Optimal Control of Dengue Transmission with Vaccination

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.

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

Symmetry ◽

10.3390/sym13101917 ◽

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.

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Determining the environmental indicators for vehicles of different categories in relation to CO2 emission based on road tests

Combustion Engines ◽

10.19206/ce-2017-310 ◽

2017 ◽

Vol 170 (3) ◽

pp. 66-72

Author(s):

Jerzy MERKISZ ◽

Łukasz RYMANIAK

Keyword(s):

Co2 Emissions ◽

Operating Time ◽

Environmental Indicators ◽

Operating Conditions ◽

Si Engine ◽

Propulsion Systems ◽

System A ◽

In Series ◽

Series Configuration ◽

Ci Engine

The article discusses the possibility of determining the environmental indicators for vehicles of different categories in relation to CO2 emissions. These are called toxicity indicators because they concern the compounds: CO, THC and NOx. Three Euro V compliant vehicles with different propulsion systems types were used for the study: a 0.9 dm3 urban passenger car with a SI engine and a start-stop system, a 2.5 dm3 off-road vehicle with a CI engine, and a city bus with a hybrid drive system in series configuration and a CI engine with a displacement of 6.7 dm3. Measurements were made in actual operating conditions in the Poznan agglomeration using a portable emissions measurement system (PEMS). The paper presents the characteristics of the operating time shares of vehicles and propulsion systems as well as CO2 emissions depending on the engine load and crankshaft rotational speed for individual vehicles. The determined toxicity indicators allowed to indicate their usefulness, to make comparisons between tested vehicles, and to identify directions for further work on the application and interpretation of these indicators.

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Optimal control approaches for combining medicines and mosquito control in tackling dengue

Royal Society Open Science ◽

10.1098/rsos.181843 ◽

2020 ◽

Vol 7 (4) ◽

pp. 181843 ◽

Cited By ~ 1

Author(s):

Thomas Rawson ◽

Kym E. Wilkins ◽

Michael B. Bonsall

Keyword(s):

Optimal Control ◽

Disease Control ◽

Mosquito Control ◽

Large Population ◽

Human Movement ◽

Mitigation Strategies ◽

Disease Dynamics ◽

Vector Ecology ◽

Dengue Disease ◽

The Impact

Dengue is a debilitating and devastating viral infection spread by mosquito vectors, and over half the world’s population currently live at risk of dengue (and other flavivirus) infections. Here, we use an integrated epidemiological and vector ecology framework to predict optimal approaches for tackling dengue. Our aim is to investigate how vector control and/or vaccination strategies can be best combined and implemented for dengue disease control on small networks, and whether these optimal strategies differ under different circumstances. We show that a combination of vaccination programmes and the release of genetically modified self-limiting mosquitoes (comparable to sterile insect approaches) is always considered the most beneficial strategy for reducing the number of infected individuals, owing to both methods having differing impacts on the underlying disease dynamics. Additionally, depending on the impact of human movement on the disease dynamics, the optimal way to combat the spread of dengue is to focus prevention efforts on large population centres. Using mathematical frameworks, such as optimal control, are essential in developing predictive management and mitigation strategies for dengue disease control.

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An optimal control problem arising from a dengue disease transmission model

Mathematical Biosciences ◽

10.1016/j.mbs.2012.11.014 ◽

2013 ◽

Vol 242 (1) ◽

pp. 9-16 ◽

Cited By ~ 48

Author(s):

Dipo Aldila ◽

Thomas Götz ◽

Edy Soewono

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Disease Transmission ◽

Transmission Model ◽

Dengue Disease ◽

Disease Transmission Model

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Stability, Bifurcation and Optimal Control Analysis of a Malaria Model in a Periodic Environment

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0221 ◽

2018 ◽

Vol 19 (6) ◽

pp. 627-642 ◽

Cited By ~ 2

Author(s):

Prabir Panja ◽

Shyamal Kumar Mondal ◽

Joydev Chattopadhyay

Keyword(s):

Optimal Control ◽

Disease Transmission ◽

Existence Condition ◽

Infected Mosquito ◽

Transmission Model ◽

Control Analysis ◽

Periodic Environment ◽

Vector Population ◽

Autonomous Case ◽

Disease Transmission Model

AbstractIn this paper, a malaria disease transmission model has been developed. Here, the disease transmission rates from mosquito to human as well as human to mosquito and death rate of infected mosquito have been constituted by two variabilities: one is periodicity with respect to time and another is based on some control parameters. Also, total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito as well as the total human population is divided into three subpopulations such as susceptible human, infected human and recovered human. The biologically feasible equilibria and their stability properties have been discussed. Again, the existence condition of the disease has been illustrated theoretically and numerically. Hopf-bifurcation analysis has been done numerically for autonomous case of our proposed model with respect to some important parameters. At last, a optimal control problem is formulated and solved using Pontryagin’s principle. In numerical simulations, different possible combination of controls have been illustrated including the comparisons of their effectiveness.

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RELATIVE RISK ESTIMATION OF DENGUE DISEASE IN BANDUNG, INDONESIA, USING POISSON-GAMMA AND BYM MODELS CONSIDERING THE SEVERITY LEVEL

Jurnal Teknologi ◽

10.11113/.v78.7664 ◽

2016 ◽

Vol 78 (11) ◽

Cited By ~ 2

Author(s):

Farah Kristiani ◽

Benny Yong ◽

Robyn Irawan

Keyword(s):

Relative Risk ◽

Spatial Model ◽

Early Stage ◽

Risk Estimation ◽

Spatial Effect ◽

Dengue Disease ◽

Relative Risks ◽

Severe Stage ◽

Dengue Transmission ◽

Severity Levels

Recently, dengue as one of the most dangerous diseases in the world has attracted more attention due to its soaring infection cases. One method to estimate the relative risks of dengue transmission commonly used is through the statistics approach. Dengue cases of all severity levels spread rapidly in every district in Bandung, Indonesia every month. There are two different severity levels of dengue disease: the early-stage known as Dengue Fever (DF) and the severe-stage manifested as Dengue Hemorrhagic Fever (DHF) and Dengue Shock Syndrome (DSS). This research investigates the early stage, the severe stage, and the combination of both stages. The non-spatial Poisson-gamma model and spatial Besag, York, and Mollie (BYM) model are applied to estimate the relative risks in each district in Bandung every month. These two models are chosen to analyze whether there is a spatial effect in dengue transmission in particular critical area. This research will use 2013’s data from St. Borromeus hospital, one of the reputable hospitals in Bandung. The results show that the implementation of non-spatial Poisson-gamma and spatial BYM models does not depict a significant difference in the result of the relative risk estimation of dengue transmission in Bandung. The Deviance Information Criterion (DIC) diagnostic indicates that non-spatial model is better than the spatial model. Therefore, it can be concluded that there is no spatial effect in dengue transmission in Bandung. It means that dengue transmission in Bandung is not affected by neighboring areas. This analysis is also applicable to every stage estimated, both for the early-stage as well as the severe-stage.

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