Hopf bifurcation analysis in a delayed system for cancer virotherapy

Ashyani, Akram; Mohammadinejad, H.M.; RabieiMotlagh, Omid

doi:10.1016/j.indag.2015.10.015

Cited by 12 publications

(8 citation statements)

References 15 publications

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“…He proposed three models that describe the interactions between uninfected and infected tumor cells with three immune responses: virus-specific Cytotoxic T Lymphocytes (CTL), tumor-specific CTL, and both virus and tumor-specific CTL responses. Later, Ashyani et al [9] presented a detailed mathematical analysis with simulations of the last model in [8] after modifying it by considering immune responses to both virus and tumor as one variable in the model. The state variables of the models in [8,9] are uninfected tumor cells, infected tumor cells, and immune cells.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Ashyani et al [9] presented a detailed mathematical analysis with simulations of the last model in [8] after modifying it by considering immune responses to both virus and tumor as one variable in the model. The state variables of the models in [8,9] are uninfected tumor cells, infected tumor cells, and immune cells. Phan and Tian [10] added another state variable to them, which describes the virus-free population.…”

Section: Introductionmentioning

confidence: 99%

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Modeling dynamics of cancer virotherapy with immune response

2020

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Virotherapy is a therapeutic treatment for cancer. It uses genetically engineered viruses to selectively infect, replicate in, and destroy cancer cells without damaging normal cells. In this paper, we present a modified model to include, within the dynamics of virotherapy, the interaction between uninfected tumor cells and immune response. The model is analyzed qualitatively to produce five equilibrium points. One of these equilibriums demonstrates the effect observed in virotherapy, where the immune system demolishes infected cells as well as viruses. Moreover, the existence and stability of the equilibrium points are established under certain criteria. Numerical simulations are performed to display the agreement with the analytical results. Finally, parameter analysis is carried out to illustrate which parameters in the model affect the outcome of virotherapy.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling dynamics of cancer virotherapy with immune response

2020

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“…The time delay may influence the dynamics of infectious diseases. In fact, many diseases have different kinds of delays when they spread, such as immunity period delay [7,8], infection period delay [9], and incubation period delay [10][11][12][13][14]. It is well known that the dynamical behaviors (including stability, attractivity, persistence, periodic oscillation, bifurcation, and chaos) of population models with time delay have become a subject of intense research activities.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period

Sirijampa

Chinviriyasit

2018

Adv Differ Equ

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In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number R 0 , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when R 0 > 1. We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.

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“…However, it is reasonable to use two parameters to present the viral oncolytic process, the infection time which is the time period from the time when viruses attach to a host cell to the time when they penetrate into the host cell, and the viral renewal time (or the lytic cycle in narrow sense) which is the time period from the time when viruses penetrate to the host cell to the time when new viruses burst out from the host cell. In the literature, there are several models which include the infection time as a delay parameter [28,31,32], and several models which include the virus renewal time as a delay parameter [1,2,15]. However, these models either have two equations or three equations for tumour cells and infected tumour cells or/and viruses, and do not incorporate immune responses.…”

Section: Introductionmentioning

confidence: 99%

Backward Hopf bifurcation in a mathematical model for oncolytic virotherapy with the infection delay and innate immune effects

Guo

Niu

Tian

2019

Journal of Biological Dynamics

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In this paper, we consider a system of delay differential equations that models the oncolytic virotherapy on solid tumours with the delay of viral infection in the presence of the innate immune response. We conduct qualitative and numerical analysis, and provide possible medical implications for our results. The system has four equilibrium solutions. Fixed point analysis indicates that increasing the burst size and infection rate of the viruses has positive contribution to the therapy. However, increasing the immune killing infection rate, the immune stimulation rate, or the immune killing virus rate may lead the treatment failed. The viral infection time delay induces backward Hopf bifurcations, which means that the therapy may fail before time delay increases passing through a Hopf bifurcation. The parameter analysis also shows how saddle-node and Hopf bifurcations occur as viral burst size and other parameters vary, which yields further insights into the dynamics of the virotherapy.

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Hopf bifurcation analysis in a delayed system for cancer virotherapy

Cited by 12 publications

References 15 publications

Modeling dynamics of cancer virotherapy with immune response

Modeling dynamics of cancer virotherapy with immune response

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period

Backward Hopf bifurcation in a mathematical model for oncolytic virotherapy with the infection delay and innate immune effects

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