A Study on Optimal Control of a COVID-19 Transmission Model with the Significance of Early Screening and Testing Measures

In this paper, we present a deterministic SEQIR mathematical model that describes the transmission dynamics of COVID-19 that also in-cludes testing procedures in the quarantine stage. The reproduction number R0 is derived with some properties of the model. The stabil-ity of equilibrium points is analyzed. An objective function is pro-posed and optimal control strategies are derived using Pontryagin's Maximum Principle. The existence and uniqueness of an optimal-ity system are demonstrated. Numerical simulations are presented in different scenarios with the control interventions early screening, prevention measures of COVID-19, and following a healthy lifestyle. The main objective of the paper is to eradicate the disease in exposed stage. The chosen control variables helps us to reduce the exposed population. (c) 2023 L&H Scientific Publishing, LLC. All rights reserved.

Vaccination Model and Optimal Control Analysis of Novel Corona Virus Transmission Dynamics

In this paper, the mathematical model of the coronavirus pandemic with vaccination is formulated and analyzed to show the impact of severe acute respiratory syndrome coronavirus 2 pathogens in the environmental reservoir. In the model analysis, the vaccination-induced reproduction number which helps us in establishing the local and global stability of COVID-19-free and endemic equilibrium points was derived. The local stability of the COVID-19-free equilibrium is established via the Jacobian matrix and Routh-Hurwitz criteria. In contrast, the global stability of the endemic equilibrium is proved by using an appropriate Lyapunov function. Sensitivity indices are also discussed. The proposed model is extended into the optimal control problem by incorporating three control variables: preventive, medical care, and surface disinfection. Then, the necessary conditions for the optimal control of the disease were analyzed by applying Pontryagin minimum principle. Finally, the numerical simulations indicated that a combination of medical care and surface disinfection strategies is effective in controlling the disease epidemic. [ FROM AUTHOR] Copyright of Journal of Mathematical Sciences is the property of Springer Nature 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.)

Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number (R0) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of R0 to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time -dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

Mathematical modeling of COVID-19 and Omicron outbreak spread: Optimal control approach for intervention strategies

In Morocco, 966,777 confirmed cases and 14,851 confirmed deaths because of COVID-19 were recorded as of January 1, 2022. Recently, a new strain of COVID-19, the so-called Omicron variant, was reported in Morocco, which is considered to be more dangerous than the existing COVID-19 virus. To end this ongoing global COVID-19 pandemic and Omicron variant, there is an urgent need to implement multiple population-wide policies like vaccination, testing more people, and contact tracing. To forecast the pandemic's progress and put together a strategy to effectively contain it, we propose a new hybrid mathematical model that predicts the dynamics of COVID-19 in Morocco, considering the difference between COVID-19 and the Omicron variant, and investigate the impact of some control strategies on their spread. The proposed model monitors the dynamics of eight compartments, namely susceptible (S)$$ (S) $$, exposed (E)$$ (E) $$, infected with COVID-19 (I)$$ (I) $$, infected with Omicron (IO)$$ \left({I}_O\right) $$, hospitalized (H)$$ (H) $$, people in intensive care units (U)$$ (U) $$, quarantined (Q)$$ (Q) $$, and recovered (R)$$ (R) $$, collectively expressed as SEIIOHUQR$$ SEI{I}_O HUQR $$. We calculate the basic reproduction number Script capital R0$$ {\mathcal{R}}_0 $$, studying the local and global infection-free equilibrium stability, a sensitivity analysis is conducted to determine the robustness of model predictions to parameter values, and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in Morocco. We incorporate two control variables that represent vaccination and diagnosis of infected individuals and we propose an optimal strategy for an awareness program that will help to decrease the rate of the virus' spread. Pontryagin's maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, extensive numerical simulations are employed with and without controls to illustrate our results using MATLAB software. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by vaccinating and diagnosing the susceptible individuals, can effectively reduce the basic reproduction number and tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended period of time. The model simulations demonstrate that the elimination of the ongoing SARS-COV-2 pandemic and its variant Omicron in Morocco is possible by implementing, at the start of the pandemic, a strategy that combines the two variables of control mentioned above. Our predictions are based on real data with reasonable assumptions.

A dynamic approach to supply chain reconfiguration and ripple effect analysis in an epidemic.

The COVID-19 pandemic has illustrated the unprecedented challenges of ensuring the continuity of operations in a supply chain as suppliers' and their suppliers stop producing due the spread of infection, leading to a degradation of downstream customer service levels in a ripple effect. In this paper, we contextualize a dynamic approach and propose an optimal control model for supply chain reconfiguration and ripple effect analysis integrated with an epidemic dynamics model. We provide supply chain managers with the optimal choice over a planning horizon among subsets of interchangeable suppliers and corresponding orders; this will maximize demand satisfaction given their prices, lead times, exposure to infection, and upstream suppliers' risk exposure. Numerical illustrations show that our prescriptive forward-looking model can help reconfigure a supply chain and mitigate the ripple effect due to reduced production because of suppliers' infected workers. A risk aversion factor incorporates a measure of supplier risk exposure at the upstream echelons. We examine three scenarios: (a) infection limits the capacity of suppliers, (b) the pandemic recedes but not at the same pace for all suppliers, and (c) infection waves affect the capacity of some suppliers, while others are in a recovery phase. We illustrate through a case study how our model can be immediately deployed in manufacturing or retail supply chains since the data are readily accessible from suppliers and health authorities. This work opens new avenues for prescriptive models in operations management and the study of viable supply chains by combining optimal control and epidemiological models.

COVID-19 SIR model: Bifurcation analysis and optimal control

This paper proposes a SIR epidemic model with vital dynamics to control or eliminate the spread of the COVID-19 epidemic considering the constant population, saturated treatment, and direct-indirect transmission rate of the model. We demonstrate positivity, boundness and calculate the disease-free equilibrium point and basic reproduction number from the model. We use the Jacobian matrix and the Lyapunov function to analyze the local and global stability, respectively. It is observed that indirect infection increases the basic reproduction number and gives rise to multiple endemic diseases. We perform transcritical, forward, backward, and Hopf bifurcation analyses. We propose two control parameters (Use of face mask, hand sanitizer, social distancing, and vaccination) to minimize the spread of the coronavirus. We use Pontryagin's maximum principle to solve the optimal control problem and demonstrate the results numerically.

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

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

Three dimensional epidemic model with non-monotonic incidence and saturated treatment: A case study of SARS infection of Hong Kong 2003 scenario

In this paper, we have proposed a mathematical compartmental model with non-monotonic incidence and saturated treatment and we have validated the model with SARS infection in Hong Kong, 2003. We have analysed the stability of disease free and endemic equilibria as well as different bifurcations. We have shown that the epidemic disappears if the cure rate of treatment crosses a threshold value. We have obtained a necessary and sufficient condition for backward bifurcation, which shows the basic reproduction number less than unity is not sufficient to eradicate the disease completely. Saddle–node and Hopf bifurcation with respect to awareness factor have been investigated, which shows that the awareness factor is effective to change the disease dynamics. The model has been fitted to SARS cases in Hong Kong. The most effective parameters for controlling infections have been identified through sensitivity analysis. Moreover, we have investigated how the number of infected cases reduces if there was some vaccination polices in SARS infection. Finally, the model has been also used as an optimal control problem as vaccination and treatment controls are time dependent functions.

Measuring the Performance of Retailers during the COVID-19 Pandemic: Embedding Optimal Control Theory Principles in a Dynamic Data Envelopment Analysis Approach

Traditional retailers (bricks-and-mortar) have been continuously increasing online sales. However, not all retail companies were able to respond to the increasing sales with the same efficiency level as their competitors. This paper aims to propose a dynamic model – incorporating principles of Optimal Control Theory (OCT) into a Data Envelopment Analysis (DEA) model - for measuring the performance of retailing companies' cost efficiency. It also aims to contribute through the application by investigating the impact of the pandemic on companies from the most prominent developing market in Latin America, Brazil. Twenty-one companies publicly traded in the São Paulo Stock Exchanges (B3) between the third quarter of 2018 (3Q2018) and the third quarter of 2020 (3Q2020) were investigated. Also, six measures - initial inventory cost (IIC), final inventory cost (FIC), net operating income (NOI), cost of goods sold (COGS), cost of the purchased product (CPP), and plant, property, and equipment (PPE) – were considered. In this way, the findings have implications for researchers and practitioners. Practitioners can discover which competitor(s) is (are) adopting the best practices at each operational aspect (e.g., inventory cost). Additionally, the proposed method can be replicated in other markets (developing or not) and for other categories of retailing companies (e.g., small- and middle-sized). Further research directions are presented, and their implications are discussed.

A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models

This paper presents a spectral approach to the uncertainty management in epidemic models through the formulation of chance-constrained stochastic optimal control problems. Specifically, a statistical moment-based polynomial expansion is used to calculate surrogate models of the stochastic state variables of the problem that allow for the efficient computation of their main statistics as well as their marginal and joint probability density functions at each time instant, which enable the uncertainty management in the epidemic model. Moreover, the surrogate models are employed to perform the corresponding sensitivity and risk analyses. The proposed methodology provides the designers of the optimal control policies with the capability to increase the predictability of the outcomes by adding suitable chance constraints to the epidemic model and formulating a proper cost functional. The chance-constrained optimal control of a COVID-19 epidemic model is considered in order to illustrate the practical application of the proposed methodology.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application.

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R0 < 1 and the exogenous reinfection rate greater than a threshold (η > Î·∗). The analytical results show that reducing R0 < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

Nonlinear analysis and dynamics of COVID-19 mathematical model with optimal control strategies

Efficacy of the healthcare system and illumination (awareness) activities control COVID-19. To defend public health, the spreading pandemic of COVID-19 disease necessitates social distancing, wearing masks, personal cleanliness, and precautions. Due to inadequate awareness programs, COVID-19 rapidly increases in India. The primary goal of this research is to investigate the spreading behavior of the COVID-19 virus in India when people are aware of the disease. We find the optimum value of disease transmission rate and detection of the unidentified asymptomatic and symptomatic populations. An optimal control problem is designed with limited resource allocation to improve the recovered individuals. A stability analysis presents for emphasizes the relevance of disease awareness in preventing the spread of the disease. The control parameters are used to explore the increase and decrease of the infected individual with and without control in optimal control analysis. The model is simulated using the Hattaf-fractional derivative to study the memory effect in the epidemic. To adapt the model to the total number of reported COVID-19 cases in India, we collected data from March 20, 2021 to September 30, 2021. According to the simulation results, the pandemic would spread faster if awareness campaigns were improperly carried out.

Lessons drawn from Shanghai for controlling highly transmissible SARS-CoV-2 variants: insights from a modelling study.

BACKGROUND: The continuous emergence of novel SARS-CoV-2 variants with markedly increased transmissibility presents major challenges to the zero-COVID policy in China. It is critical to adjust aspects of the policy about non-pharmaceutical interventions (NPIs) by searching for and implementing more effective ways. We use a mathematical model to mimic the epidemic pattern of the Omicron variant in Shanghai to quantitatively show the control challenges and investigate the feasibility of different control patterns in avoiding other epidemic waves. METHODS: We initially construct a dynamic model with a core step-by-step release strategy to reveal its role in controlling the spread of COVID-19, including the city-based pattern and the district-based pattern. We used the least squares method and real reported case data to fit the model for Shanghai and its 16 districts, respectively. Optimal control theory was utilized to explore the quantitative and optimal solutions of the time-varying control strength (i.e., contact rate) to suppress the highly transmissible SARS-CoV-2 variants. RESULTS: The necessary period for reaching the zero-COVID goal can be nearly 4 months, and the final epidemic size was 629,625 (95%CI: [608,049, 651,201]). By adopting the city-based pattern, 7 out of 16 strategies released the NPIs more or earlier than the baseline and ensured a zero-resurgence risk at the average cost of 10 to 129 more cases in June. By adopting the district-based pattern, a regional linked release can allow resumption of social activity to ~ 100% in the boundary-region group about 14 days earlier and allow people to flow between different districts without causing infection resurgence. Optimal solutions of the contact rate were obtained with various testing intensities, and higher diagnosis rate correlated with higher optimal contact rate while the number of daily reported cases remained almost unchanged. CONCLUSIONS: Shanghai could have been bolder and more flexible in unleashing social activity than they did. The boundary-region group should be relaxed earlier and more attention should be paid to the centre-region group. With a more intensive testing strategy, people could return to normal life as much as possible but still ensure the epidemic was maintained at a relatively low level.

Fractional modeling and optimal control strategies for mutated COVID‐19 pandemic

As the COVID‐19 continues to mutate, the number of infected people is increasing dramatically, and the vaccine is not enough to fight the mutated strain. In this paper, a SEIR‐type fractional model with reinfection and vaccine inefficacy is proposed, which can successfully capture the mutated COVID‐19 pandemic. The existence, uniqueness, boundedness, and nonnegativeness of the fractional model are derived. Based on the basic reproduction number R0$$ {R}_0 $$, locally stability and globally stability are analyzed. The sensitivity analysis evaluate the influence of each parameter on the R0$$ {R}_0 $$ and rank key epidemiological parameters. Finally, the necessary conditions for implementing fractional optimal control are obtained by Pontryagin's maximum principle, and the corresponding optimal solutions are derived for mitigation COVID‐19 transmission. The numerical results show that humans will coexist with COVID‐19 for a long time under the current control strategy. Furthermore, it is particularly important to develop new vaccines with higher protection rates. [ FROM AUTHOR] Copyright of Mathematical Methods in the Applied Sciences is the property of John Wiley & Sons, Inc. 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.)

Mathematical Modeling of Covid-19 Transmission in Jakarta with Optimal Control Strategy

Covid19 has infected many individuals around the world, this virus is spreading rapidly. In the context of controlling and handling the spread of COVID-19, appropriate strategies and policies are needed, mathematics will play a very important role in this problem, especially to provide information about this with an understanding of the dynamics of the transmission of this covid virus. To suppress the spread of the Covid-19 virus which is currently hitting, several countries have implemented large-scale social restrictions. To identify the best approach to reduce of this Covid-19 disease spreading at minimal cost, we developed a mathematical model of the covid 19 virus by implementing large-scale social restrictions and applying optimal control theory. We provide two types of control: the first is in the form of an education campaign about covid-19 and an awareness program, and the second is in the form of a quarantine program. Compared with no optimal control, giving optimal control can provide a more significant reduction in the number of populations S, Sr, O, P, I and increase the number of individual populations that recover more significantly.

Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies

The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of a COVID-19 model that provides insights into the dynamics of the disease. For this, we propose a new L S H S E A I H R COVID-19 model, where susceptible populations are divided into two sub-classes: low-risk susceptible populations, L S , and high-risk susceptible populations, H S . The aim of the subdivision of susceptible populations is to construct a model that is more reliable and realistic for disease control. We first prove the existence of a unique solution to the purposed model with the help of fundamental theorems of functional analysis and show that the solution lies in an invariant region. We compute the basic reproduction number and describe constraints that ensure the local and global asymptotic stability at equilibrium points. A sensitivity analysis is also carried out to identify the model's most influential parameters. Next, as a disease transmission control technique, a class of isolation is added to the intended L S H S E A I H R model. We suggest simple fixed controls through the adjustment of quarantine rates as a first control technique. To reduce the spread of COVID-19 as well as to minimize the cost functional, we constitute an optimal control problem and develop necessary conditions using Pontryagin's maximum principle. Finally, numerical simulations with and without controls are presented to demonstrate the efficiency and efficacy of the optimal control approach. The optimal control approach is also compared with an approach where the state model is solved numerically with different time-independent controls. The numerical results, which exhibit dynamical behavior of the COVID-19 system under the influence of various parameters, suggest that the implemented strategies, particularly the quarantine of infectious individuals, are effective in significantly reducing the number of infected individuals and achieving herd immunity. [ FROM AUTHOR] Copyright of Mathematics (2227-7390) is the property of MDPI 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.)

A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries.

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number (R0). Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population.

A novel mathematical model for prioritization of individuals to receive vaccine considering governmental health protocols.

Infectious diseases drive countries to provide vaccines to individuals. Due to the limited supply of vaccines, individuals prioritize receiving vaccinations worldwide. Although, priority groups are formed based on age groupings due to the restricted decision-making time. Governments usually ordain different health protocols such as lockdown policy, mandatory use of face masks, and vaccination during the pandemics. Therefore, this study considers the case of COVID-19 with a SEQIR (susceptible-exposed-quarantined-infected-recovered) epidemic model and presents a novel prioritization technique to minimize the social and economic impacts of the lockdown policy. We use retail units as one of the affected parts to demonstrate how a vaccination plan may be more effective if individuals such as retailers were prioritized and age groups. In addition, we estimate the total required vaccine doses to control the epidemic disease and compute the number of vaccine doses supplied by various suppliers. The vaccine doses are determined using optimal control theory in the solution technique. In addition, we consider the effect of the mask using policy in the number of vaccine doses allocated to each priority group. The model's performance is evaluated using an illustrative scenario based on a real case.

Some Forms of Open Multifunctions in Ideal Topological Spaces

We applied sensitivity analysis and optimum control to the COVID-19 model in this research. In addition, the basic reproduction number calculated as 1.57 indicates that this illness is widespread across Indonesia. The most important factor in this model is the contact rate with infected people, with or without comorbidity. Optimal control will minimize the number of infected populations without and with comorbidity, and costs. Numerical experiments will be carried out to describe and compare the graphical models of the spread of COVID-19 with and without controls. From the numerical results and cost-effectiveness analysis on the optimal control problem, it is found that applying a combination of controls can give the best results compared to a single control.

Dynamic stability and optimal control of SIS q I q RS epidemic network.

We develop a complex network-based SIS q I q RS model, calculate the threshold R 0 of infectious disease transmission and analyze the stability of the model. In the model, three control measures including isolation and vaccination are considered, where the isolation is structured in isolation of susceptible nodes and the isolation of infected nodes. We regard these three kinds of controls as time-varying variables, and obtain the existence and the solution of the optimal control by using the optimal control theory. With regard to the stability of the model, sensitivity analysis of the parameters and optimal control, we carry out numerical simulations. From the simulation results, it is obvious that when the three kinds of controls exist simultaneously, the scale and cost of the disease are minimal. Finally, we fit the real data of COVID-19 to the numerical solution of the model.