Optimal Control Problem of Vacination for The Spread of Measles Diseases Model

2018 ◽  
Vol 2 (2) ◽  
pp. 76
Author(s):  
Dani Suandi
Keyword(s):  
Optimal Control ◽  
Mortality Rate ◽  
Equation System ◽  
Vaccination Program ◽  
Control Analysis ◽  
Differential Equation System ◽  
Third Order ◽  
Vaccination Programs ◽  
The Cost ◽  
Very High

Measles is a disease in humans that is very contagious. Before the vaccine was known, the incidence of measles was very high, even the measles mortality rate reached 2.6 million every year. With the introduction of vaccines, the mortality rate in 2000-2016 can be reduced to 20.4 million deaths. Therefore, vaccination programs are very useful in reducing the incidence of measles. Unfortunately, we cannot know the optimal conditions for administering vaccines. The study of optimal control analysis of vaccination is needed in optimizing the prevention of the spread of measles. In this paper, a mathematical model which is a third-order differential equation system is constructed based on characteristic information on measles. The existence and locally stability of the equilibrium point are analyzed here. In addition, optimal control of the vaccination program also occurred. The results of our analysis suggest that the incidence of measles can decrease as the effectiveness of vaccination increases. But the effectiveness of vaccination is directly proportional to the costs incurred. If the cost incurred for the vaccination program more significant, the incidence of measles will decrease.

scholarly journals Flattening the Curve of COVID-19 Vaccine Rejection—An International Overview

Vaccines ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 44
Author(s):  
Wojciech Feleszko ◽  
Piotr Lewulis ◽  
Adam Czarnecki ◽  
Paweł Waszkiewicz
Keyword(s):  
Czech Republic ◽  
General Population ◽  
Herd Immunity ◽  
Vaccination Program ◽  
Vaccination Programs ◽  
National Surveys ◽  
Legislative Power ◽  
Preventive Vaccination ◽  
Very High ◽  
Socioeconomic Benefits

Background: If globally implemented, a safe coronavirus disease 2019 (COVID-19) vaccination program will have broad clinical and socioeconomic benefits. However, individuals who anticipate that the coronavirus vaccine will bring life back to normality may be disappointed, due to the emerging antivaccination attitude within the general population. Methods: We surveyed a sample of adult Polish citizens (n = 1066), and compared it with the data on international COVID-19 vaccine reluctance. Results: In 20 national surveys, the vaccine averseness for the anticipated COVID-19 vaccine varied from meager (2–6% China) to very high (43%, Czech Republic, and 44%, Turkey) and in most countries was much higher than regular vaccination reluctance, which varies between 3% (Egypt) and 55% (Russia). Conclusions: These results suggest that a 67% herd immunity may be possible only if mandatory preventive vaccination programs start early and are combined with coordinated education efforts supported by legislative power and social campaigns.

scholarly journals Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 971
Author(s):  
Mlyashimbi Helikumi ◽  
Moatlhodi Kgosimore ◽  
Dmitry Kuznetsov ◽  
Steady Mushayabasa
Keyword(s):  
Optimal Control ◽  
Trypanosoma Brucei ◽  
Backward Bifurcation ◽  
Effective Control ◽  
Control Analysis ◽  
Trypanosoma Brucei Rhodesiense ◽  
Awareness Campaigns ◽  
Human Animal ◽  
The Cost ◽  
Insecticide Control

In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns.

OPTIMAL CONTROL FOR A NONLINEAR n-DIMENSIONAL COMPETING SYSTEM WITH AGE-STRUCTURE

2012 ◽  
Vol 05 (03) ◽  
pp. 1260008 ◽  
Author(s):  
ZHI-XUE LUO ◽  
JIAN-YU YANG ◽  
YA-JUAN LUO
Keyword(s):  
Optimal Control ◽  
Age Structure ◽  
Normal Cone ◽  
Equation System ◽  
Optimal Harvesting ◽  
Order Partial Differential Equation ◽  
Differential Equation System ◽  
Optimal Control Strategy ◽  
First Order

This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland's variational principle, the existence and unique characterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.

scholarly journals A MATHEMATIC MODEL OF TWO MUTUALLY INTERACTING SPECIES WITH MORTALITY RATE FOR THE SECOND SPECIES

2017 ◽  
Vol 3 (2) ◽  
pp. 21-25
Author(s):  
Annisa Rahayu ◽  
Yuni Yulida ◽  
Faisal Faisal
Keyword(s):  
Mortality Rate ◽  
Interaction Model ◽  
Mathematic Model ◽  
Equation System ◽  
Differential Equation System ◽  
Interacting Species ◽  
Stability Model ◽  
Species Population ◽  
The Stability ◽  
Type Of Stability

One of the interactions that occur withinthe ecosystem is the interaction of mutualism. Such mutualism interactions can be modeled into mathematical models. Reddy (2011) study suggests a model of two mutually interacting species that assumes that each species can live without its mutualism partner. In fact, not all mutual species survive without their mutualism pairs. If it is assumed that the second species lives without its mutualism partner, the first species, then the natural growth rate of the second species population will decrease (the mortality rate). The purpose of this research is to explain the model of two mutually interacting species with mortality rate for the second species, to determine the equilibrium point and the type of stability, and to simulate them with several parameters. This research was done by way of literature studies. The result of this research is the model of two mutually interacting species with mortality rate for second species modeled using Nonlinear Differential Equation System. In the model, it was obtained 3 (three) points of equilibrium, with each type and type of stability investigated. Next up from the stability, model simulations were done. Based on several simulations conducted can be seen the value of parameters and initial values affect the population growth of both species. The interaction model of two mutual species will be stable if the first species survive and the second species over time will be extinct.

scholarly journals Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2217
Author(s):  
Khaled S. Al Noufaey
Keyword(s):  
Growth Rate ◽  
Mortality Rate ◽  
Diffusion Coefficients ◽  
Time Delays ◽  
Equation System ◽  
Top Predator ◽  
Differential Equation System ◽  
Small Delay ◽  
The Galerkin Method ◽  
Delay Differential

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

scholarly journals Asian-Origin Approved COVID-19 Vaccines and Current Status of COVID-19 Vaccination Program in Asia: A Critical Analysis

Vaccines ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 600
Author(s):  
Chiranjib Chakraborty ◽  
Ashish Ranjan Sharma ◽  
Manojit Bhattacharya ◽  
Govindasamy Agoramoorthy ◽  
Sang-Soo Lee
Keyword(s):  
Vaccine Development ◽  
Vaccination Program ◽  
Vaccine Hesitancy ◽  
Current Status ◽  
Asian Countries ◽  
Asian Origin ◽  
Vaccination Programs ◽  
Factors Affecting ◽  
The Cost ◽  
Vaccination Campaigns

COVID-19 vaccination has started throughout the globe. The vaccination program has also begun in most Asian countries. This paper analyzed the Asian-origin COVID-19 vaccines and vaccination program status in Asia till March 2021 under three sections. In the first section, we mapped the approved vaccines that originated from Asia, their technological platforms, collaborations during vaccine development, and regulatory approval from other countries. We found that a total of eight Asian COVID-19 vaccines originated and got approval from three countries: China, India, and Russia. In the second section, we critically evaluated the recent progress of COVID-19 vaccination programs. We analyzed the overall vaccination status across the Asian region. We also calculated the cumulative COVID-19 vaccine doses administered in different Asian countries, vaccine rolling in 7-day average in various Asian countries, and COVID-19 vaccine per day doses administrated in several Asian countries. We found that China and India vaccinated the maximum number of people. Finally, we evaluated the factors affecting the COVID-19 vaccination program in Asia, such as vaccine hesitancy, basic reproduction numbers (R0) and vaccination campaigns, and the cost of the vaccines. Our analysis will assist the implementation of the COVID-19 vaccination program successfully in Asia.

scholarly journals Optimal Control Applied to Vaccination and Testing Policies for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3100
Author(s):  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Optimal Control Problems ◽  
Vaccination Rate ◽  
Control Problems ◽  
Vaccination Programs ◽  
Infected People ◽  
Control Approach ◽  
Algebraic Constraints ◽  
The Cost

In this paper, several policies for controlling the spread of SARS-CoV-2 are determined under the assumption that a limited number of effective COVID-19 vaccines and tests are available. These policies are calculated for different vaccination scenarios representing vaccine supply and administration restrictions, plus their impacts on the disease transmission are analyzed. The policies are determined by solving optimal control problems of a compartmental epidemic model, in which the control variables are the vaccination rate and the testing rate for the detection of asymptomatic infected people. A combination of the proportion of threatened and deceased people together with the cost of vaccination of susceptible people, and detection of asymptomatic infected people, is taken as the objective functional to be minimized, whereas different types of algebraic constraints are considered to represent several vaccination scenarios. A direct transcription method is employed to solve these optimal control problems. More specifically, the Hermite–Simpson collocation technique is used. The results of the numerical experiments show that the optimal control approach offers healthcare system managers a helpful resource for designing vaccination programs and testing plans to prevent COVID-19 transmission.

Dengue and Chikungunya simulating model with mosquito periodic mortality rate

2017 ◽  
pp. 2919-2931
Author(s):  
Oscar A. Manrique A. ◽  
Steven Raigosa O. ◽  
Dalia M. Munoz P. ◽  
Mauricio Ropero P. ◽  
Anibal Munoz L. ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mortality Rate ◽  
Differential Equations ◽  
Dynamic System ◽  
Ordinary Differential Equations ◽  
Equation System ◽  
Nonlinear Ordinary Differential Equations ◽  
Differential Equation System ◽  
Infectious Process ◽  
Population Mortality

A dynamic system of nonlinear ordinary differential equations to display the infectious process of Dengue-Chikungunya, is presented. The system including a mosquito periodic mortality rate and simulations of the differential equation system by MATLAB software to determine the effect of climatic variables (temperature, humidity, pluviosity) in the infectious population mortality, is carried out.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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