Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

Ahmed, Nauman; Fatima, Mehreen; Băleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, İlyas; Rafiq, Muhammad; Rehman, M. A.; Ahmad, Maqbool

doi:10.3389/fphy.2019.00220

Cited by 16 publications

(11 citation statements)

References 27 publications

(43 reference statements)

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“…Consequently, u(B) ≤ _ L/L − b for t > T by (23), and ( 31) and (32), where b � min ξ, (q 1 − 1)εL/q 1 B 􏼈 􏼉 > 0. For each answer x(t, x 0 ) of system (3) satisfying x 0 ∈ K and t > T, there is…”

Section: Stability Of the Virose Equilibriummentioning

confidence: 93%

“…susceptible-exposed-infected-recovered (SEIR) models [14][15][16][17], susceptible-exposed-infected-recovered-susceptible (SEIRS) models [18][19][20][21], susceptible-exposed-infectedquarantined-vaccinated (SEIQV) models [22,23], and susceptible-exposed-infected-quarantined-recovered-susceptible (SEIQRS) models [24][25][26]. To explicitly compare the individual characteristics of computer virus propagation models, we have made tabular discussions in Table 1.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical Behavior of Hybrid Propagation of Computer Viruses

Zhu

Xiang

Luo

et al. 2022

Security and Communication Networks

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Considering the horizontal and vertical propagation of computer viruses over the Internet, this article proposes a hybrid susceptible-latent-breaking-recovered-susceptible (SLBRS) model. Through mathematical analysis of the model, two equilibria (virus-free and virose equilibria) and their global stabilities are both proved depending on the basic reproduction number R 0 , which is affected by the vertical propagation of infected computers. Moreover, the feasibility of the obtained results is verified by numerical simulations. Finally, the dependence of R 0 on system parameters and the parameters affecting the stability level of infected computers are both analyzed.

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Section: Stability Of the Virose Equilibriummentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Dynamical Behavior of Hybrid Propagation of Computer Viruses

Zhu

Xiang

Luo

et al. 2022

Security and Communication Networks

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“…( 1) to ( 5) subject to initial and boundary conditions Eqs. ( 6) to (7). Then the numerical solutions S, E, I, A, R, of Eqs.…”

Section: Convergencementioning

confidence: 99%

“…In this study, a classical disease model is modified to the advection model by considering the advection terms and some appropriate parameters. By considering these terms, the extended model has become more realistic [7,8]. Jiang et al [9] investigated the dynamics of coronavirus with clinical signs and symptoms, by using artificial intelligence.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Novel Coronavirus (2019-nCov) Pandemic Model with Advection

Azam¹,

Ahmed²,

Raza³

et al. 2021

Computers, Materials &Amp; Continua

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Recently, the world is facing the terror of the novel corona-virus, termed as COVID-19. Various health institutes and researchers are continuously striving to control this pandemic. In this article, the SEIAR (susceptible, exposed, infected, symptomatically infected, asymptomatically infected and recovered) infection model of COVID-19 with a constant rate of advection is studied for the disease propagation. A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system. The continuous model is transposed into a discrete numerical model by discretizing the domains, finitely. To analyze the disease dynamics, a structure preserving non-standard finite difference scheme is designed. Two steady states of the continuous system are described i.e., virus free steady state and virus existing steady state. Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model. Positivity of the state variables is ensured by applying the M-matrix theory. A result for the positivity property is established. For the proposed numerical design, two different types of the stability are investigated. Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results. Von Neuman stability test is applied to ensure linear stability. The reproductive number is described and its pivotal role in stability analysis is also discussed. Consistency and convergence of the numerical model is also studied. Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically, which is helpful in controlling the disease dynamics. In the end, the conclusion of the study is also rendered.

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“…Consequently, epidemic models governed by ordinary differential equations are extended to spatiotemporal epidemic models, which are expressed by a system consisting of reaction-diffusion equations. In this sense, many models have been studied and some pioneering results, in terms of extending the definition of the basic reproduction number, establishing the conditions under which the disease persists or vanishes as well as proposing adequate numerical methods, have been established [16][17][18][19][20][21][22][23]. Recently, epidemic models incorporating the heterogeneity of the population together with the spatial diffusion have started to gain the attention of several researchers, due to the little amount of research done on these models, compared to the above-mentioned types.…”

Section: Introductionmentioning

confidence: 99%

Optimal control for a multi-group reaction–diffusion SIR model with heterogeneous incidence rates

Mehdaoui

Alaoui

Tilioua

2022

Int. J. Dynam. Control

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This paper is devoted to the study of an optimal control problem for a generalized multi-group reaction-diffusion SIR epidemic model, with heterogeneous nonlinear incidence rates. The proposed model incorporates a wide range of spatiotemporal epidemic models. Primarily, the ones used to describe the propagation of zoonotic and sexually transmitted diseases, as well as epidemics that propagate disparately within populations. For the aforementioned diseases, dividing the susceptible, infected and recovered populations into several subpopulations is necessary in order to capture all the possible ways of the disease transmission. This makes the problem of finding the possible optimal control strategies and the division of the available control resources complicated. To address this problem mathematically, for each subpopulation, we introduce two types of control variables, namely vaccination for the susceptible and treatment for the infected. The existence and uniqueness of a biologically feasible solution to the proposed model, for fixed controls, is derived by means of a truncation technique and a semigroup approach. Moreover, first-order necessary optimality conditions for the introduced optimal control problem are obtained using the adjoint state method. Finally, numerical simulations are performed for a two-group epidemic model with particular incidence rates and by considering three cases in the maximal control resources allowed for each subpopulation.

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Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

Cited by 16 publications

References 27 publications

Dynamical Behavior of Hybrid Propagation of Computer Viruses

Dynamical Behavior of Hybrid Propagation of Computer Viruses

Numerical Analysis of Novel Coronavirus (2019-nCov) Pandemic Model with Advection

Optimal control for a multi-group reaction–diffusion SIR model with heterogeneous incidence rates

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