Modelling pulsed immunotherapy of tumour-immune interaction

We develop a mathematical model that describes the tumour-immune interaction and the effect on it of pulsed immunotherapy, based on the administration of adoptive cellular immunotherapy (ACI) combined with interleukin-2 (IL-2). The stability conditions for the tumour-free periodic solution are provided with different frequencies of ACI applications and IL-2 infusions. Furthermore, the effects of period, dosage and times of drug deliveries on the amplitudes of the tumour-free periodic solution were investigated. The most feasible immunotherapy strategy was determined by comparing immunotherapy with ACI treatment with or without IL-2. However, to investigate how to enhance the efficacy of chemotherapy (radiotherapy) and reduce its sideeffects, we developed a model involving periodic applications of immunotherapy with chemotherapy (radiotherapy) applied only when the density of the tumour reached a given threshold. The results revealed that the initial densities, the effector cell: tumour cell ratios, the periods T and a given critical number of tumour cells CT are crucial for cancer treatment, which confirms that it is important to customise treatment strategies for individual patients

A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy regimens. Using optimal control theory with constraints and numerical simulations, we obtain new therapy protocols that we then compare with traditional pulsed periodic treatment. The optimal control generated therapies produce larger oscillations in the tumor population over time. However, by the end of the treatment period, total tumor size is smaller than that achieved through traditional pulsed therapy, and the normal cell population suffers nearly no oscillations

Hormetic and synergistic effects of cancer treatments revealed by modelling combinations of radio ‑ or chemotherapy with immunotherapy

Background: Radio/chemotherapy and immune systems provide examples of hormesis, as tumours can be stimulated (or reduced) at low radio/chemical or antibody doses but inhibited (or stimulated) by high doses. Methods: Interactions between effector cells, tumour cells and cytokines with pulsed radio/chemo-immunotherapy were modelled using a pulse differential system. Results: Our results show that radio/chemotherapy (dose) response curves (RCRC) and/or immune response curves (IRC) or a combination of both, undergo homeostatic changes or catastrophic shifts revealing hormesis in many parameter regions. Some mixed response curves had multiple humps, posing challenges for interpretation of clinical trials and experimental design, due to a fuzzy region between an hormetic zone and the toxic threshold. Mixed response curves from two parameter bifurcation analyses demonstrated that low-dose radio/chemotherapy and strong immunotherapy counteract side-effects of radio/chemotherapy on effector cells and cytokines and stimulate effects of immunotherapy on tumour growth. The implications for clinical applications were confirmed by good fits to our model of RCRC and IRC data. Conclusions: The combination of low-dose radio/chemotherapy and high-dose immunotherapy is very effective for many solid tumours. The net benefit and synergistic effect of combined therapy is conducive to the treatment and inhibition of tumour cells

Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Periodical applications of immunotherapy and chemotherapy play significant roles in cancer treatment and studies have shown that the evolution of tumour cells is subject to random events. In order to capture the effects of such noise we developed a stochastic tumour-immune dynamical model with pulsed treatment to describe combinations of immunotherapy with chemotherapy. By using theorems of the impulsive stochastic dynamical equation, the tumour free solution and the global positive solution of the proposed system were investigated. We then show that the expectations of the solutions are bounded. Furthermore, threshold conditions for extinction, non-persistence in the mean, weak persistence and stochastic persistence of tumour cells are provided. The results reveal that comprehensive therapy or noise can dominate the evolution of tumours. Finally, biological implications are addressed and a conclusion is presented

Generalized Hopf Bifurcation in a Cancer Model with Antigenicity under Weak and Strong Allee Effects

This article deals with an autonomous differential equation model that studies the interaction between the immune system and the growth of tumor cells with strong and weak Allee effects. The Allee effect refers to interspecific competition, and when the population is small, it can retard population growth. The work focuses on describing analytically, using a set of parameters, the conditions in the phases of the immunoediting theory, particularly in the equilibrium phase, where a latent tumor would exist. Saddle-Node, Saddle-symmetric, Hopf, generalized Hopf, and Takens-Bogdanov bifurcations get presented for both Allee effects, and their biological interpretation regarding cancer dynamics gets discussed. The Hopf and generalized Hopf bifurcation curves get analyzed through hyper-parameter projections of the model, where it gets observed that with a strong Allee effect, more tumor control persists as it has higher antigenicity, in contrast to the weak Allee effect, where lower antigenicity gets observed. Also, we observe that the equilibrium phase persists as antigenicity increases with a strong Allee effect. Finally, the numerical continuation gets performed to replicate the analytical curves' bifurcations and draw the limit and double limit cycles

Mathematical Modeling of BCG-based Bladder Cancer Treatment Using Socio-Demographics

Cancer is one of the most widespread diseases around the world with millions of new patients each year. Bladder cancer is one of the most prevalent types of cancer affecting all individuals alike with no obvious prototypical patient. The current standard treatment for BC follows a routine weekly Bacillus Calmette-Guerin (BCG) immunotherapy-based therapy protocol which is applied to all patients alike. The clinical outcomes associated with BCG treatment vary significantly among patients due to the biological and clinical complexity of the interaction between the immune system, treatments, and cancer cells. In this study, we take advantage of the patient's socio-demographics to offer a personalized mathematical model that describes the clinical dynamics associated with BCG-based treatment. To this end, we adopt a well-established BCG treatment model and integrate a machine learning component to temporally adjust and reconfigure key parameters within the model thus promoting its personalization. Using real clinical data, we show that our personalized model favorably compares with the original one in predicting the number of cancer cells at the end of the treatment, with 14.8% improvement, on average

Mathematical Modelling and Analysis of the Tumor Treatment Regimens with Pulsed Immunotherapy and Chemotherapy

To begin with, in this paper, single immunotherapy, single chemotherapy, and mixed treatment are discussed, and sufficient conditions under which tumor cells will be eliminated ultimately are obtained. We analyze the impacts of the least effective concentration and the half-life of the drug on therapeutic results and then find that increasing the least effective concentration or extending the half-life of the drug can achieve better therapeutic effects. In addition, since most types of tumors are resistant to common chemotherapy drugs, we consider the impact of drug resistance on therapeutic results and propose a new mathematical model to explain the cause of the chemotherapeutic failure using single drug. Based on this, in the end, we explore the therapeutic effects of two-drug combination chemotherapy, as well as mixed immunotherapy with combination chemotherapy. Numerical simulations indicate that combination chemotherapy is very effective in controlling tumor growth. In comparison, mixed immunotherapy with combination chemotherapy can achieve a better treatment effect