scholarly journals The Dynamics and Optimal Control of a Hand-Foot-Mouth Disease Model

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongwu Tan ◽  
Hui Cao
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Disease Model ◽  
Mouth Disease ◽  
Infected People ◽  
Hand Foot Mouth Disease ◽  
The Cost ◽  
Existence Of Equilibria ◽  
Disease Free

We build and study the transmission dynamics of a hand-foot-mouth disease model with vaccination. The reproduction number is given, the existence of equilibria is obtained, and the global stability of disease-free equilibrium is proved by constructing the Lyapunov function. We also apply optimal control theory to the hand-foot-mouth disease model. The treatment and vaccination interventions are considered in the hand-foot-mouth disease model, and the optimal control strategies based on minimizing the cost of intervention and minimizing the number of the infected people are given. Numerical results show the usefulness of the optimization strategies.

scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

scholarly journals Transmission dynamics model of Tuberculosis with optimal control strategies in Haramaya district, Ethiopia

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Doyo Kereyu ◽  
Seleshi Demie
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Cost ◽  
Optimal Level ◽  
Qualitative Behavior ◽  
Dynamics Model ◽  
Haramaya District ◽  
Disease Free

AbstractIn this study, we use a compartmental nonlinear deterministic mathematical model to investigate the effect of different optimal control strategies in controlling Tuberculosis (TB) disease transmission in the community. We employ stability theory of differential equations to investigate the qualitative behavior of the model by obtaining the basic reproduction number and determining the local stability conditions for the disease-free and endemic equilibria. We consider three control strategies representing distancing, case finding, and treatment efforts and numerically compare the levels of exposed and infectious populations with and without control strategies. The results suggest that combination of all controls is the best strategy to eradicate TB disease from the community at an optimal level with minimum cost of interventions.

scholarly journals Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Oluwole Daniel Makinde ◽  
David Malonza
Keyword(s):  
Optimal Control ◽  
Typhoid Fever ◽  
Control Strategies ◽  
Cost Effective ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Effective Strategies ◽  
Next Generation Matrix ◽  
The Cost ◽  
Disease Free

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

scholarly journals Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

2021 ◽  
Vol 9 (1) ◽  
pp. 198-212
Author(s):  
Cheryl Q. Mentuda
Keyword(s):  
Optimal Control ◽  
Vector Control ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Model Comparison ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Transmitted Disease ◽  
The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

scholarly journals Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yi Song ◽  
Zhenqing Li
Keyword(s):  
Control Strategy ◽  
Plant Disease ◽  
Control Strategies ◽  
Disease Model ◽  
Infected Plant ◽  
Transcendental Equation ◽  
Cultural Control ◽  
Dynamical Analysis ◽  
Positive Equilibrium ◽  
Disease Free

Delayed plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are presented and investigated. Firstly, we consider continuous cultural control strategy in which continuous replanting of healthy plants is taken. The existence and local stability of disease-free equilibrium and positive equilibrium are studied by analyzing the associated characteristic transcendental equation. And then, plant disease model with impulsive replanting of healthy plants is also considered; the sufficient condition under which the infected plant-free periodic solution is globally attritive is obtained. Moreover, permanence of the system is studied. Some numerical simulations are also given to illustrate our results.

Stability analysis and optimal control of an epidemic model with vaccination

2015 ◽  
Vol 08 (03) ◽  
pp. 1550030 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Asymptotically Stable ◽  
Control Pair ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
The Cost ◽  
Objective Functional ◽  
Disease Free

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0when R0< 1. When R0> 1 endemic equilibrium E1exists and the system becomes locally asymptotically stable at E1under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.

scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals Foot-and-Mouth Disease

2004 ◽  
Vol 17 (2) ◽  
pp. 465-493 ◽  
Author(s):  
Marvin J. Grubman ◽  
Barry Baxt
Keyword(s):  
Control Strategies ◽  
Disease Outbreaks ◽  
Foot And Mouth Disease ◽  
Developed Countries ◽  
Etiologic Agent ◽  
Mouth Disease ◽  
Receptor Interactions ◽  
Foot And Mouth ◽  
Virus Replication Cycle ◽  
Disease Free

SUMMARY Foot-and-mouth disease (FMD) is a highly contagious disease of cloven-hoofed animals. The disease was initially described in the 16th century and was the first animal pathogen identified as a virus. Recent FMD outbreaks in developed countries and their significant economic impact have increased the concern of governments worldwide. This review describes the reemergence of FMD in developed countries that had been disease free for many years and the effect that this has had on disease control strategies. The etiologic agent, FMD virus (FMDV), a member of the Picornaviridae family, is examined in detail at the genetic, structural, and biochemical levels and in terms of its antigenic diversity. The virus replication cycle, including virus-receptor interactions as well as unique aspects of virus translation and shutoff of host macromolecular synthesis, is discussed. This information has been the basis for the development of improved protocols to rapidly identify disease outbreaks, to differentiate vaccinated from infected animals, and to begin to identify and test novel vaccine candidates. Furthermore, this knowledge, coupled with the ability to manipulate FMDV genomes at the molecular level, has provided the framework for examination of disease pathogenesis and the development of a more complete understanding of the virus and host factors involved.

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