SIQR Model Research Articles

Optimal control analysis of fractional order delayed SIQR model for COVID-19

Optimal control analysis of fractional order delayed SIQR model for COVID-19

Time-Delay Dynamic Model and Cost-Effectiveness Analysis of Major Emergent Infectious Diseases with Transportation-Related Infection and Entry-Exit Screening

We analyze a time-delayed SIQR model that considers transportation-related infection and entry–exit screening. This model aims to determine the measures for preventing and controlling major emergent infectious diseases and the associated costs. We calculate the basic reproduction number (R0) and prove that the disease-free equilibrium is locally and globally asymptotically stable. We collect COVID-19 infection data from two regions in the United States in 2020 for data fitting, obtain a set of optimal parameter values, and find that transportation-related infection rates increase the basic reproduction number, enhancing the impact on disease spread. Entry–exit screening effectively suppresses the spread of disease by reducing the basic reproduction number. Furthermore, we investigate the influence of the incubation period on disease and find that a shorter incubation period results in a shorter duration but a larger scale of infection and that the peaks are reduced. We conduct a sensitivity analysis of the R0 and propose three measures to prevent the spread of new infectious diseases based on the most sensitive parameters: wearing masks, implementing urban closures, and administering medication to sick but not yet hospitalized patients promptly. In the case of COVID-19, optimal control effectively controls the development and deterioration of the disease. Finally, several control measures are compared through cost-effectiveness analysis, and the results show that wearing masks is the most cost-effective measure.

MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by a coronavirus originating from the city of Wuhan in 2019. This disease affects the respiratory system. The city of Pontianak has the highest population density in West Kalimantan. This density results in a higher spread of Covid-19. In this article, the spread of COVID-19 is formulated into a mathematical model, equilibrium points are sought, stability is analyzed, and a delay time is introduced to reduce the spread of COVID-19. The magnitude of the delay time given during quarantine complies with health protocols, which is between 2 – 14 days. This article aims to analyze the influence of the delay time in modeling the spread of Covid-19. The problem of COVID-19 spread is constructed into an SIQR model, with a sub-population of recovered individuals returning to the susceptible sub-population. The population is divided into four sub-populations: susceptible (S), Infected (I), Quarantined (Q), and Recovered (R). The parameters used include the natural birth rate ( ), the rate of susceptibility to infection ( ), the rate of infection under quarantine ( ), the recovery rate from infection ( ), the recovery rate from infection under quarantine ( ), the death rate from infection ( ), the death rate under quarantine ( ), the delay time from infection to quarantine process ( ), the natural death rate ( ), and the rate of recovered immunity returning to susceptibility ( ). The simulation results show that when the basic reproduction number is less than , the disease-free equilibrium is stable, and when the basic reproduction number is greater than , the endemic equilibrium point is stable. The addition of a time delay ( ) in the SIQR model affects the stability of the endemic equilibrium point but does not affect the stability of the disease-free equilibrium point.

Global stability of a fractional epidemiological SIQR model with two strains: delta and omicron coronavirus mutations

Global stability of a fractional epidemiological SIQR model with two strains: delta and omicron coronavirus mutations

Study of an SIQR model with optimal control techniques: A mathematical approach

In this article, a SIQR deterministic model with a non-linear incidence function for an infectious disease is formulated and analyzed. The well-posedness of the model is ensured with the help of the non-negativity and boundedness of the solution of the system. The basic reproduction number (R0) of the model is found. The sensitivity analysis of the basic reproduction number is discussed. The local and global stability of different equilibria of the model are discussed in terms of basic reproduction number. We use the center manifold theory to analyze the transcritical bifurcation exhibited by the system at R0=1 and found that the disease does not vanish even if R0<1 due to the occurrence of backward bifurcation. Furthermore, this model is extended to the optimal control model and is analyzed to determine the effect of screening and treatment as controls on the population dynamics through Pontryagin’s Maximum Principle. Moreover, we performed numerical analysis to illustrate our theoretical findings. We aim at determining the best intervention strategy to control the infectious diseases among screening, treatment and quarantine. We conclude that only screening is economically effective as compared to only treatment but the combined effort of screening and treatment is most effective and less expensive than single implementation of any control measure. Our study reveals that both the control interventions not only reduce the severity of disease burden but also minimize the economic burden to control the disease.

Optimal control strategies for a SAIQR model of epidemic disease

In this paper, an extended SIR mathematical model (SAIQR) along with an optimal control strategy is proposed to investigate the prevalence of a hypothetical epidemic. By providing controls and examining suitable strategies for control, the cost of control has been minimized. This is while the infected people have been reduced to a minimum in order to control the epidemic. After the full introduction of the model, while explaining the controls used in it, we will check the dimensions of these controls on different compartments. The simulations performed with the MATLAB software show the effectiveness of the controls applied on the model in the significant reduction of infected people.

Stability Analysis for the Spread of Mumps Based on SIQR Model

Mumps is an infectious disease caused by a virus that is quite dangerous because vaccine strategies often fail. In severe cases, mumps can lead to infection of the covering of the brain (15%), pancreatitis (4%), permanent deafness, and painful swelling of the testes which rarely causes infertility. In addition, genetic mutations that are continuously carried out by the virus and the movement of individuals from one area to another can result in the spread of causing an epidemic in an area. This study discusses the spread of mumps by assuming there is a population of individuals who are quarantined. In addition, it is possible to die from mumps in the presence of complications from other diseases. The purpose of this research is to look at the behavior of the system solution analytically depending on the basic reproduction number ( ) accompanied by numerical simulations on initial values with certain parameters. The SIQR model is used by assumes that individuals who have recovered will get permanent immunity against Mumps. The analysis was carried out around the disease-free equilibrium point and the endemic equilibrium point. It was found that the disease-free equilibrium point is locally asymptotically stable with conditions . This means that if the birth rate is less than the natural death rate and the contact rate between individuals infected with mumps and susceptible individuals is less than the sum of the recovery rate, death rate and quarantine rate, then the mumps outbreak will eventually disappear from the population. On the other hand, the local asymptotically stable endemic equilibrium point if . This means that if the mumps disease is about to become epidemic and infected individuals are still in the population. This can be interpreted as if the birth rate is greater than the natural death rate and the contact rate between individuals infected with mumps and susceptible individuals is greater than the sum of the recovery rate, death rate and quarantine rate then the mumps outbreak will still exist in the population. However, if the value of the quarantine rate is increased, the value will decrease and the quarantined individual population approaches the infected individual population. This means that the proposed quarantine scenario with the addition of class Q makes the system solution better. Furthermore, a simulation was carried out with the Maple 18 program.

Epidemic threshold of a COVID-19 model with gaussian white noise and semi-Markov switching

In this study, we investigate the COVID-19 propagation dynamics using a stochastic SIQR model with Gaussian white noise and semi-Markovian switching, focusing on the impacts of Gaussian white noise and semi-Markovian switching on the propagation dynamics of COVID-19. It is suggested that the fate of COVID-19 is entirely determined by the basic reproduction number R0, under mild extra conditions. By making sensitivity analysis on R0, we found that the effect of quarantine rate on R0 was more significant compared to transmission rate. Our results demonstrate that: (i) The presence of Gaussian white noise, while reducing the basic reproduction number R0 of COVID-19, also poses more challenges for the prediction and control of COVID-19 propagation. (ii) The conditional holding time distribution has a significant effect on the kinetics of COVID-19. (iii) The semi-Markov switching and Gaussian white noise can support irregular recurrence of COVID-19 outbreaks.

Asymptotic behavior of an SIQR epidemic model driven by Lévy jumps on scale-free networks

To investigate the effect of information transmission, Lévy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic, a stochastic SIQR epidemic model with non-monotone incidence rate and Lévy jumps on scale-free networks is constructed. At first, the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions. Then the stochastic model is made in accordance with the ecological significance, the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested. Next, by constructing suitable stochastic Lyapunov functions and applying Itô formula with jump, the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked. At last, the correctness of the analytical results is verified by numerical simulations.

Nonlinear PI control for semi-global asymptotic stabilization and robustness of SIQR model with inflow perturbations

For mitigation of the spread of human infectious diseases, this paper proposes nonlinear PI control laws of vaccination, isolation, and contact regulation. Using the SIQR model, the control laws are designed to achieve not only internal stability on an arbitrarily large domain in the state space, but also input-to-state stability with respect to inflow perturbations of immigrants and newborns. The control laws get rid of the precise knowledge of the nominal rates required by feedback control. This paper pursues incorporation of integral action in control to render a coarse estimate a real equilibrium. It is demonstrated how to accomplish it in the presence of severe range limitations of control inputs.

About the identifiability and observability of the SIR epidemic model with quarantine

We analyze the identifiability and observability of the well-known SIR epidemic model with an additional compartment Q of the sub-population of infected individuals that are placed in quarantine (SIQR model), considering that the flow of individuals placed in quarantine and the size of the quarantine population are known at any time. Then, we focus on the problem of identification of the model parameters and review different techniques.

Asymptotic comportment of a stochastic SIQR model with mean-reverting inhomogeneous geometric Brownian motion

Asymptotic comportment of a stochastic SIQR model with mean-reverting inhomogeneous geometric Brownian motion

Global Dynamics of a Filippov SIQR Model with Delayed Relay Control

Global Dynamics of a Filippov SIQR Model with Delayed Relay Control

MATHEMATICAL AND NUMERICAL ANALYSIS OF SIQR EPIDEMIC MODEL OF MEASLES DISEASE DYNAMICS

Measles is a highly transmissible disease in children around the world. According to the World Health Organization (WHO), 73% of deaths of children were due to measles in 2018. This study describes the physical solution of the SIQR model for measles spread under the effect of natural delay amongst different compartments. By three different numerical techniques, the efficacies of solutions of the underlying system have been compared and a clear preference of nonstandard finite-difference (NSFD) scheme over the rest has been established. It has also been observed, on principle, that the NSFD formulation recovers all the essential traits of a continuous model namely the boundedness, positivity and stability of equilibriums of populations. The numerical results have also been supported by a very strong classical analysis of the model where the existence of a solution vector in explicit subsets of the function spaces has been guaranteed which leads to optimization of fixed-point methods.

Isolation‐oriented Lyapunov‐based design of simultaneous feedback strategies for disease control of SIQR

AbstractThis article pursues a new approach to the design of feedback control laws mitigating the spread of human infectious diseases. The control inputs of vaccination, isolation, and outing/gathering regulation are derived as the gradient of a positive definite function of all the population variables of the SIQR model. Lyapunov functions in which susceptible and infected populations are decoupled are known to be non‐self‐sufficient for proving stability of the SIQR model as well as other variants of the SIR model. This fact has been hampering Lyapunov‐based control design of infectious disease models. This article demonstrates that a popular decoupled function can still serve as a control Lyapunov function as long as isolation is made state‐dependent. Techniques realizing this novel idea are presented and shown to allow the Lyapunov function to establish a robustness guarantee in terms of input‐to‐state stability with respect to immigration and newborn perturbation on an arbitrarily large domain. The effectiveness of the proposed simultaneous controller is illustrated through numerical simulations performed with a parameter set of COVID‐19.

A stochastic SIQR epidemic model with Lévy jumps and three-time delays

Isolation and vaccination are the two most effective measures in protecting the public from the spread of illness. The SIQR model with vaccination is widely used to investigate the dynamics of an infectious disease at population level having the compartments: susceptible, infectious, quarantined and recovered. The paper mainly aims to extend the deterministic model to a stochastic SQIR case with Lévy jumps and three-time delays, which is more suitable for modeling complex and instable environment. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. The dynamic properties of stochastic solution are studied around the disease-free and endemic equilibria of the deterministic model. Our results reveal that stochastic perturbation affect the asymptotic properties of the model. Numerical simulation shows the effects of interested parameters of theoretical results, including quarantine, vaccination and jump parameters. Finally, we apply both the stochastic and deterministic models to analyze the outbreak of mutant COVID-19 epidemic in Gansu Province, China.

Modified SIQR model for the COVID-19 outbreak in several countries.

In this paper, we propose a modified Susceptible‐Infected‐Quarantine‐Recovered (mSIQR) model, for the COVID‐19 pandemic. We start by proving the well‐posedness of the model and then compute its reproduction number and the corresponding sensitivity indices. We discuss the values of these indices for epidemiological relevant parameters, namely, the contact rate, the proportion of unknown infectious, and the recovering rate. The mSIQR model is simulated, and the outputs are fit to COVID‐19 pandemic data from several countries, including France, US, UK, and Portugal. We discuss the epidemiological relevance of the results and provide insights on future patterns, subjected to health policies.

Semi-global input-to-state stabilization of SIQR model with isolation, outing regulation, and vaccination in staircase form

This paper proposes staircase-like feedback laws for control of human infectious diseases based on the SIQR model in the situation where vaccine administration alone cannot be sufficient. The control inputs consisting of isolation, contact regulation, and vaccination are designed to achieve input-to-state stability (ISS) with respect to uncertainty that includes perturbation of immigrants and newborns. The designed controller is semi-global so that the ISS guarantee can be obtained on an arbitrary large compact set in the state space. To accomplish the practical control implementation, this paper qualifies a simple separable function as a control Lyapunov function.

SARS-CoV-2 Disease in Cameroon:&amp;nbsp; Theoretical and Computational Analysis of a Delayed SIQR Model with Optimal Control

SARS-CoV-2 Disease in Cameroon:&amp;nbsp; Theoretical and Computational Analysis of a Delayed SIQR Model with Optimal Control

Propagation dynamics in a diffusive SIQR model for childhood diseases

&lt;p style='text-indent:20px;'&gt;This paper is concerned with the propagation dynamics in a diffusive susceptible-infective nonisolated-isolated-removed model that describes the recurrent outbreaks of childhood diseases. To model the spatial-temporal modes on disease spreading, we study the traveling wave solutions and the initial value problem with special decay condition. When the basic reproduction ratio of the corresponding kinetic system is larger than one, we define a threshold that is the minimal wave speed of traveling wave solutions as well as the spreading speed of some components. From the viewpoint of mathematical epidemiology, the threshold is monotone decreasing in the rate at which individuals leave the infective and enter the isolated classes.&lt;/p&gt;