Optimal Control of a Delayed Alcoholism Model with Saturated Treatment

2021 ◽  
Author(s):  
Rachid Bouajaji ◽  
Abdelhadi Abta ◽  
Hassan Laarabi ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Saturated Treatment

scholarly journals Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

2021 ◽  
Author(s):  
Jayanta Kumar Ghosh ◽  
Prahlad Majumdar ◽  
Uttam Ghosh
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Logistic Growth ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Susceptible Population ◽  
Saturated Treatment

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

scholarly journals Optimal control analysis of vector-host model with saturated treatment

2020 ◽  
Vol 135 (10) ◽  
Author(s):  
Saif Ullah ◽  
Muhammad Farooq Khan ◽  
Syed Azhar Ali Shah ◽  
Muhammad Farooq ◽  
Muhammad Altaf Khan ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Analysis ◽  
Saturated Treatment

scholarly journals A biological mathematical model of vector-host disease with saturated treatment function and optimal control strategies

2020 ◽  
Vol 17 (4) ◽  
pp. 3972-3997 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
◽  
Navid Iqbal ◽  
Yasir Khan ◽  
Ebraheem Alzahrani ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategies ◽  
Host Disease ◽  
Treatment Function ◽  
Saturated Treatment
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