Mutual inhibition in presence of a virus in continuous culture

Alsahafi, Salah; Woodcock, Stephen

doi:10.3934/mbe.2021162

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…It can be easily shown that W1 = { Ē} . Using LaSalle's invariance principle [14] (see [15,16,17,9,10,11,18,19] for more applications), one can easily deduce that Ē is GAS when R ≤ 1. Then the solution of system (2.1) converges to Ē since t → +∞.…”

Section: Global Stability Analysismentioning

confidence: 99%

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Alhmadi¹

2022

ARJOM

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In this paper, an SEIR epidemic model with nonlinear incidence is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R. If the basic reproduction number \(\mathcal{R}\) < 1, the disease-free equilibrium \(\mathcal{E}\) is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number \(\mathcal{R}\) > 1, the disease is uniformly persistent and the unique endemic equilibrium \(\mathcal{E}\) * of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

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Section: Global Stability Analysismentioning

confidence: 99%

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Alhmadi¹

2022

ARJOM

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“…The contribution of mathematics is made initially through modelling [6][7][8][9][10][11][12][13][14]. This stage of mathematical modelling makes it possible to test, without wasting time or expense, the control measures that are envisaged: preventive measures, isolation of patients, treatments, vaccinations, and so forth.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate

Alsahafi¹,

Woodcock²

2021

Mathematics

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In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (R0) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if R0≤1, and the CHIKV endemic point is locally asymptotically stable if R0>1. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained.

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Exploring HIV Dynamics and an Optimal Control Strategy

Alsahafi

Woodcock

2022

Mathematics

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In this paper, we propose a six-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, the short-lived productively infected cells, and the long-lived productively infected cells. The basic reproduction number was established, and the local and global stability of the equilibria of the model were studied. A sensitivity analysis with respect to the model parameters was undertaken. Based on this study, an optimal strategy is proposed to decrease the number of infected cells. Finally, some numerical simulations are presented to illustrate the theoretical findings.

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Mutual inhibition in presence of a virus in continuous culture

Cited by 4 publications

References 15 publications

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Mathematical Analysis of a SEIR Model with Nonlinear Incidence Rate for COVID-19 Dynamics

Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate

Exploring HIV Dynamics and an Optimal Control Strategy

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