Modeling and bifurcation analysis of a viral infection with time delay and immune impairment

Krishnapriya, P.; Pitchaimani, M.

doi:10.1007/s13160-017-0240-5

Cited by 14 publications

(11 citation statements)

References 22 publications

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“…Pathogen infection models with immune impairment have been studied in several works (see e.g. [2,17,19,20,35,43]). …”

Section: Introductionmentioning

confidence: 99%

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Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Ełaiw¹,

Raezah²,

Alofi³

2018

J. Nonlinear Sci. Appl.

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We study the global stability analysis of pathogen infection models with immune impairment. Both pathogen-to-susceptible and infected-to-susceptible transmissions have been considered. We drive the basic reproduction parameter R 0 , which determines the global dynamics of models. Using the method of Lyapunov function, we established the global stability of the steady states of the models. Numerical simulations are used to confirm the theoretical results.

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“…Pathogen infection models with immune impairment have been studied in several works (see e.g. [2,17,19,20,35,43]). …”

Section: Introductionmentioning

confidence: 99%

“…The works presented in [2,17,19,20,35,43] assume that the susceptible cells become infected due to pathogen contacts. However, pathogen can also spread by direct infected-to-susceptible transmission.…”

Section: Introductionmentioning

confidence: 99%

Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Ełaiw¹,

Raezah²,

Alofi³

2018

J. Nonlinear Sci. Appl.

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“…Pathogen dynamics models with CTL immune impairment have been studied in many papers (see e.g. [27]- [30]). In papers [27]- [30], only pathogen-to-susceptible transmission has been considered.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of immune impairment pathogen dynamics model with two routes of infection and Holling type-II function

Ełaiw¹,

Alofi²

2018

ams

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We study a pathogen infection model with immune impairment. The infected-susceptible and pathogen-susceptible incidence rates are given by Holling type-II. The existence and global stability of the equilibria are determined by the basic reproduction number. The global stability of the two equilibria are proven using Lyapunov method. We conduct numerical simulations to support the theoretical results.

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“…Many mathematical models have been developed to describe the immunological response to infection with different types of biological models, for example human immunodeficiency virus (HIV), H1N1 influenza-A, tumour models and so on [16][17][18][19]21]. Modelling tumour-immune interaction has attracted much attention in the last decades.…”

Section: Introductionmentioning

confidence: 99%

Analysis of tumour-immune evasion with chemo-immuno therapeutic treatment with quadratic optimal control

Ravindran

Sheriff

Krishnapriya

2017

Journal of Biological Dynamics

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A simple mathematical model for the growth of tumour with discrete time delay in the immune system is considered. The dynamical behaviour of our system by analysing the existence and stability of our system at various equilibria is discussed elaborately. We set up an optimal control problem relative to the model so as to minimize the number of tumour cells and the chemo-immunotherapeutic drug administration. Sensitivity analysis of tumour model reveals that parameter value has a major impact on the model dynamics. We numerically illustrate how does these delay can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumour. Finally, epidemiological implications of our analytical findings are addressed critically. ARTICLE HISTORY

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Modeling and bifurcation analysis of a viral infection with time delay and immune impairment

Cited by 14 publications

References 22 publications

Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Stability of pathogen dynamics models with viral and cellular infections and immune impairment

Stability analysis of immune impairment pathogen dynamics model with two routes of infection and Holling type-II function

Analysis of tumour-immune evasion with chemo-immuno therapeutic treatment with quadratic optimal control

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