## 1 Introduction  
Cancer is one of the most complex diseases, and as such, scientists are deeply involved in studying not only the biological nature and interactions of the processes involved in cancer but also in creating mathematical models of these processes. Chemotherapy remains a cornerstone of cancer treatment but is often associated with significant drawbacks, including severe toxicity, adverse side effects, and a lack of specificity in targeting tumor cells while sparing healthy tissues. Conventional chemotherapy protocols do not account for individual patient characteristics. As a result, patients may experience suboptimal treatment outcomes, either due to under-dosing, which fails to eradicate the tumor, or excessive dosing, which leads to unnecessary toxicity and immune suppression. Therefore, the identical cancer treatment applied to a large group of patients can effectively cure only some of them [1; 2]. Often, we are unable to fully explain the mechanisms why the treatment fails in some patients [3]. Due to a complex interplay of factors such as the type, aggressiveness, and stage of cancer, patient genetics, diet, immune system status, body weight, and gender, the efficiency of cancer therapies can vary significantly [4; 5]. Another important factor affecting the response of the organism is the chemotherapy substance chosen for the treatment [6]. The design of chemotherapy dosing protocols for cancer patients often relies on empirical determination or systematic design based on population models [7; 8; 9; 10]. These models typically derive their parameters from clinical data across large groups of patients. As a result, chemotherapy doses and treatment outcomes have a mean-population character, failing to account for individual patient variability [11]. Consequently, the application of such therapy carries risks, potentially hindering the success of chemotherapy [12]. To compensate for inter-subject variability by aligning the model parameters with the observed patient's response to the treatment, advanced techniques are necessary [13]. These issues have given rise to the concept of personalized (precision) medicine (PMed), a new healthcare approach that seeks to address why patients with similar clinical symptoms often exhibit different responses to the same treatment [14]. Personalized medicine focuses on tailoring treatment to the individual characteristics of each patient [15]. This approach leverages a set of patient-specific information or characteristics to design customized therapeutic strategies [16]. Unlike the \"one-size-fits-all approach\", which aims to develop treatments for the average person, precision medicine focuses on the differences between individuals [17]. This shift towards a patient-centered approach has the potential to improve survival rates, enhance quality of life, and reduce the burden of chemotherapy-related complications. In the case of model-based personalization, an adequately parsimonious mathematical model is required [18; 19]. Numerous mathematical models have been developed to describe tumor growth, its interactions with the immune system, and responses to various cancer therapies, including chemotherapy [9; 20; 21; 22; 23; 24], immunotherapy [25; 26; 27], radiotherapy [28], anti-angiogenesis [29], and their combinations [8; 30; 31]. A comprehensive review of cancer modeling can be found in [9; 32; 33]. Current efforts in the field are focused on two distinct approaches to developing personalized therapies:  
* Iteratively and heuristically adjusting the therapy during treatment. This suggests an adaptive, trial-and-error approach where therapy is modified based on patient response. This is common in clinical practice but may lack a formal mathematical framework. * Rigorous approach using a mathematical model to guide therapy, followed by model-based optimization to refine treatment strategies.