Hopf and backward bifurcations induced by immune effectors in a cancer oncolytic virotherapy dynamics

Nono, Martial Kabong; Ngouonkadi, Elie Bertrand Megam; Bowong, Samuel; Fotsin, Hilaire Bertrand

doi:10.1007/s40435-020-00703-1

Cited by 4 publications

(15 citation statements)

References 46 publications

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“…In any system, quantifying uncertainties is an important task. A method to achieve this goal is sensitivity analysis (SA) [54][55][56][57]. Its objective is to identify crucial inputs of a system and to present how their uncertainties affect its issue.…”

Section: Parameter's Sensitivity Analysis On System's Dynamicsmentioning

confidence: 99%

“…They will subsequently be considered as bifurcations control factors. Recall that for nonlinear systems as those studied here, mesures are generally based on rank transform such as Partial Rank Correlation Coefficients (PRCCs) [54][55][56][57]. It is evaluated to have estimation of correlation between values of the systems' dynamics when they increase or decrease.…”

Section: Parameter's Sensitivity Analysis On System's Dynamicsmentioning

confidence: 99%

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Hopf and quasi-periodic Hopf bifurcations and deterministic coherence in coupled Duffing-Holmes and Van der Pol oscillators: the Arnol’d resonance web

Ngouonkadi¹,

Nono²,

Fotsin³

et al. 2022

Phys. Scr.

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A survey on coupled Van der Pol (VDP) and Duffing-Holmes (DH) oscillators, a model widely encountered in various branches of Physics and engineering is done. A bifurcation analysis of the model is presented when both unidirectional and mutual couplings are considered. It is found that stable, unstable and chaotic behaviors appear in the models. Using the method of charts of dynamics regimes in parameter planes, numerical study of the parameters space of the initial differential equations is done. Results from both approaches are compared and discussed. Features of the bifurcation picture are discussed when varying control parameters and analysis of slow-flow equations is presented. We show that the local bifurcation transition from an invariant one-torus (IT1) to an invariant two-torus (IT2) is caused by a Neimark-Saker (NS) bifurcation, also known as a one dimension-higher quasi- periodic Hopf (QH) bifurcation, these by analysing the graph of Lyapunov exponents. We observe that in the mutual coupling case, a complex structure generally-called Arnold’s resonance web phenomenon appears. Numerical simulations are compared to experimental measurements to illustrate the above behaviors. We also note the birth of coherence resonance in the slave oscillator for a certain coupling strength in the case of unidirectional coupling. We also analyze the effect of the coupling strength on the generalized synchronization between the master system and the slave system in the case of unidirectional coupling, through the concept of mutual false nearest neighbors. It allows us to understand when and how closeness in response space implies closeness in driving space.

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Section: Parameter's Sensitivity Analysis On System's Dynamicsmentioning

confidence: 99%

Section: Parameter's Sensitivity Analysis On System's Dynamicsmentioning

confidence: 99%

Hopf and quasi-periodic Hopf bifurcations and deterministic coherence in coupled Duffing-Holmes and Van der Pol oscillators: the Arnol’d resonance web

Ngouonkadi¹,

Nono²,

Fotsin³

et al. 2022

Phys. Scr.

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“…In this section, we consider the case when has a pair of purely imaginary eigenvalues. Hopf bifurcation occurs when this pair of complex conjugate eigenvalues around non-trivial equilibrium cross-imaginary axis [ 44 ]. In this case, endemic equilibria loses stability through Hopf bifurcation under some parametric restriction.…”

Section: Bifurcation Analysismentioning

confidence: 99%

Complex dynamics and control analysis of an epidemic model with non-monotone incidence and saturated treatment

Saha

Ghosh

2022

Int. J. Dynam. Control

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In this manuscript, we consider an epidemic model having constant recruitment of susceptible individuals with non-monotone disease transmission rate and saturated-type treatment rate. Two types of disease control strategies are taken here, namely vaccination for susceptible individuals and treatment for infected individuals to minimize the impact of the disease. We study local as well as global stability analysis of the disease-free equilibrium point and also endemic equilibrium point based on the values of basic reproduction number . Therefore, disease eradicates from the population if basic reproduction number less than unity and disease persists in the population if basic reproduction number greater than unity. We use center manifold theorem to study the dynamical behavior of the disease-free equilibrium point for . We investigate different bifurcations such as transcritical bifurcation, backward bifurcation, saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation of co-dimension 2. The biological significance of all types of bifurcations are described. Some numerical simulations are performed to check the reliability of our theoretical approach. Sensitivity analysis is performed to identify the influential model parameters which have most impact on the basic reproduction number of the proposed model. To control or eradicate the influence of the emerging disease, we need to control the most sensitive model parameters using necessary preventive measures. We study optimal control problem using Pontryagin’s maximum principle. Finally using efficiency analysis, we determine most effective control strategy among applied controls.

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“…Tumor-selective replication phenomenon of oncolytic viruses has also received some success. For example, the use of tissue or tumor specific promoter to lead expression of an indispensable viral gene [26][27][28][29], the modification of viral-surface receptors to selectively direct on ligands (they are highly expressed tumor microenvironment or tumor cells) [4,[30][31][32][33][34]. However, despite the current clinical development of most oncolytic viruses [35], virotherapy still has some limitations in terms of efficacy [16,36].…”

Section: Introductionmentioning

confidence: 99%

Bistability and chaotic behaviors in a 4D cancer oncolytic Virotherapy mathematical model: Pspice and FPGA implementations

Kabong Nono,

Megam Ngouonkadi

et al. 2024

Phys. Scr.

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Oncolytic viruses (OVs) exploit characteristics of mass cells and tumor-related reaction of the body to the presence of antigen, to lyse malignant cells and modulate the tumor microenvironment. However, the effective clinical utilization of these powerful treatment modules necessitates their logical control, especially in order to prevent solid and metastatic outgrowths. Hence, it is imperative to develop methods to protect a virus from the annihilating surroundings from the bloodstream when traveling to tumor locations. Our article reports on bistability and chaotic behavior in a 4D cancer virotherapy model. We find that unstable, stable and chaotic behaviors can appear in the model when tuning some of its parameters. With the help of the chart of dynamic behaviors in parameter spaces, numerical investigations of the system's characteristics are analyzed followed by a discussion of the obtained results. It appears that the local transition change from an invariant one-torus (IT1) to its two-torus (IT2) counterpart can be found in the system and this undergoes a Neimark-Saker (NS) change of direction. Based on analytical analysis, it is foretold that the model exhibits striking behaviors. We also focus our study on the deign of ad-hoc electronic and FPGA implementations of the cancer virotherapy's model, to illustrate the obtained analytical results.

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Hopf and backward bifurcations induced by immune effectors in a cancer oncolytic virotherapy dynamics

Cited by 4 publications

References 46 publications

Hopf and quasi-periodic Hopf bifurcations and deterministic coherence in coupled Duffing-Holmes and Van der Pol oscillators: the Arnol’d resonance web

Hopf and quasi-periodic Hopf bifurcations and deterministic coherence in coupled Duffing-Holmes and Van der Pol oscillators: the Arnol’d resonance web

Complex dynamics and control analysis of an epidemic model with non-monotone incidence and saturated treatment

Bistability and chaotic behaviors in a 4D cancer oncolytic Virotherapy mathematical model: Pspice and FPGA implementations

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