A Mathematical Study of a Generalized SEIR Model of COVID-19

Abstract

In this work (Part I), we reinvestigate the study of the stability of the Covid-19 mathematical model constructed by Shah et al. (2020) [1]. In their paper, the transmission of the virus under different control strategies is modeled thanks to a generalized SEIR model. This model is characterized by a five dimensional nonlinear dynamical system, where the basic reproduction number can be established by using the next generation matrix method. In this work (Part I), it is established that the disease free equilibrium point is locally as well as globally asymptotically stable when . When , the local and global asymptotic stability of the equilibrium are determined employing the second additive compound matrix approach and the Li-Wang’s (1998) stability criterion for real matrices [2]. In the second paper (Part II), some control parameters with uncertainties will be added to stabilize the five-dimensional Covid-19 system studied here, in order to force the trajectories to go to the equilibria. The stability of the Covid-19 system with these new parameters will also be assessed in Intissar (2020) [3] applying the Li-Wang criterion and compound matrices theory. All sophisticated technical calculations including those in part I will be provided in appendices of the part II.

Excision theory in the dihedral and reflexive (co)homology of algebras

“…The results of the excision theorem of the dihedral cohomology equipped with the results of Intissar (2020) and Kostikov and Romanenkov (2020). Also, our results can introduce this application in a new form.…”

“…We discussed and proved some theorems in the cyclic and dihedral cohomology of an associative algebra and we studied a new form and new theorems in this area. We can apply this theorem in the operator algebra in the next work and apply this result in our life working as by Intissar (2020) to improve results. Our result can be equipped with the result by Kostikov and Romanenkov (2020) and can improve it by using our result.…”

Prediction of COVID-19 Confirmed Cases after Vaccination: Based on Statistical and Deep Learning Models

“…The case studies for COVID-19 can be found in [4][5][6][7][8][9][10][11][12][13][14][15][16], especially for Wuhan, China [4][5][6][7][8]. For example, Li et al (2020) [4] described the characteristic of positive cases, the distributions of epidemiological time delay, the disease doubling time, and the breeding number, based on the data of Wuhan.…”

“…There are case studies for COVID-19 [4][5][6][7][8][9][10][11][12][13][14][15][16], especially for Wuhan, China [4][5][6][7][8]. Various models for the disease have been studied in 2020, including mathematical models [7][8][9][10][11][12][13][14][15][16][17][18][19], statistical modeling [20][21][22], and artificial intelligence (AI) models [15,[22][23][24]. Details of the studies are presented in section 2.…”

Expeditious COVID-19 similarity measure tool based on consolidated SCA algorithm with mutation and opposition operators

“…Studies have been performed for modeling the physical transportation of COVID-19 in the air [6] , [7] . In [8] , the stability of the transmission model of COVID-19 that was developed based on the SEIR model was investigated under different control strategies. In [9] , The transmission of the airborne germ of COVID-19 was provided from a physics view based on fluid dynamics analysis methodology.…”