scholarly journals Local and Global Stability Analysis of Dengue Disease with Vaccination and Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1917
Author(s):  
Anusit Chamnan ◽  
Puntani Pongsumpun ◽  
I-Ming Tang ◽  
Napasool Wongvanich
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Numerical Solutions ◽  
Dengue Infection ◽  
Transmission Model ◽  
Dengue Vaccine ◽  
Dengue Disease ◽  
Global Stability Analysis ◽  
Aedes Mosquitoes ◽  
Dengue Transmission

Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV-1, DENV-2, DENV-3, and DENV-4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD-TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.

scholarly journals Optimal Control of Dengue Transmission with Vaccination

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1833
Author(s):  
Anusit Chamnan ◽  
Puntani Pongsumpun ◽  
I-Ming Tang ◽  
Napasool Wongvanich
Keyword(s):  
Optimal Control ◽  
Dengue Infection ◽  
Dynamical Models ◽  
Dengue Disease ◽  
Vector Population ◽  
Dengue Transmission ◽  
In Series ◽  
Series Configuration ◽  
Si Model ◽  
Two Populations

Dengue disease is caused by four serotypes of the dengue virus: DEN-1, DEN-2, DEN-3, and DEN-4. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV) is a vaccine currently used in Thailand. This research investigates what the optimal control is when only individuals having documented past dengue infection history are vaccinated. This is the present practice in Thailand and is the latest recommendation of the WHO. The model used is the Susceptible-Infected-Recovered (SIR) model in series configuration for the human population and the Susceptible-Infected (SI) model for the vector population. Both dynamical models for the two populations were recast as optimal control problems with two optimal control parameters. The analysis showed that the equilibrium states were locally asymptotically stable. The numerical solution of the control systems and conclusions are presented.

scholarly journals SIR Model for Dengue Disease with Effect of Dengue Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
I. Ming Tang ◽  
Puntani Pongsumpun
Keyword(s):  
Mathematical Model ◽  
Mortality Rate ◽  
Dengue Virus ◽  
Numerical Solutions ◽  
Specific Treatment ◽  
Sir Model ◽  
Dengue Vaccine ◽  
Dengue Disease ◽  
Modelling Methods

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.

scholarly journals Multiobjective approach to optimal control for a dengue transmission model

10.19139/144 ◽  
2015 ◽  
Vol 3 (3) ◽  
Author(s):  
Roman Denysiuk ◽  
Helena Sofia Rodrigues ◽  
M. Teresa T. Monteiro ◽  
Lino Costa ◽  
Isabel Espírito Santo ◽  
...  
Keyword(s):  
Optimal Control ◽  
Transmission Model ◽  
Dengue Transmission ◽  
Multiobjective Approach

scholarly journals Maxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc—Numerical Solutions

Robotics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 88
Author(s):  
Marek Stodola ◽  
Matej Rajchl ◽  
Martin Brablc ◽  
Stanislav Frolík ◽  
Václav Křivánek
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Control Problems ◽  
Affine Control Systems ◽  
Dynamical Control ◽  
And Control ◽  
Analytical Approaches ◽  
Maxwell Points

We study two nilpotent affine control systems derived from the dynamic and control of a vertical rolling disc that is a simplification of a differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated and optimal control problems are formulated, and their Hamiltonian systems of ODEs are derived using the Pontryagin maximum principle. These optimal control problems completely determine the energetically optimal trajectories between two states. Then, a novel numerical algorithm based on optimisation for finding the Maxwell points is presented and tested on these control systems. The results show that the use of such numerical methods can be beneficial in cases where common analytical approaches fail or are impractical.

scholarly journals Multiobjective approach to optimal control for a dengue transmission model

2015 ◽  
Vol 3 (3) ◽  
Author(s):  
Roman Denysiuk ◽  
Helena Sofia Rodrigues ◽  
M. Teresa T. Monteiro ◽  
Lino Costa ◽  
Isabel Espírito Santo ◽  
...  
Keyword(s):  
Optimal Control ◽  
Transmission Model ◽  
Dengue Transmission ◽  
Multiobjective Approach

scholarly journals Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Jafaruddin ◽  
Sapto W. Indratno ◽  
Nuning Nuraini ◽  
Asep K. Supriatna ◽  
Edy Soewono
Keyword(s):  
Dengue Fever ◽  
Dengue Infection ◽  
Early Growth ◽  
Infected Mosquito ◽  
Transmission Model ◽  
Cumulative Number ◽  
Basic Reproductive Ratio ◽  
Early States ◽  
Dengue Transmission ◽  
Dengue Epidemic

Estimating the basic reproductive ratioR0of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimateR0which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008–Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates ofR0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction ofR0accommodates the take-off rate differences between mosquitoes and humans. Our second construction of theR0estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

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