Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness

A novel collocation method with a coronavirus optimization algorithm for the optimal control of COVID-19: A case study of Wuhan, China

In this study, we develop a numerical optimization approach to address the challenge of optimal control in the spread of COVID-19. We evaluate the impact of various control strategies aimed at reducing the number of exposed and infectious individuals. Our novel approach employs Legendre wavelets, their derivative operational matrix, and a collocation method to transform the COVID-19 transmission optimal control model into a nonlinear programming (NLP) problem. To solve this problem, we employ a coronavirus optimization algorithm (COVIDOA) to determine the optimal control, state variables, and objective value. We investigate three control plans for this highly contagious disease, focusing on individual protection, rapid detection and treatment, detection with delay in treatment, and environmental viral dispersion as time-based control functions. These strategies are applied within an SEIR-type control model specific to COVID-19 in China, designed to mitigate disease spread. Lastly, we analyze the effects of various parameters within the COVID-19 spread model. Our numerical results highlight the significant impact of strategies that minimize the number of exposed and infectious individuals, particularly those related to rapid detection, detection delay, and environmental viral dispersion, in controlling and preventing the transmission of the COVID-19 virus.

Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach

COVID-19 is an infectious disease that causes millions of deaths worldwide, and it is the principal leading cause of morbidity and mortality in all nations. Although the governments of developed and developing countries are enforcing their universal control strategies, more precise and cost-effective single or combination interventions are required to control COVID-19 outbreaks. Using proper optimal control strategies with appropriate cost-effectiveness analysis is important to simulate, examine, and forecast the COVID-19 transmission phase. In this study, we developed a COVID-19 mathematical model and considered two important features including direct link between vaccination and latently population, and practical healthcare cost by separation of infections into Mild and Critical cases. We derived basic reproduction numbers and performed mesh and contour plots to explore the impact of different parameters on COVID-19 dynamics. Our model fitted and calibrated with number of cases of the COVID-19 data in Bangladesh as a case study to determine the optimal combinations of interventions for particular scenarios. We evaluated the cost-effectiveness of varying single and combinations of three intervention strategies, including transmission control, treatment, and vaccination, all within the optimal control framework of the single-intervention policies; enhanced transmission control is the most cost-effective and prompt in declining the COVID-19 cases in Bangladesh. Our finding recommends that a three-intervention strategy that integrates transmission control, treatment, and vaccination is the most cost-effective compared to single and double intervention techniques and potentially reduce the overall infections. Other policies can be implemented to control COVID-19 depending on the accessibility of funds and policymakers' judgments.

Anti-infection effects of heparin on SARS-CoV-2 in a diabetic mouse model

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can result in more severe syndromes and poorer outcomes in patients with diabetes and obesity. However, the precise mechanisms responsible for the combined impact of corona virus disease 2019 (COVID-19) and diabetes have not yet been elucidated, and effective treatment options for SARS-CoV-2-infected diabetic patients remain limited. To investigate the disease pathogenesis, K18-hACE2 transgenic (hACE2 Tg) mice with a leptin receptor deficiency (hACE2-Lepr -/-) or high-fat diet (hACE2-HFD) background were generated. The two mouse models were intranasally infected with a 5×10 5 median tissue culture infectious dose (TCID 50) of SARS-CoV-2, with serum and lung tissue samples collected at 3 days post-infection. The hACE2-Lepr -/- mice were then administered a combination of low-molecular-weight heparin (LMWH) (1 mg/kg or 5 mg/kg) and insulin via subcutaneous injection prior to intranasal infection with 1×10 4 TCID 50 of SARS-CoV-2. Daily drug administration continued until the euthanasia of the mice. Analyses of viral RNA loads, histopathological changes in lung tissue, and inflammation factors were conducted. Results demonstrated similar SARS-CoV-2 susceptibility in hACE2 Tg mice under both lean (chow diet) and obese (HFD) conditions. However, compared to the hACE2-Lepr +/+ mice, hACE2-Lepr -/- mice exhibited more severe lung injury, enhanced expression of inflammatory cytokines and hypoxia-inducible factor-1α, and increased apoptosis. Moreover, combined LMWH and insulin treatment effectively reduced disease progression and severity, attenuated lung pathological changes, and mitigated inflammatory responses. In conclusion, pre-existing diabetes can lead to more severe lung damage upon SARS-CoV-2 infection, and LMWH may be a valuable therapeutic approach for managing COVID-19 patients with diabetes.

Cost of the COVID-19 pandemic versus the cost-effectiveness of mitigation strategies in EU/UK/OECD: a systematic review

OBJECTIVES

The economic burden of COVID-19 pandemic is substantial, with both direct and indirect costs playing a significant role.

DESIGN

A systematic literature review was conducted to estimate the cost of the COVID-19 pandemic and the cost-effectiveness of pharmaceutical or non-pharmaceutical interventions. All cost data were adjusted to the 2021 Euro, and interventions compared with null.

DATA SOURCES

Ovid MEDLINE and EMBASE were searched from January 2020 through 22 April 2021.

ELIGIBILITY CRITERIA

Studies regarding COVID-19 outbreak or public health preparedness measures or interventions with outcome measures related to the direct and indirect costs for disease and preparedness and/or response in countries of the European Union (EU), the European Economic Area (EEA), the UK and the Organisation for Economic Co-operation and Development (OECD) of all relevant epidemiological designs which estimate cost within the selected time frame were considered eligible.

DATA EXTRACTION AND SYNTHESIS

Studies were searched, screened and coded independently by two reviewers with high measure of inter-rater agreement. Data were extracted to a predefined data extraction sheet. The risk of bias was assessed using the Consensus on Health Economic Criteria checklist.

RESULTS

We included data from 41 economic studies. Ten studies evaluated the cost of the COVID-19 pandemic, while 31 assessed the cost-benefit of public health surveillance, preparedness and response measures. Overall, the economic burden of the COVID-19 pandemic was found to be substantial. Community screening, bed provision policies, investing in personal-protective-equipment and vaccination strategies were cost-effective. Physical distancing measures were associated with health benefits; however, their cost-effectiveness was dependent on the duration, compliance and the phase of the epidemic in which it was implemented.

CONCLUSIONS

COVID-19 pandemic is associated with substantial short-term and long-term economic costs to healthcare systems, payers and societies, while interventions including testing and screening policies, vaccination and physical distancing policies were identified as those presenting cost-effective options to deal with the pandemic, dependent on population vaccination and the Re at the stage of the pandemic.

A nonlinear mathematical model on the Covid-19 transmission pattern among diabetic and non-diabetic population

In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples.

Sliding dynamics and bifurcations of a human influenza system under logistic source and broken line control strategy

This paper proposes a non-smooth human influenza model with logistic source to describe the impact on media coverage and quarantine of susceptible populations of the human influenza transmission process. First, we choose two thresholds $ I_{T} $ and $ S_{T} $ as a broken line control strategy: Once the number of infected people exceeds $ I_{T} $, the media influence comes into play, and when the number of susceptible individuals is greater than $ S_{T} $, the control by quarantine of susceptible individuals is open. Furthermore, by choosing different thresholds $ I_{T} $ and $ S_{T} $ and using Filippov theory, we study the dynamic behavior of the Filippov model with respect to all possible equilibria. It is shown that the Filippov system tends to the pseudo-equilibrium on sliding mode domain or one endemic equilibrium or bistability endemic equilibria under some conditions. The regular/virtulal equilibrium bifurcations are also given. Lastly, numerical simulation results show that choosing appropriate threshold values can prevent the outbreak of influenza, which implies media coverage and quarantine of susceptible individuals can effectively restrain the transmission of influenza. The non-smooth system with logistic source can provide some new insights for the prevention and control of human influenza.

Fractional model analysis of COVID-19 spread based on big data platform

Based on the data of COVID-19, this paper establishes the FCSEIR model for the spread through data analysis and designs the related simulation software. Using the data from Shanghai, the spread of the virus was simulated and predicted, and the process from outbreak to control of this infectious disease was better analyzed.

A fractal-fractional COVID-19 model with a negative impact of quarantine on the diabetic patients

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange’s interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.

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%.

A patchy theoretical model for the transmission dynamics of SARS-Cov-2 with optimal control

Short-term human movements play a major part in the transmission and control of COVID-19, within and between countries. Such movements are necessary to be included in mathematical models that aim to assist in understanding the transmission dynamics of COVID-19. A two-patch basic mathematical model for COVID-19 was developed and analyzed, incorporating short-term human mobility. Here, we modeled the human mobility that depended on its epidemiological status, by the Lagrangian approach. A sharp threshold for disease dynamics known as the reproduction number was computed. Particularly, we portrayed that when the disease threshold is less than unity, the disease dies out and the disease persists when the reproduction number is greater than unity. Optimal control theory was also applied to the proposed model, with the aim of investigating the cost-effectiveness strategy. The findings were further investigated through the usage of the results from the cost objective functional, the average cost-effectiveness ratio (ACER), and then the infection averted ratio (IAR).

A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function☆

The aim of this paper is to present and analyze the fractional optimal control model for COVID-19 and diabetes co-dynamics, using the Atangana-Baleanu derivative. The positivity and boundedness of the solutions was shown by the method of Laplace transform. The existence and uniqueness of the solutions of the proposed model were established using Banach fixed point Theorem and Leray–Schauder alternative Theorem. The fractional model was also shown to be Hyers-Ulam stable. The model was fitted to the cumulative confirmed daily COVID-19 cases for Indonesia. The simulations of the total number of hospitalized individuals co-infected with COVID-19 and diabetes, at different face-mask compliance levels, when vaccination strategy is maintained reveals that the total number of hospitalized co-infection cases decreases with increase in face-mask compliance levels, while maintaining COVID-19 vaccination. The simulation results show that to curtail COVID-19 and diabetes co-infections, policies and measures to enforce mass COVID-19 vaccination and strict face-mask usage in the public must be put in place. To further cut down the spread of COVID-19 and diabetes co-infection, time dependent controls are added into the fractional model, and the obtained optimal control problem investigated via the Pontryagin’s Maximum Principle.

Optimal control design incorporating vaccination and treatment on six compartment pandemic dynamical system

In this paper, a mathematical model of the COVID-19 pandemic with lockdown that provides a more accurate representation of the infection rate has been analyzed. In this model, the total population is divided into six compartments: the susceptible class, lockdown class, exposed class, asymptomatic infected class, symptomatic infected class, and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method and presented graphically based on different progression rates and effective contact rates of infective individuals. The COVID-19 epidemic model exhibits the disease-free equilibrium and endemic equilibrium. The local and global stability analysis has been done at the disease-free and endemic equilibrium based on R0. The stability analysis of the model shows that the disease-free equilibrium is both locally and globally stable when R0<1, and the endemic equilibrium is locally and globally stable when R0>1 under some conditions. A control strategy including vaccination and treatment has been studied on this pandemic model with an objective functional to minimize. Finally, numerical simulation of the COVID-19 outbreak in India is carried out using MATLAB, highlighting the usefulness of the COVID-19 pandemic model and its mathematical analysis.

On fractal-fractional Covid-19 mathematical model

In this article, we are studying a Covid-19 mathematical model in the fractal-fractional sense of operators for the existence of solution, Hyers-Ulam (HU) stability and computational results. For the qualitative analysis, we convert the model to an equivalent integral form and investigate its qualitative analysis with the help of iterative convergent sequence and fixed point approach. For the computational aspect, we take help from the Lagrange's interpolation and produce a numerical scheme for the fractal-fractional waterborne model. The scheme is then tested for a case study and we obtain interesting results.

Mathematical modeling and stability analysis of the COVID-19 with quarantine and isolation

The present paper focuses on the modeling of the COVID-19 infection with the use of hospitalization, isolation and quarantine. Initially, we construct the model by spliting the entire population into different groups. We then rigorously analyze the model by presenting the necessary basic mathematical features including the feasible region and positivity of the problem solution. Further, we evaluate the model possible equilibria. The theoretical expression of the most important mathematical quantity of major public health interest called the basic reproduction number is presented. We are taking into account to study the disease free equilibrium by studying its local and global asymptotical analysis. We considering the cases of the COVID-19 infection of Pakistan population and find the parameters using the estimation with the help of nonlinear least square and have R 0 ≈ 1 . 95 . Further, to determine the influence of the model parameters on disease dynamics we perform the sensitivity analysis. Simulations of the model are presented using estimated parameters and the impact of various non-pharmaceutical interventions on disease dynamics is shown with the help of graphical results. The graphical interpretation justify that the effective utilization of keeping the social-distancing, making the quarantine of people (or contact-tracing policy) and to make hospitalization of confirmed infected people that dramatically reduces the number of infected individuals (enhancing the quarantine or contact-tracing by 50% from its baseline reduces 84% in the predicted number of confirmed infected cases). Moreover, it is observed that without quarantine and hospitalization the scenario of the disease in Pakistan is very worse and the infected cases are raising rapidly. Therefore, the present study suggests that still, a proper and effective application of these non-pharmaceutical interventions are necessary to curtail or minimize the COVID-19 infection in Pakistan.

Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey

In the present paper, interactions between COVID-19 and diabetes are investigated using real data from Turkey. Firstly, a fractional order pandemic model is developed both to examine the spread of COVID-19 and its relationship with diabetes. In the model, diabetes with and without complications are adopted by considering their relationship with the quarantine strategy. Then, the existence and uniqueness of solution are examined by using the fixed point theory. The dynamic behaviors of the equilibria and their stability analysis are studied. What is more, with the help of least-squares curve fitting technique (LSCFT), the fitting of the parameters is implemented to predict the direction of COVID-19 by using more accurately generated parameters. By trying to minimize the mean absolute relative error between the plotted curve for the infected class solution and the actual data of COVID-19, the optimal values of the parameters used in numerical simulations are acquired successfully. In addition, the numerical solution of the mentioned model is achieved through the Adams-Bashforth-Moulton predictor-corrector method. Meanwhile, the sensitivity analysis of the parameters according to the reproduction number is given. Moreover, numerical simulations of the model are obtained and the biological interpretations explaining the effects of model parameters are performed. Finally, in order to point out the advantages of the fractional order modeling, the memory trace and hereditary traits are taken into consideration. By doing so, the effect of the different fractional order derivatives on the COVID-19 pandemic and diabetes are investigated.

A new fuzzy fractal control approach of non-linear dynamic systems: The case of controlling the COVID-19 pandemics

This article is presenting a first attempt on a proposed fuzzy fractal control method for efficiently controlling nonlinear dynamic systems. The main goal is to combine the main advantages of fractal theoretical concepts and fuzzy logic theory for achieving efficient control of nonlinear dynamic systems. The concept coming from Fractal theory, known as the fractal dimension, can be utilized to measure the complexity of the dynamic behavior of a non-linear plant. On the other hand, fuzzy logic theory can be used to represent and capture the expert knowledge in controlling a plant. In addition, fuzzy logic enables to manage the uncertainty involved in the decision-making process for achieving efficient control of a non-linear plant. We illustrate the proposed fuzzy fractal control method with the current worldwide situation that requires achieving an efficient control of the COVID-19 pandemics.