scholarly journals Optimal control versus stochastic target problems: An equivalence result

2012 ◽  
Vol 61 (2) ◽  
pp. 343-346 ◽  
Author(s):  
Bruno Bouchard ◽  
Ngoc Minh Dang
Keyword(s):  
Optimal Control ◽  
Stochastic Target Problems ◽  
Control Versus ◽  
Equivalence Result

Optimal control application to the epidemiology of HBV and HCV co-infection

2021 ◽  
Author(s):  
Muhammad Naeem Jan ◽  
Gul Zaman ◽  
Nigar Ali ◽  
Imtiaz Ahmad ◽  
Zahir Shah
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Local Stability ◽  
Equilibrium Points ◽  
Optimality System ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Before And After ◽  
Control Versus ◽  
Order Four

It is very important to note that a mathematical model plays a key role in different infectious diseases. Here, we study the dynamical behaviors of both hepatitis B virus (HBV) and hepatitis C virus (HCV) with their co-infection. Actually, the purpose of this work is to show how the bi-therapy is effective and include an inhibitor for HCV infection with some treatments, which are frequently used against HBV. Local stability, global stability and its prevention from the community are studied. Mathematical models and optimality system of nonlinear DE are solved numerically by RK4. We use linearization, Lyapunov function and Pontryagin’s maximum principle for local stability, global stability and optimal control, respectively. Stability curves and basic reproductive number are plotted with and without control versus different values of parameters. This study shows that the infection will spread without control and can cover with treatment. The intensity of HBV/HCV co-infection is studied before and after optimal treatment. This represents a short drop after treatment. First, we formulate the model then find its equilibrium points for both. The models possess four distinct equilibria: HBV and HCV free, and endemic. For the proposed problem dynamics, we show the local as well as the global stability of the HBV and HCV. With the help of optimal control theory, we increase uninfected individuals and decrease the infected individuals. Three time-dependent variables are also used, namely, vaccination, treatment and isolation. Finally, optimal control is classified into optimality system, which we can solve with Runge–Kutta-order four method for different values of parameters. Finally, we will conclude the results for implementation to minimize the infected individuals.

The More Control, the Better?

2014 ◽  
Vol 26 (2) ◽  
pp. 81-91 ◽  
Author(s):  
Jeeyun Oh ◽  
Mun-Young Chung ◽  
Sangyong Han
Keyword(s):  
Mixed Design ◽  
Negative Effects ◽  
Story Structure ◽  
Content Type ◽  
High User ◽  
User Control ◽  
Rigorous Research ◽  
Control Versus ◽  
The Media ◽  
The Impact

Despite of the popularity of interactive movie trailers, rigorous research on one of the most apparent features of these interfaces – the level of user control – has been scarce. This study explored the effects of user control on users’ immersion and enjoyment of the movie trailers, moderated by the content type. We conducted a 2 (high user control versus low user control) × 2 (drama film trailer versus documentary film trailer) mixed-design factorial experiment. The results showed that the level of user control over movie trailer interfaces decreased users’ immersion when the trailer had an element of traditional story structure, such as a drama film trailer. Participants in the high user control condition answered that they were less fascinated with, absorbed in, focused on, mentally involved with, and emotionally affected by the movie trailer than participants in the low user control condition only with the drama movie trailer. The negative effects of user control on the level of immersion for the drama trailer translated into users’ enjoyment. The impact of user control over interfaces on immersion and enjoyment varies depending on the nature of the media content, which suggests a possible trade-off between the level of user control and entertainment outcomes.

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