Global dynamics and optimal control of an influenza model with vaccination, media coverage and treatment

2017 ◽  
Vol 10 (05) ◽  
pp. 1750068 ◽  
Author(s):  
Lianwen Wang ◽  
Zhijun Liu ◽  
Dashun Xu ◽  
Xinan Zhang
Keyword(s):  
Optimal Control ◽  
Media Coverage ◽  
Control Strategies ◽  
Dominant Role ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Control Measures ◽  
Global Dynamics ◽  
Effective Measure ◽  
The Cost

In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Furthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.

scholarly journals Multiple Control Strategies for Prevention of Avian Influenza Pandemic

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Multiple Control ◽  
Control Functions ◽  
The Cost

We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.

scholarly journals Prevention of Influenza Pandemic by Multiple Control Strategies

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Roman Ullah ◽  
Gul Zaman ◽  
Saeed Islam
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Antiviral Treatment ◽  
Cost Effective ◽  
Effective Control ◽  
Numerical Techniques ◽  
Multiple Control ◽  
Control Functions ◽  
Transmission Of Disease

We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method.

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.

scholarly journals Controlling the Spatial Spread of a Xylella Epidemic

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Sebastian Aniţa ◽  
Vincenzo Capasso ◽  
Simone Scacchi
Keyword(s):  
Spatial Structure ◽  
Numerical Simulations ◽  
Control Strategies ◽  
Xylella Fastidiosa ◽  
Cost Effective ◽  
Olive Tree ◽  
Control Measures ◽  
Weed Biomass ◽  
Spatial Spread ◽  
Olive Trees

AbstractIn a recent paper by one of the authors and collaborators, motivated by the Olive Quick Decline Syndrome (OQDS) outbreak, which has been ongoing in Southern Italy since 2013, a simple epidemiological model describing this epidemic was presented. Beside the bacterium Xylella fastidiosa, the main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model was based on a system of ordinary differential equations, the analysis of which provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. Although the model presented there was mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed, numerical simulations support the outcomes of the mathematical analysis, according to which the removal of a suitable amount of weed biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted in the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen. In this paper for a more realistic description and a clearer interpretation of the proposed control measures, a spatial structure of the epidemic system has been included, but, in order to keep mathematical technicalities to a minimum, only two players have been described in a dynamical way, trees and insects, while the weed biomass is taken to be a given quantity. The control measures have been introduced only on a subregion of the whole habitat, in order to contain costs of intervention. We show that such a practice can lead to the eradication of an epidemic outbreak. Numerical simulations confirm both the results of the previous paper and the theoretical results of the model with a spatial structure, though subject to regional control only.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

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 Multi-Objective Optimization for Selecting and Siting the Cost-Effective BMPs by Coupling Revised GWLF Model and NSGAII Algorithm

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 235 ◽  
Author(s):  
Zuoda Qi ◽  
Gelin Kang ◽  
Xiaojin Wu ◽  
Yuting Sun ◽  
Yuqiu Wang
Keyword(s):  
Best Management Practices ◽  
Management Practices ◽  
Cost Effective ◽  
Control Measures ◽  
Multi Objective Optimization ◽  
Watershed Model ◽  
Filter Strips ◽  
Multi Objective ◽  
Dissolved Nitrogen ◽  
The Cost

Best management practices (BMPs) are an effective way to control water pollution. However, identification of the optimal distribution and cost-effect of BMPs provides a great challenge for watershed policy makers. In this paper, a semi-distributed, low-data, and robust watershed model, the Revised Generalized Watershed Loading Function (RGWLF), is improved by adding the pollutant attenuation process in the river channel and a bank filter strips reduction function. Three types of pollution control measures—point source wastewater treatment, bank filter strips, and converting farmland to forest—are considered, and the cost of each measure is determined. Furthermore, the RGWLF watershed model is coupled with a widely recognized multi-objective optimization algorithm, the non-dominated sorting genetic algorithm II (NSGAII), the combination of which is applied in the Luanhe watershed to search for spatial BMPs for dissolved nitrogen (DisN). Fifty scenarios were finally selected from numerous possibilities and the results indicate that, at a minimum cost of 9.09 × 107 yuan, the DisN load is 3.1 × 107 kg and, at a maximum cost of 1.77 × 108 yuan, the total dissolved nitrogen load is 1.31 × 107 kg; with the no-measures scenario, the DisN load is 4.05 × 107 kg. This BMP optimization model system could assist decision-makers in determining a scientifically comprehensive plan to realize cost-effective goals for the watershed.

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.

Emissions Reductions From Vehicle Retirement Programs

1997 ◽  
Vol 1587 (1) ◽  
pp. 121-127 ◽  
Author(s):  
Beth Deysher ◽  
Don Pickrell
Keyword(s):  
Vehicle Emissions ◽  
Motor Vehicle ◽  
Cost Effective ◽  
Control Measures ◽  
Emissions Reductions ◽  
Reduction Strategies ◽  
Alternative Measures ◽  
Reduce Emissions ◽  
Ozone Precursor ◽  
The Cost

Nonattainment areas taking advantage of EPA’s modified enforcement of the 1990 Clean Air Act mandates for unpopular emissions control measures will be required to identify alternative measures to reduce emissions, and several areas have indicated their intention to implement scrappage programs for older vehicles as a means of “replacing” the emissions reductions originally expected to result from these other measures. The potential reductions in fleetwide motor vehicle emissions from scrappage of all older light-duty vehicles in a typical urban area’s fleet are analyzed, and the sensitivity of those reductions to the timing of the program’s implementation and to alternative assumptions about more intensive use of vehicles remaining in the fleet are explored. The cost-effectiveness of such a program in reducing ozone precursor emissions is investigated and the reliability of estimates of the program’s effectiveness developed by using the MOBILE5a vehicle emissions model are evaluated. The likely emissions reductions from even so comprehensive a vehicle scrappage program cannot replace those anticipated to result from measures such as enhanced inspection and maintenance and sales of reformulated gasoline, but smaller-scale retirement programs may be a cost-effective element of a larger package of emissions reduction strategies.

scholarly journals Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Ozair ◽  
Abid Ali Lashari ◽  
Il Hyo Jung ◽  
Kazeem Oare Okosun
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Control Technique ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Impact

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive numberR0and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.

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