A mathematical model of tumour growth with Beddington-DeAngelis functional response: a case of cancer without disease

Modeling tumor growth using fractal calculus: Insights into tumor dynamics

Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)". We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer. In addition, the research investigates "double-size cancer" in the fractal temporal dimension with respect to various mathematical models.

Control analysis of virotherapy chaotic system

In this work, we consider a chaotic system that plays a vital role in the treatment of cancer by injection of a virus externally. Due to the sensitivity of this disease, most of its treatments are highly risky. Therefore, we have designed control inputs using adaptive and passive control techniques for virotherapy. Both controllers are designed to bring global stability to the cancer system with the aid of a quadratic Lyapunov function. Furthermore, we use simulations to verify our controllers. Moreover, we show that our adaptive control technique gives better results in comparison.

Quantitative Systems Pharmacology Approaches for Immuno-Oncology: Adding Virtual Patients to the Development Paradigm

Drug development in oncology commonly exploits the tools of molecular biology to gain therapeutic benefit through reprograming of cellular responses. In immuno‐oncology (IO) the aim is to direct the patient’s own immune system to fight cancer. After remarkable successes of antibodies targeting PD1/PD‐L1 and CTLA4 receptors in targeted patient populations, the focus of further development has shifted toward combination therapies. However, the current drug‐development approach of exploiting a vast number of possible combination targets and dosing regimens has proven to be challenging and is arguably inefficient. In particular, the unprecedented number of clinical trials testing different combinations may no longer be sustainable by the population of available patients. Further development in IO requires a step change in selection and validation of candidate therapies to decrease development attrition rate and limit the number of clinical trials. Quantitative systems pharmacology (QSP) proposes to tackle this challenge through mechanistic modeling and simulation. Compounds’ pharmacokinetics, target binding, and mechanisms of action as well as existing knowledge on the underlying tumor and immune system biology are described by quantitative, dynamic models aiming to predict clinical results for novel combinations. Here, we review the current QSP approaches, the legacy of mathematical models available to quantitative clinical pharmacologists describing interaction between tumor and immune system, and the recent development of IO QSP platform models. We argue that QSP and virtual patients can be integrated as a new tool in existing IO drug development approaches to increase the efficiency and effectiveness of the search for novel combination therapies.

Dynamics of Breast Cancer under Different Rates of Chemoradiotherapy

A type of cancer which originates from the breast tissue is referred to as breast cancer. Globally, it is the most common cause of death in women. Treatments such as radiotherapy, chemotherapy, hormone therapy, immunotherapy, and gene therapy are the main strategies in the fight against breast cancer. The present study aims at investigating the effects of the combined radiotherapy and chemotherapy as a way to treat breast cancer, and different treatment approaches are incorporated into the model. Also, the model is fitted to data on patients with breast cancer in Tanzania. We determine new treatment strategies, and finally, we show that when sufficient amount of chemotherapy and radiotherapy with a low decay rate is used, the drug will be significantly more effective in combating the disease while health cells remain above the threshold.