scholarly journals Legendre-Galerkin Method, Dynamical System, and Optimal Control for Solving Covid-19 Model

Author(s):  
A. Mahdy ◽  
khaled lotfy

Abstract The advancement of numerical demonstrating of irresistible illnesses is a key examination territory in different fields including the nature and the study of disease transmission. One point of these models is to comprehend the elements of conduct in irresistible infections. For the new strain of Covid (Coronavirus), there is no immunization to secure individuals and to forestall its spread up until now. All things being equal, control procedures related to medical services, for example, social separating, isolation, travel limitations, can be adjusted to control the pandemic of Coronavirus. This article reveals insights into the dynamical practices of nonlinear Coronavirus models dependent on strategy: the Legendre-Galerkin strategy. We summon a novel sign stream chart that is utilized to depict the Coronavirus model. Based on the Legendre-Galerkin method, the covid-19 model. Mathematica, as one of the world's leading computational software, was employed for the implementation of solutions. The proposed numerical techniques provide are excellent. Through our numerical investigations, it is uncovered that social removing between possibly tainted people who are conveying the infection and solid people can diminish or intrude on the spread of the infection. The mathematical reenactment results are insensible concurrence with the investigation forecasts. The free balance and dependability focus for the Coronavirus model is researched. Likewise, the presence of a consistently steady arrangement is demonstrate.

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

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Dania Altulea ◽  
Rafida M. Elobaid

AbstractRecently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.


2017 ◽  
Vol 130 ◽  
pp. 07001 ◽  
Author(s):  
Sergey Shevtsov ◽  
Ilya Tarasov ◽  
Vladimir Axenov ◽  
Igor Zhilyaev ◽  
Jiing-Kae Wu ◽  
...  

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.


2021 ◽  
Vol 19 (2) ◽  
pp. 1677-1695
Author(s):  
Boli Xie ◽  
◽  
Maoxing Liu ◽  
Lei Zhang

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>


Author(s):  
Yuriy Romasevych ◽  
Viatcheslav Loveikin ◽  
Oleksandr Shevchuk

Author(s):  
Sanchez Edgar N. ◽  
Vega Carlos J. ◽  
Suarez Oscar J. ◽  
Guanrong Chen
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