Dynamic analysis of an antitumor model and investigation of the therapeutic effects for different treatment regimens

Pang, Liuyong; Zhao, Zhentang; Liu, Sanhong; Zhang, Xinan

doi:10.1007/s40314-015-0241-4

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…As discussed above, radiotherapy is usually used in cancer treatment because it permanently damages the DNA of tumour cells, destroying these cells [ 18 , 19 ]. While nearby healthy tissue cells can suffer temporary damage from this radiation, these cells can repair the DNA damage and continue to grow normally.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an Antitumour Model with Pulsed Radioimmunotherapy

Wang

Tang

2022

Computational and Mathematical Methods in Medicine

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In this paper, an antitumour model for characterising radiotherapy and immunotherapy processes at different fixed times is proposed. The global attractiveness of the positive periodic solution for each corresponding subsystem is proved with the integral inequality technique. Then, based on the differentiability of the solutions with respect to the initial values, the eigenvalues of the Jacobian matrix at a fixed point corresponding to the tumour-free periodic solution are determined, resulting in a sufficient condition for local stability. The solutions to the ordinary differential equations are compared, the threshold condition for the global attractiveness of the tumour-free periodic solution is provided in terms of an indicator R 0 , and the permanence of a system with at least one tumour-present periodic solution is investigated. Furthermore, the effects of the death rate, effector cell injection dosage, therapeutic period, and effector cell activation rate on indicator R 0 are determined through numerical simulations, and the results indicate that radioimmunotherapy is more effective than either radiotherapy or immunotherapy alone.

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Section: Introductionmentioning

confidence: 99%

Dynamics of an Antitumour Model with Pulsed Radioimmunotherapy

Wang

Tang

2022

Computational and Mathematical Methods in Medicine

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“…In the same year, Bi and Ruan 13 researched the bifurcation of lymphocytes and solid spherical tumors model. In 2017, Pang et al 14 used an impulsive differential equation to study the combination treatment of radiotherapy with immunotherapy at the same fixed periodic time. In the same year, Li et al 15 investigated the stochastic responses of tumor‐immune system competition model with environmental noise and periodic treatment.…”

Section: Introductionmentioning

confidence: 99%

“…First, we take account of the immunotherapy of direct injection of ex vivo activated T cells at the fixed periodic time for treating general tumor patients into the model of a published paper 20 . Since the duration of injection of activated T cells (or immune‐drug) which are subject to short‐term perturbations is negligible in comparison with the whole treatment stage, the models with impulsive treatments conform better to the reality than the continuous models (see Pang et al 14 ). Thus, we obtain the following antitumor constant impulsive model with single immunotherapy:

\begin{matrix} right \dot{C_{H}} (τ) & left = \tilde{r} [1 - \frac{C_{H} (τ)}{κ}] C_{H} (τ) - \tilde{c} C_{H} (τ) N_{T} (τ), τ \neq n \tilde{T}, \\ right \dot{N_{T}} (τ) & left = \tilde{b} N_{T} (τ) N_{D C} (τ) - δ_{T} N_{T} (τ), τ \neq n \tilde{T}, \\ right \dot{N_{D C}} (τ) & left = ã N_{T} (τ) C_{H} (τ) - δ_{D C} N_{D C} (τ), τ \neq n \tilde{T}, \\ right C_{H} (n {\tilde{T}}^{+}) & left = C_{H} \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

Dynamics of immunotherapy antitumor models with impulsive control strategy

Wang

Zhang

2021

Math Methods in App Sciences

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In this paper, using the methods of killing tumors and impulsive differential equations, two immunotherapy antitumor models for describing therapies of general tumors and advanced solid tumors are established. By using the theories of impulsive equations, small amplitude perturbation techniques, and the comparison technique, we obtain the conditions which guarantee the global asymptotical stability of the tumor‐eliminated periodic solution and system permanence, when immunotherapy alone is performed. The numerical results of the influences of the impulsive perturbation on the inherent oscillation show rich dynamics, such as period‐doubling bifurcation and chaos. Moreover, the effects of the combination of radiotherapy with immunotherapy on antitumor are obtained, including the threshold value of stability conditions of tumor‐eradication periodic solution when the mixed combination treatment of immunotherapy and radiotherapy is performed. Some numerical simulations for the effects of the timing of radiotherapy application and the timing of injection T cells on the threshold value are performed. Finally, we present some theoretical methods for suppressing the growth of tumors.

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