OPTIMAL CONTROL OF VECTOR-BORNE DISEASE WITH DIRECT TRANSMISSION

2015 ◽  
Vol 76 (13) ◽  
Author(s):  
Nurul Aida Nordin ◽  
Rohanin Ahmad ◽  
Rashidah Ahmad
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Optimal Control Theory ◽  
Existence And Uniqueness ◽  
Blood Donation ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne ◽  
Vector Control Strategy

This paper introduces the usage of three controls as a way to reduce the occurrence of vector-borne disease. The governing equation of the dynamical system used in this paper describes both direct and indirect transmission mode of vector-borne disease. This means that the disease can be transmitted in two different ways. First, it can be transmitted through mosquito bites and the other is through human blood transfusion. The three controls that are incorporated in the dynamical system include a measurement of basic practice for blood donation procedure, self-prevention effort and vector control strategy by health authority. The optimality system of the three controls is characterized using optimal control theory and the existence and uniqueness of the optimal control are established. Then, the effect of the incorporation of the three controls is investigated by performing numerical simulation. 

scholarly journals Global Dynamics of a Vector-Borne Disease Model with Two Transmission Routes

2020 ◽  
Vol 30 (06) ◽  
pp. 2050083
Author(s):  
Sk Shahid Nadim ◽  
Indrajit Ghosh ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Transmission Coefficient ◽  
Disease Model ◽  
Psychological Effect ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne

In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a nonmonotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptotically stable when the basic reproduction number ([Formula: see text]) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to [Formula: see text] and the epidemic growth rate. Local stability of endemic equilibrium is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when [Formula: see text] although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bistable dynamics. However, efficient application of temporary control in bistable regions will curb the disease to lower endemicity. Additionally, numerical simulations reveal that the equilibrium level of infected hosts decreases as psychological effect increases.

scholarly journals Global dynamics of a general vector-borne disease model with two transmission routes

2018 ◽  
Author(s):  
Sk Shahid Nadim ◽  
Indrajit Ghosh ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Transmission Coefficient ◽  
Disease Model ◽  
Case Fatality ◽  
Hysteresis Phenomenon ◽  
Global Dynamics ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne

In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a non-monotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptomatically stable when the basic reproduction number (R_0) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to R_0 and the epidemic growth rate. Local stability of endemic equilibria is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when R_0<1 although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bi-stable dynamics. However, efficient application of temporary control in bi-stable regions will curb the disease to lower endemicity. In addition, increase in transmission heterogeneity will increase the chance of disease eradication.

Vector Control, Optimal Control, and Vector-Borne Disease Dynamics

2020 ◽  
pp. 267-288
Author(s):  
Michael B. Bonsall
Keyword(s):  
Optimal Control ◽  
Population Genetics ◽  
Population Dynamics ◽  
Vector Control ◽  
Cost Effective ◽  
Disease Suppression ◽  
Medical Interventions ◽  
Vector Borne Disease ◽  
Vector Borne

Understanding methods of vector control is essential to vector-borne disease (VBD) management. Vaccines or standard medical interventions for many VDBs do not exist or are poorly developed so disease control is focused on managing vector numbers and dynamics. This involves understanding not only the population dynamics but also the population genetics of vectors. Using mosquitoes as a case study, in this chapter, the modern genetics-based methods of vector control (self-limiting, self-sustaining) on mosquito population and disease suppression will be reviewed. These genetics-based methods highlight the importance of understanding the interplay between genetics and ecology to develop optimal, cost-effective solutions for control. The chapter focuses on how these genetics-based methods can be integrated with other interventions, and concludes with a summary of regulatory and policy perspectives about the use of these approaches in the management of VBDs.

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.

Study of different optimization strategies for analogue circuits

2016 ◽  
Vol 35 (3) ◽  
Author(s):  
Alexander Zemliak ◽  
Fernando Reyes ◽  
Sergio Vergara
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Lyapunov Function ◽  
Optimal Control Theory ◽  
Design Methodology ◽  
Initial Part ◽  
Circuit Optimization ◽  
Optimization Strategy ◽  
Analogue Circuit ◽  
Cpu Time

Purpose In this paper, we propose further development of the generalized methodology for analogue circuit optimization. This methodology is based on optimal control theory. This approach generates many different circuit optimization strategies. We lead the problem of minimizing the CPU time needed for circuit optimization to the classical problem of minimizing a functional in optimal control theory. Design/methodology/approach The process of analogue circuit optimization is defined mathematically as a controllable dynamical system. In this context, we can formulate the problem of minimizing the CPU time as the minimization problem of a transitional process of a dynamical system. To analyse the properties of such a system, we propose to use the concept of the Lyapunov function of a dynamical system. This function allows us to analyse the stability of the optimization trajectories and to predict the CPU time for circuit optimization by analysing the characteristics of the initial part of the process. Findings We present numerical results that show that we can compare the CPU time for different circuit optimization strategies by analysing the behaviour of a special function. We establish that, for any optimization strategy, there is a correlation between the behaviour of this function and the CPU time that corresponds to that strategy. Originality/value The analysis shows that Lyapunov function of optimization process and its time derivative can be informative sources for searching a strategy, which has minimal processor time expense. This permits to predict the best optimization strategy by analyzing only initial part of the optimization process.

scholarly journals Viscosity solutions of fully nonlinear functional parabolic PDE

2005 ◽  
Vol 2005 (22) ◽  
pp. 3539-3550
Author(s):  
Liu Wei-an ◽  
Lu Gang
Keyword(s):  
Optimal Control ◽  
Viscosity Solutions ◽  
Parabolic Equations ◽  
Optimal Control Theory ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fully Nonlinear ◽  
Nonlinear Functional ◽  
Parabolic Pde

By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

Mathematical modeling and projections of a vector-borne disease with optimal control strategies: A case study of the Chikungunya in Chad

2021 ◽  
Vol 150 ◽  
pp. 111197
Author(s):  
Hamadjam Abboubakar ◽  
Albert Kouchéré Guidzavaï ◽  
Joseph Yangla ◽  
Irépran Damakoa ◽  
Ruben Mouangue
Keyword(s):  
Mathematical Modeling ◽  
Optimal Control ◽  
Control Strategies ◽  
Vector Borne Disease ◽  
Vector Borne
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