockdown in their countries. A trade-off between health-related aspects and economic aspects should be achieved.This paper uses a discrete-time Markov Chain (DTMC) SIS model to find the optimal time to stop the lockdown. Two models are proposed: Model 1 assumes that the reproduction number R is constant over time, while Model 2 considers that R is time-dependent. The analysis of Model 1 leads to simple optimal policies. © 2022 IEEE.

Multi-state Discrete-time Markov Chain SVIRS Model on the Spread of COVID-19

This article discusses the spread of infectious diseases using the multi-state SVIRS model with the assumption that a discrete-time Markov chain (DTMC) occurs in a closed population that is regularly examined. This article aims to generate transition probabilities, which are then used to predict the number of confirmed cases in the next period. The multi-state SVIRS model uses four states, namely susceptible, vaccinated, infected, and recovered, followed by calculating the probabilities of each transition between states that are different from the compartment model. The model was applied to the COVID-19 data in Indonesia, which was analyzed using the statistical software R. The result showed that the transition probability of a person being infected according to the multistate model with the assumption of DTMC SVIRS on the COVID-19 data was around 25.38% including those with and without vaccination. In comparison, the probability of being recovered was about 92.34%. Then this transition probability was used to predict the confirmed cases of COVID-19 in the next few days. The prediction results were highly accurate with a MAPE value less than 10%. The main contribution of this research is the use of the DTMC assumption, which is a stochastic model in determining the parameters of the differential equation formed by the compartment model and adding the vaccinated state in the model. The vaccinated cases in this article used the proportion of the efficacy of each vaccine used by several susceptible individuals, which, according to WHO recommendations, should be given in two doses. The multi-state model with the assumption of DTMC can model chronic diseases and infectious diseases. This can be seen from the results of the analysis of the COVID-19 data in Indonesia, in which the short-term prediction results had a high level of accuracy. [ FROM AUTHOR] Copyright of Engineering Letters is the property of Newswood Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Inverse optimal control for positive impulsive systems toward personalized therapeutic regimens

Infectious diseases are latent threats to humankind. Control theoretical approaches can help practitioners to advance the scheduling of drugs. For the case of infectious diseases, it is not possible to keep continuous flow of drug administration over all time-steps, thus the action of the control input has to be restricted at some of the kth instants. This paper presents the adaptation of inverse optimal control to positive impulsive systems in discrete-time to schedule therapies. The properties of positive systems are used to simplify the control design. Thus, the problem of scheduling therapies in infectious diseases is illustrated with influenza and COVID-19. Numerical results show the applicability of the control algorithms. © 2022 John Wiley & Sons Ltd.

Quantitative feedback control of health care demand via non-pharmaceutical interventions during an epidemic

Once an infectious disease has become an epidemic and can no longer be contained, non-pharmaceutical public health interventions may be used to reduce infection rates so as to control demand on health care resources including staff and hospital facilities. Feedback control is shown to have limited possibilities due to (often unmodeled) non-minimum phase lag;uncertainty in model parameters and measurements;and the discrete time nature of practical controller implementation for the interventions. Classical susceptible-exposed-infected models do not capture real time delays in disease progression, or phase lag effects of discrete time feedback control. Non-minimum phase lag constraints are more severe if the number of hospitalized individuals rather than the number of infected individuals is used as the measurement variable.

On the Continuous-time and Discrete-Time Versions of an Alternative Epidemic Model of the SIR Class

The well-known SIR epidemic model is revisited. Continuous-time and discrete-time versions of an alternative model of this class are presented, discussed and validated with actual data. The proposed model follows from the calculation of the mean number of new infected cases due to the eventual meeting of susceptible and infected individuals, based on a simple probabilistic argument. Determination of the invariant set in the state space and convergence conditions towards equilibrium are established. For numerical analysis, data of daily number of new diagnosed cases provided by the Brazilian Ministry of Health and World Health Organization of COVID-19 outbreak that currently occurs respectively in Brazil and in the UK are used. Illustrations and model prediction analysis are provided and discussed from full data of both aforementioned countries which include more than 400 epidemic days. Three different and complementary strategies for parameter identification including the impact of causality on the optimal solution of the nonlinear mean square problem are discussed.

Effects of test timing and isolation length to reduce the risk of COVID-19 infection associated with airplane travel, as determined by infectious disease dynamics modeling.

Effective measures to reduce the risk of coronavirus disease 2019 (COVID-19) infection in overseas travelers are urgently needed. However, the effectiveness of current testing and isolation protocols is not yet fully understood. Here, we examined how the timing of testing and the number of tests conducted affect the spread of COVID-19 infection associated with airplane travel. We used two mathematical models of infectious disease dynamics to examine how different test protocols changed the density of infected individuals traveling by airplane and entering another country. We found that the timing of testing markedly affected the spread of COVID-19 infection. A single test conducted on the day before departure was the most effective at reducing the density of infected individuals travelling; this effectiveness decreased with increasing time before departure. After arrival, immediate testing was found to overlook individuals infected on the airplane. With respect to preventing infected individuals from entering the destination country, isolation with a single test on day 7 or 8 after arrival was comparable with isolation only for 11 or 14 days, respectively, depending on the model used, indicating that isolation length can be shortened with appropriately timed testing.