Optimal Control Analysis Research Articles

Optimal Control Analysis of COVID-19 Transmission Model with Physical Distance and Treatment

Optimal Control Analysis of COVID-19 Transmission Model with Physical Distance and Treatment

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.

Modelling the impact of some control strategies on the transmission dynamics of Ebola virus in human-bat population: An optimal control analysis

Qualitative research and comprehensive public awareness to nip the transmission of Ebola virus in the bud before it becomes a global threat is fast becoming imperative especially now that the Gambia Ebola virus is mutated. It is therefore necessary to consider and investigate a vector-host transmission model for possible control strategy of this deadly disease. Hence, in this study, we presented a novel and feasible human-bat (host-vector) ShEhIhRhisRhni−SbEbIb model which foretells the spread and severity of the Ebola virus from bats to humans to investigate the combined effects of three control strategies viz: (1) allowing specialized and designated agencies to bury deceased from Ebola infection without relatives touching or curdling the remains as usually practiced in most part of Africa as last respect for their departed love ones (k1), (2) systematic and deliberate depopulation of bats in the metropolis (through persecution with pesticide exposure, pre capturing, chemical timber treatment for roosts destruction) to discourage hunting them for food by virtue of their proximity (k2) and (3) immediate treatment of infected individuals in isolation (k3). We established, among others, the endemic equilibrium, disease-free equilibrium, global and local stability, non-negativity, and boundedness of the model to prove the epidemiological feasibility of the model. The reality of the presence of optimal control remarkably influences the dynamics of transmission of the virus and simulated results also confirm the great effect of the combination of the control strategies k1, k2 and k3 in flattening the curve of Ebola transmission (fig 1 – fig 8). Health workers and policy makers are better informed with fundamental precautions that could help eradicate Ebola from the populace.

Optimum Control of SEIR Model on COVID-19 Spread with Delay Time and Vaccination Effect in South Sulawesi Province

The increasing number of cases and the development of new variants of the Covid-19 virus globally including the territory of Indonesia, especially in the province of South Sulawesi are increasingly worrying and need to be prevented. Therefore, this study aims to develop a SEIR model on the spread of Covid-19 with vaccination control, optimal control analysis, stability analysis and numerical simulation of the SEIR model on the spread of Covid-19 in South Sulawesi. This study uses the SEIR epidemic model to predict the spread of Covid-19 in South Sulawesi Province with parameters such as birth rate, cure rate, mortality rate, interaction rate and vaccination. The SEIR model was chosen because it is one of the basic methods in the epidemiological model. The method used to build the model is a time delay model by considering the vaccination factor as a model parameter, model analysis using the next generation matrix method to determine the basic reproduction number and stability of the Covid-19 distribution model in South Sulawesi. Numerical model simulation using secondary data on the number of Covid-19 cases in South Sulawesi starting in 2021 which was obtained from the South Sulawesi Provincial Health Office. The results obtained are model analysis provides evidence of the existence of optimal control in the model. Based on the results obtained, it can also be seen that vaccination greatly influences the spread of Covid-19 in South Sulawesi, so that awareness is needed for the people of South Sulawesi to follow the government's recommendation to vaccinate to prevent or reduce the rate of transmission of Covid-19 in South Sulawesi.

Approximation and convergence analysis of optimal control for non-instantaneous impulsive fractional evolution hemivariational inequalities

In this work, a fractional evolution hemivariational inequalities driven by non-instantaneous impulses is studied. The solvability of the proposed system is obtained by fractional calculus, properties of generalized Clarke’s subdifferential and Dhage fixed point theorem. This article also presents the construction of the lower-dimensional approximation system for the proposed model, and its convergence of the mild solution is obtained. Besides, by considering suitable assumptions, the local approximation and uniform convergence results are established for the proposed system’s mild solution. Furthermore, sufficient conditions for the existence of Lagrange optimal control problem and convergence analysis of optimal control for the proposed model are formulated and proved. At last, an example is given for the illustration of invented new theoretical results.

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

The Internet era has brought great convenience to our life and communication. Meanwhile, it also makes a bunch of rumors propagate faster and causes even more harm to human life. Therefore, it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors. Thereout, firstly, we formulate a rumor spreading model considering psychological factors and thinking time, then, we add white noise (i.e., stochastic interference) and two pulse control strategies which denote education mechanism and refutation mechanism into the model. Secondly, we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution. Thirdly, we discuss the extinction and persistence of rumor. Moreover, we use Pontriagin’s minimum principle to explore the optimal impulse control. Finally, several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis. We conclude that the pulse control strategies have a great influence on controlling rumor spreading, and different control strategies should be adopted under different transmission scenarios.

MODELLING OF PATHOGENS IMPACT ON THE HUMAN DISEASE TRANSMISSION WITH OPTIMAL CONTROL STRATEGIES

This study concentrates on a nonlinear deterministic mathematical model for the impact of pathogens on human disease transmission with optimal control strategies. Both pathogen-free and coexistence equilibria are computed. The basic reproduction number R0, which plays a vital role in mathematical epidemiology, was derived. The qualitative analysis of the model revealed the scenario for both pathogen-free and coexistence equilibria together with R0. The local stability of the equilibria is established via the Jacobian matrix and Routh-Hurwitz criteria, while the global stability of the equilibria is proven by using an appropriate Lyapunov function. Also, the normalized sensitivity analysis has been performed to observe the impact of different parameters on R0. The proposed model is extended into optimal control problem by incorporating three control variables, namely, preventive measure variable based on separation of susceptible from contacting the pathogens, integrated vector management based on chemical, biological control, ... etc. to kill pathogens and their carriers, and supporting infective medication variable based on the care of the infected individual in quarantine center. Optimal disease control analysis is examined using Pontryagin minimum principle. Numerical simulations are performed depending on analytical results and discussed quantitatively.

ANALYSIS OF MATERIAL INVENTORY CONTROL THE METROSTATER CONSTRUCTION PROJECT IN DEPOK

In the last 10 years the construction sector boom has increased rapidly. The Government's Long-Term Plan and the leniency of government policies on investors wishing to invest in Indonesia have stimulated the growth of the construction sector in Indonesia. Increasingly adequate infrastructure encourages entrepreneurs or contractors to invest in public and private projects. One of the private construction projects being handled is the Depok Metrostater Project. This project is located in the city of Depok which has a Transit Oriented Development (TOD) concept. Currently the project is still in the construction stage of the foundation and in its implementation it requires concrete iron as raw material. To ensure material availability, the contractor will perform a scheduled recapitulation of materials according to usage needs. This material scheduling implements material stock inventory control that must be available in the warehouse, so as not to overstock. For this reason, an optimal inventory control analysis is needed through the Economic Order Quantity (EOQ) method, Lot For Lot, Fixed Period Requirement (FPR), and the Wagner and Within algorithms. The comparative results of the inventory method analysis based on the Wagner and Within Algorithm methods provide the most economical results with the minimum total cost of Rp. 583,466,945, - among the other three methods. and Contractors can make efficiency by 35%

Global stability and optimal control analysis of a knowledge transmission model in multilayer networks

Knowledge dissemination plays an important role in many aspects. The control strategy to improve the performance of knowledge transmission in couple networks is a meaningful work, which is little consideration in the existing work. This paper addresses the problem of optimal control for a class of knowledge transmission models. Firstly, the multilayer complex networks are built according to how knowledge is acquired. Secondly, inspiration from the spread of a disease, a model of knowledge transmission is established. Moreover, the basic reproduction number R0, knowledge-free equilibrium (KFE), and knowledge endemic equilibrium (KEE), as well as their stability, are deduced. Then, the imposition of optimal control, including improving the digestion and absorption of knowledge contacts and increasing the review rate of knowledge-forgotten persons, can increase the number of knowledge communicators. Afterward, Pontryagin’s maximum principle is used to deal with the nonlinear optimal control problem. Finally, through numerical simulations, the stability of the equilibriums are confirmed, the effect of knowledge dissemination is the best and the range of the knowledge dissemination is widest when two control strategies are applied at the same time.

Assessing the Impact of Relapse, Reinfection and Recrudescence on Malaria Eradication Policy: A Bifurcation and Optimal Control Analysis.

In the present study, we propose and analyze an epidemic mathematical model for malaria dynamics, considering multiple recurrent phenomena: relapse, reinfection, and recrudescence. A limitation in hospital bed capacity, which can affect the treatment rate, is modeled using a saturated treatment function. The qualitative behavior of the model, covering the existence and stability criteria of the endemic equilibrium, is investigated rigorously. The concept of the basic reproduction number of the proposed model is obtained using the concept of the next-generation matrix. We find that the malaria-free equilibrium point is locally asymptotically stable if the basic reproduction number is less than one and unstable if it is larger than one. Our observation on the malaria-endemic equilibrium of the proposed model shows possible multiple endemic equilibria when the basic reproduction number is larger or smaller than one. Hence, we conclude that a condition of a basic reproduction number less than one is not sufficient to guarantee the extinction of malaria from the population. To test our model in a real-life situation, we fit our model parameters using the monthly incidence data from districts in Central Sumba, Indonesia called Wee Luri, which were collected from the Wee Luri Health Center. Using the first twenty months’ data from Wee Luri district, we show that our model can fit the data with a confidence interval of 95%. Both analytical and numerical experiments show that a limitation in hospital bed capacity and reinfection can trigger a more substantial possibility of the appearance of backward bifurcation. On the other hand, we find that an increase in relapse can reduce the chance of the appearance of backward bifurcation. A non-trivial result appears in that a higher probability of recrudescence (treatment failure) does not always result in the appearance of backward bifurcation. From the global sensitivity analysis using a combination of Latin hypercube sampling and partial rank correlation coefficient, we found that the initial infection rate in humans and the mosquito infection rate are the most influential parameters in determining the increase in total new human infections. We expand our model as an optimal control problem by including three types of malaria interventions, namely the use of bed net, hospitalization, and fumigation as a time-dependent variable. Using the Pontryagin maximum principle, we characterize our optimal control problem. Results from our cost-effectiveness analysis suggest that hospitalization only is the most cost-effective strategy required to control malaria disease.

Deciphering the transmission dynamics of COVID-19 in India: optimal control and cost effective analysis

In this paper we assess the effectiveness of different non-pharmaceutical interventions (NPIs) against COVID-19 utilizing a compartmental model. The local asymptotic stability of equilibria (disease-free and endemic) in terms of the basic reproduction number have been determined. We find that the system undergoes a backward bifurcation in the case of imperfect quarantine. The parameters of the model have been estimated from the total confirmed cases of COVID-19 in India. Sensitivity analysis of the basic reproduction number has been performed. The findings also suggest that effectiveness of face masks plays a significant role in reducing the COVID-19 prevalence in India. Optimal control problem with several control strategies has been investigated. We find that the intervention strategies including implementation of lockdown, social distancing, and awareness only, has the highest cost-effectiveness in controlling the infection. This combined strategy also has the least value of average cost-effectiveness ratio (ACER) and associated cost.

Optimal control analysis of a multigroup SEAIHRD model for COVID-19 epidemic.

The COVID‐19 pandemic has threatened public health and caused substantial economic loss to most countries worldwide. A multigroup susceptible–exposed–asymptomatic–infectious–hospitalized–recovered–dead (SEAIHRD) compartment model is first constructed to model the spread of the disease by dividing the population into three age groups: young (aged 0–19), prime (aged 20–64), and elderly (aged 65 and over). Then, we develop a free terminal time, partially fixed terminal state optimal control problem to minimize deaths and costs associated with hospitalization and the implementation of different control strategies. And the optimal strategies are derived under different assumptions about medical resources and vaccination. Specifically, we explore optimal control strategies for reaching herd immunity in the COVID‐19 outbreak in a free terminal time situation to evaluate the effect of nonpharmaceutical interventions (NPIs) and vaccination as control measures. The transmission rate of SARS‐CoV‐2 is calibrated by using real data in the United States at the early stage of the epidemic. Through numerical simulation, we conclude that the outbreak of COVID‐19 can be contained by implementing appropriate control of the prime age population and relatively strict control measures for young and elderly populations. Within a specific period, strict control measures should be implemented before the vaccine is marketed.

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 R0. 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 R0≈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%.

Personalizing repetitive transcranial magnetic stimulation for precision depression treatment based on functional brain network controllability and optimal control analysis

Brain neuromodulation effectively treats neurological diseases and psychiatric disorders such as Depression. However, due to patient heterogeneity, neuromodulation treatment outcomes are often highly variable, requiring patient-specific stimulation protocols throughout the recovery stages to optimize treatment outcomes. Therefore, it is critical to personalize neuromodulation protocol to optimize the patient-specific stimulation targets and parameters by accommodating inherent interpatient variability and intersession alteration during treatments. The study aims to develop a personalized repetitive transcranial magnetic stimulation (rTMS) protocol and evaluate its feasibility in optimizing the treatment efficiency using an existing dataset from an antidepressant experimental imaging study in depression. The personalization of the rTMS treatment protocol was achieved by personalizing both stimulation targets and parameters via a novel approach integrating the functional brain network controllability analysis and optimal control analysis. First, the functional brain network controllability analysis was performed to identify the optimal rTMS stimulation target from the effective connectivity network constructed from patient-specific resting-state functional magnetic resonance imaging data. The optimal control algorithm was then applied to optimize the rTMS stimulation parameters based on the optimized target. The performance of the proposed personalized rTMS technique was evaluated using datasets collected from a longitudinal antidepressant experimental imaging study in depression (n = 20). Simulation models demonstrated that the proposed personalized rTMS protocol outperformed the standard rTMS treatment by efficiently steering a depressive resting brain state to a healthy resting brain state, indicated by the significantly less control energy needed and higher model fitting accuracy achieved. The node with the maximum average controllability of each patient was designated as the optimal target region for the personalized rTMS protocol. Our results also demonstrated the theoretical feasibility of achieving comparable neuromodulation efficacy by stimulating a single node compared to stimulating multiple driver nodes. The findings support the feasibility of developing personalized neuromodulation protocols to more efficiently treat depression and other neurological diseases.

Correction to: Mathematical Modeling of Covid-19 and Dengue Co-Infection Dynamics in Bangladesh: Optimal Control and Data-Driven Analysis

Correction to: Mathematical Modeling of Covid-19 and Dengue Co-Infection Dynamics in Bangladesh: Optimal Control and Data-Driven Analysis

Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness

This paper is focused on the design of optimal control strategies for COVID-19 and the model containing susceptible individuals with awareness of protection and susceptible individuals without awareness of protection is established. The goal of this paper is to minimize the number of infected people and susceptible individuals without protection awareness, and to increase the willingness of susceptible individuals to take protection measures. We conduct a qualitative analysis of this mathematical model. Based on the sensitivity analysis, the optimal control method is proposed, namely personal protective measures, vaccination and awareness raising programs. It is found that combining the three methods can minimize the number of infected people. Moreover, the introduction of awareness raising program in society will greatly reduce the existence of susceptible individuals without protection awareness. To evaluate the most cost-effective strategy we performed a cost-effectiveness analysis using the ICER method.

Optimal Control and Stability Analysis of an SEIR Model with Infectious Force in Latent Period.

In this paper, an SEWIR epidemic model with the government control rate and infectious force in latent period is proposed. The conditions to the existence and uniqueness of disease-free and endemic equilibrium points in the SEWIR model are obtained. By using the Hurwitz criterion, the locally asymptotic stability of disease-free and endemic equilibrium points is proved. We show the global asymptotic stability of the disease-free equilibrium point by the construction of Lyapunov function and LaSalle invariance principle. The globally asymptotic stability of the endemic equilibrium is verified by numerical simulation. Several optimal control strategies are proposed on controlling infectious diseases.

Optimal control analysis for the coinfection of COVID-19 and TB

The COVID-19 pandemic continues to clame the lives of many people globally and controlling the disease has became the most challenging part of the modern health care system. Tuberculosis (TB) is also a major global health threat affecting millions of people every year. In this study, we extended the deterministic mathematical model to provide insight for the coinfection of COVID-19 and TB into an optimal control problem. The validity of the coinfection model is qualitatively studied by showing the well-posedness and positivity of the solutions. The analytical computations on the impacts of the disease revealed that an increase in infected individuals with TB has a positive impact on the spread of COVID-19 while under some conditions, an increase in the number of COVID-19 cases has a positive impact on the spread of TB disease. We add four control measures in the deterministic model such as: the prevention effort against TB, prevention techniques against COVID-19, treatments for TB infections and medical care for COVID-19 infection to optimally manage the diseases. The extended optimal control problem is analyzed with the help of Pontryagin’s Minimum Principle. The existence and uniqueness of optimal control are proved. We fitted the parameter values of our proposed model with collected epidemiological data using a modified combination of the Bayesian and least square estimation technique. Different simulation cases were performed to compare the analytical results and to identify the most appropriate control intervention strategies. The simulation results show that the prevalence of the coinfection reduced when all the four control measures were concurrently implemented.

Combined Trojan Y Chromosome Strategy and Sterile Insect Technique to Eliminate Mosquitoes: Modelling and Analysis

Sterile insect technique has been successfully applied in the control of agricultural pests; however, it has a limited ability to control mosquitoes. A promising alternative approach is the Trojan Y Chromosome strategy, which works by manipulating the sex ratio of a population through the introduction of YY supermales that guarantee male offspring. To take the advantages of both approaches, a combined Trojan Y chromosome strategy and sterile insect technique (TYC-SIT) strategy considering intraspecies competition is modeled. The pure TYC method is compared with the pure SIT method by cancelling one-state variable. The dynamical analysis leads to results on both local and global stabilities of this combined TYC-SIT model. Optimal control analysis is also implemented to investigate the optimal mechanisms for extinction of mosquitoes. In particular, the numerical results affirm that the combined TYC-SIT enables near elimination of mosquitoes and works better than the pure TYC or pure SIT method. These conclusions have great significance for species controls with an XX-XY sex determinism system or ZZ-ZW system.

Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

A model depicting the transmission of onchocerciasis disease in human host community with two distinct groups of infected humans exhibiting low and high microfilariae (mf) output with saturated treatment function is developed and analyzed. The model equilibrium solutions are obtained, and it is found that the model exhibits forward bifurcation and the effective basic reproduction number governing the spread of the disease is computed by the use of the next generation matrix method. The sensitivity results of model parameters reveal that the rates describing the recruitment of humans, blackflies, onchocerciasis disease transmission, and the biting rate of blackflies are positively sensitive to , which necessitate the need for controls to be implemented in order to curtail the infectious contact between humans and blackflies in the host environment. To this effect, the model is further transformed into an optimal control problem by applying control strategies of personal protection of using treated bednets and wearing of permethrin‐treated cloths , surgical care for humans with body deformation and impaired vision , education campaign , and the use of insecticide , respectively. The existence and uniqueness of the optimal control model are established, and the Pontryagin maximum principle (PMP) is employed to characterize the controls. The optimal control model is solved using the Runge–Kutta numerical scheme via MATLAB, and the simulations under different control combinations show that each of the controls have its own effect in minimizing onchocerciasis transmission, but the combined effects of the four control strategies proved to be more beneficial towards the elimination of the disease in human and blackfly host community. Also, the simulations of the control profiles reveal that each of these controls are sustained at maximum until 3 months before gradually declining to zero in terminal time of 12 months.