Exploring the dynamics of a tumor-immune interplay with time delay

Sardar, Mrinmoy; Khajanchi, Subhas; Biswas, Santosh; Abdelwahab, Sayed F.; Nisar, Kottakkaran Sooppy

doi:10.1016/j.aej.2021.03.041

Cited by 22 publications

(5 citation statements)

References 43 publications

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“…Liu et al study the characteristics of key nodes in complex networks [31]. Sardar et al propose and analyse a conceptual mathematical model for the tumor-immune interaction [32]. Masood et al develop an autonomous epidemic virus model to depict the transmission of malicious computer code in active networks with preexisting immunity and quarantine as effective control strategies [33].…”

Section: Related Workmentioning

confidence: 99%

Modeling and Analysis in Peer-To-Peer Botnet with Virtual Patching and Quarantine Strategy

Yang

Yao

et al. 2022

Mathematical Problems in Engineering

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Botnets, especially peer-to-peer (P2P) botnets have become the root because of many Internet attacks recently. To effectively suppress P2P botnets, quarantine and virtual patching strategy are proposed and two dynamical models (SIIQR model and SIIQPR model) are given based on the SIIR model. The two models can examine the impact of different containment strategies on the growth of the P2P botnets. In addition, the stability of equilibrium is investigated and the basic reproduction number is obtained, which governs whether or not P2P botnets are extinct. The virtual patching strategy and quarantine strategy can effectively contain the propagation of the P2P botnets. Numerical and simulation results show the effectiveness of our models, larger infected rate, and larger deploying rate of virtual patching can control the number of infected hosts more effectively.

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Section: Related Workmentioning

confidence: 99%

Modeling and Analysis in Peer-To-Peer Botnet with Virtual Patching and Quarantine Strategy

Yang

Yao

et al. 2022

Mathematical Problems in Engineering

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“…Using mathematical modeling, many researchers have studied tumor-immune system interactions with immunotherapy and/or chemotherapy to provide important insights on tumor evolution and treatment strategies [7][8][9][10][11][12][13][14][15][16][17]. Investigations of effects of discrete delay on the stability of tumor-immune system were performed in [18][19][20][21][22][23]. Distributed delay was also adopted in [24] to study its impact on stability of equilibria.…”

Section: Introductionmentioning

confidence: 99%

The role of tumor activation and inhibition with saturation effects in a mathematical model of tumor and immune system interactions undergoing oncolytic viral therapy

Vithanage

Wei

Jang

2023

Math Methods in App Sciences

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We propose and study a mathematical model governing interactions between cancer and immune system with an oncolytic viral therapy (OVT), wherein cancer cells can activate and inhibit immune cells simultaneously with saturations.When the therapy is not applied, it is shown that the interaction can support at most three hyperbolic positive equilibria where two of them are always asymptotically stable and the other is a saddle point. The reachable stable tumor burden can be either small or large depending on initial tumor size. We analyze the full model by proving global asymptotic stability of the virus-free equilibrium that corresponds to OVT failure. Sufficient conditions based on model parameters are derived under which the model is uniformly persistent. The proposed system is validated using a mouse model of human pancreatic cancer carried out by Koujima et al. Global sensitivity analysis indicates that the rates of tumor-mediated killing and immune cell exhaustion are critical for tumor progression and therapy success. Numerical bifurcation analysis reveals that the saddle point can be utilized to estimate the maximum tumor load for eradication by OVT. Moreover, an immunosuppressive microenvironment may enhance viral therapy efficacy.

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“…In recent decades, both mathematicians and biologists have constructed numerous mathematical models to study the transmission of various infectious diseases, according to the study of Sunthrayuth et al [19], Fantaye and Birhanu [20], Li et al [21], Alqarni et al [22], Fantaye [23], Fantaye and Muchie [24], Tiwari et al [25], Sardar et al [26], Khajanchi et al [27], Tiwari et al [28], Das et al [29], Birhanu and Fantaye [30], Das et al [31], Misra et al [32], and Wong et al [33].…”

Section: Introductionmentioning

confidence: 99%

Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis

Fantaye

Birhanu

2022

Journal of Applied Mathematics

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In this study, the authors proposed a nonlinear deterministic model and stability analysis for the transmission dynamics of chewing khat. The model’s solution is proved to be positive and bounded, and the basic reproduction number ( R 0 ) is calculated using the next-generation matrix method. Following that, the authors have looked at the local and global stability of the model’s khat-free and endemic equilibrium points. When R 0 < 1 , the chewing khat-free equilibrium point is locally and globally asymptotically stable, whereas when R 0 > 1 , the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.

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Exploring the dynamics of a tumor-immune interplay with time delay

Cited by 22 publications

References 43 publications

Modeling and Analysis in Peer-To-Peer Botnet with Virtual Patching and Quarantine Strategy

Modeling and Analysis in Peer-To-Peer Botnet with Virtual Patching and Quarantine Strategy

The role of tumor activation and inhibition with saturation effects in a mathematical model of tumor and immune system interactions undergoing oncolytic viral therapy

Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis

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