Optimal control applied to immunotherapy

Burden, Thalya; Ernstberger, Jon; Fister, K. Renee

doi:10.3934/dcdsb.2004.4.135

Cited by 31 publications

(5 citation statements)

References 12 publications

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“…In this respect, experimental evidence supports the idea that the efficacy of anti-cancer protocols can be enhanced by combining immune-boosters, that favor the recruiting of effector immune cells, together with chemotherapy relying on lower concentrations of cytotoxic agents [4,6,18,25,35,38,43,44].…”

Section: Introductionmentioning

confidence: 94%

Evolutionary Dynamics of Cancer Cell Populations under Immune Selection Pressure and Optimal Control of Chemotherapy

Dimitriu

Lorenzi

Ştefanescu

2014

Math. Model. Nat. Phenom.

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Increasing experimental evidence suggests that epigenetic and microenvironmental factors play a key role in cancer progression. In this respect, it is now generally recognized that the immune system can act as an additional selective pressure, which modulates tumor development and leads, through cancer immunoediting, to the selection for resistance to immune effector mechanisms. This may have serious implications for the design of effective anti-cancer protocols. Motivated by these considerations, we present a mathematical model for the dynamics of cancer and immune cells under the effects of chemotherapy and immunity-boosters. Tumor cells are modeled as a population structured by a continuous phenotypic trait, that is related to the level of resistance to receptor-induced cell death triggered by effector lymphocytes. The level of resistance can vary over time due to the effects of epigenetic modifications. In the asymptotic regime of small epimutations, we highlight the ability of the model to reproduce cancer immunoediting. In an optimal control framework, we tackle the problem of designing effective anti-cancer protocols. The results obtained suggest that chemotherapeutic drugs characterized by high cytotoxic effects can be useful for treating tumors of large size. On the other hand, less cytotoxic chemotherapy in combination with immunity-boosters can be effective against tumors of smaller size. Taken together, these results support the development of therapeutic protocols relying on combinations of less cytotoxic agents and immune-boosters to fight cancer in the early stages.

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Section: Introductionmentioning

confidence: 94%

Evolutionary Dynamics of Cancer Cell Populations under Immune Selection Pressure and Optimal Control of Chemotherapy

Dimitriu

Lorenzi

Ştefanescu

2014

Math. Model. Nat. Phenom.

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“…All variables S, V 1 , V 2 , A, C, R and U are bounded on ½0, t f . To prove the boundedness, we use the method by [27]. To end this, we use the fact that the super solutions of system equation (51) given by…”

Section: Extension Of the Model Into An Optimal Controlmentioning

confidence: 99%

Mathematical Model of Hepatitis B Disease with Optimal Control and Cost‐Effectiveness Analysis

Belay

Abonyo

Theuri

2023

Computational and Mathematical Methods in Medicine

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In this paper, a mathematical model of hepatitis B disease with a two-dose vaccine series has been formulated and analyzed. We demonstrated that the model’s disease-free equilibrium is globally asymptotically stable when the basic reproduction number R 0 is less than one, whereas the model’s endemic equilibrium is locally asymptotically stable when R 0 is greater than one. Sensitivity analysis is performed, and based on its results, the model is extended to an optimal control problem by incorporating two control interventions, namely, prevention and enhanced newborn vaccination. Finally, simulation analyses of the model are conducted to illustrate the theoretical findings and effectiveness of each strategy, which indicates that the use of prevention efforts is the most cost-saving strategy.

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“…Interface 14: 20170150 mass tended to start regrowth. Ghafferi & Naserifar [39] improved upon the model of Burden et al [38] by including a linear penalty, 2vy(t f ), where v is constant, y is the quantity of cancer cells and t f is the final time-point of observation, such that their objective functional is J 2 (u) ¼ 2vy(t f ) þ J 1 (u) (note that 2vy(t f ) is the terminal payoff for J 2 (u), as defined above). The updated objective functional allowed for identification of a treatment that stops tumour regrowth and also acts faster than the treatment identified with J 1 (u).…”

Section: Optimal Control Theorymentioning

confidence: 99%

“…Toxicity, which is generally caused by targeting of self-antigens by the treatment-strengthened immune response, is often associated with clinical response [72]. Incorporation of immunotherapy-related toxicity into models can result in estimates of therapy dose that take into account toxicity-related effects, as was already done in [38]. Development of more mechanistic models can help to optimize therapies to maximize effectiveness and minimize toxicity if mechanisms for each are not entirely overlapping.…”

Section: Addressing Toxicitymentioning

confidence: 99%

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Addressing current challenges in cancer immunotherapy with mathematical and computational modelling

Konstorum

Vella

Adler

et al. 2017

J. R. Soc. Interface.

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The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.

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Optimal control applied to immunotherapy

Cited by 31 publications

References 12 publications

Evolutionary Dynamics of Cancer Cell Populations under Immune Selection Pressure and Optimal Control of Chemotherapy

Evolutionary Dynamics of Cancer Cell Populations under Immune Selection Pressure and Optimal Control of Chemotherapy

Mathematical Model of Hepatitis B Disease with Optimal Control and Cost‐Effectiveness Analysis

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling

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