scholarly journals Stability analysis and optimal control of Covid-19 pandemic SEIQR fractional mathematical model with harmonic mean type incidence rate and treatment

2021 ◽  
Vol 22 ◽  
pp. 103873
Author(s):  
Muhammad Sinan ◽  
Amjad Ali ◽  
Kamal Shah ◽  
Taghreed A. Assiri ◽  
Taher A. Nofal
Author(s):  
Subhas Khajanchi

AbstractWe investigate a mathematical model using a system of coupled ordinary differential equations, which describes the interplay of malignant glioma cells, macrophages, glioma specific CD8+T cells and the immunotherapeutic drug Adoptive Cellular Immunotherapy (ACI). To better understand under what circumstances the glioma cells can be eliminated, we employ the theory of optimal control. We investigate the dynamics of the system by observing biologically feasible equilibrium points and their stability analysis before administration of the external therapy ACI. We solve an optimal control problem with an objective functional which minimizes the glioma cell burden as well as the side effects of the treatment. We characterize our optimal control in terms of the solutions to the optimality system, in which the state system coupled with the adjoint system. Our model simulation demonstrates that the strength of treatment $u_{1}(t)$ plays an important role to eliminate the glioma cells. Finally, we derive an optimal treatment strategy and then solve it numerically.


2020 ◽  
Vol 135 (6) ◽  
Author(s):  
Amir Khan ◽  
Rahat Zarin ◽  
Mustafa Inc ◽  
Gul Zaman ◽  
Bandar Almohsen

2021 ◽  
Vol 136 (1) ◽  
Author(s):  
Adnane Boukhouima ◽  
El Mehdi Lotfi ◽  
Marouane Mahrouf ◽  
Silvério Rosa ◽  
Delfim F. M. Torres ◽  
...  

1976 ◽  
Vol 98 (2) ◽  
pp. 161-166 ◽  
Author(s):  
J. S. Ansari

A heat exchanger with boiling is considered. The final temperature of steam is controlled with the help of a controller which regulates the flow rate of by-pass water mixing with the outcoming steam. The simplest known mathematical model retaining the nonlinear and distributed parameter nature of the process is adopted. A known method of analysis, namely, Liapunov-Razumikhin theorem, is used to derive results on stability. An interesting feature of the system is that a positive feedback is required for stability. If the control is designed on the basis of minimization of the error in the final temperature alone, then the optimal control, requiring a negative feeedback, leads to sustained oscillations in the intermediate variables, even when the output is steady. The analysis, therefore suggests that meaningful optimization must take into account fluctuations in intermediate variables in addition to the error. A derivative control is shown to improve the transient response.


2021 ◽  
Vol 20 ◽  
pp. 103703
Author(s):  
Amir Khan ◽  
Rahat Zarin ◽  
Ghulam Hussain ◽  
Noor Atinah Ahmad ◽  
Mohd Hafiz Mohd ◽  
...  

2020 ◽  
Author(s):  
Aidalina Mahmud ◽  
Poh Ying Lim ◽  
Hayati Kadir Shahar

BACKGROUND On March 18, 2020, the Malaysian government implemented Movement Control Order (MCO) to limit the contact rates among the population and infected individuals. OBJECTIVE The objective of this study was to forecast the trend of the COVID-19 epidemic in Malaysia in terms of its magnitude and duration. METHODS Data for this analysis was obtained from publicly available databases, from March 17 until March 27, 2020. By applying the Susceptible, Exposed, Infectious and Removed (SEIR) mathematical model and several predetermined assumptions, two analyses were carried out: without and with MCO implementation. RESULTS Without MCO, it is forecasted that it would take 18 days to reach the peak of infection incidence. The incidence rate would plateau at day 80 and end by day 94, with 43% of the exposed population infected. With the implementation of the MCO, it is forecasted that new cases of infection would peak at day 25, plateau at day 90 and end by day 100. At its peak, the infection could affect up to about 40% of the exposed population. CONCLUSIONS It is forecasted that the COVID-19 epidemic in Malaysia will subside soon after the mid-year of 2020. Although the implementation of MCO can flatten the epidemiological curve, it also prolongs the duration of the epidemic. The MCO can result in several unfavorable consequences in economic and psychosocial aspects. A future work of an exit plan for the MCO should also be devised and implemented gradually. The exit plan raises several timely issues of re-infection resurgence after MCO are lifted.


2021 ◽  
Vol 145 ◽  
pp. 110789
Author(s):  
Parthasakha Das ◽  
Samhita Das ◽  
Pritha Das ◽  
Fathalla A. Rihan ◽  
Muhammet Uzuntarla ◽  
...  

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