Frontiers in Applied Mathematics and Statistics

Background: Tuberculosis remains a persistent infectious disease whose control is complicated by latent infection, delayed treatment, incomplete recovery, reinfection, and continuing transmission from infectious individuals. Although treatment is central to tuberculosis management, it is frequently represented only as a transition parameter in mathematical models rather than as a separate epidemiological state. In this study, treatment was therefore incorporated explicitly as an independent compartment so that its influence on transmission, recovery, disease-induced mortality, and long-term disease persistence could be evaluated. Methods: A deterministic nonlinear compartmental model was formulated by dividing the total population into susceptible, exposed, actively infected, treated, and recovered classes. Reinfection of recovered individuals, progression from latent infection to active disease, movement of infectious individuals into treatment, treatment-associated recovery, natural mortality, and disease-induced mortality were included. Positivity and boundedness of the solutions were examined to establish biological validity. The basic reproduction number, R0, was derived through the next-generation matrix approach. Disease-free and endemic equilibria were determined, and their local and conditional global stability properties were investigated using Jacobian analysis, the Routh-Hurwitz criterion, center manifold theory, Lyapunov functions, and LaSalles invariance principle. Normalized sensitivity indices, Latin hypercube sampling, partial rank correlation coefficients, and numerical simulations were also applied. Results: The disease-free equilibrium was shown to be locally asymptotically stable when ,R0<1 whereas sustained transmission and a unique endemic equilibrium were associated with R0>1. Under the stated reduced-model assumptions, stability of the endemic equilibrium was established. Transmission-related parameters were identified as the strongest positive contributors to disease persistence. In contrast, treatment and recovery parameters were found to reduce the reproduction number and infectious burden. Numerical simulations indicated that stronger treatment implementation and reduced transmission opportunities produced substantial reductions in active tuberculosis cases. Conclusion: Treatment was shown to function as both a clinical pathway and an epidemiological control mechanism. The proposed framework may support the design of treatment-centered strategies for reducing tuberculosis prevalence and preventing long-term endemic persistence.

The measurement of light received at the cornea of the eye is a paramount consideration for the understanding of the relation between environmental illumination and the non-image-forming effects of light. The field of view (FOV) at the cornea is less than a full hemisphere, because it is partially occluded by human facial morphology. The International Commission on Illumination (CIE) has defined a standard model of human FOV. A suitably designed physical occluder attached to the sensor (of a light meter) has been proposed as a means of incorporating the effect of human FOV when taking measurements. Similarly, when using simulation to predict light received at the cornea, a geometrical description of the occluder at the eye point(s) can be added to the 3D model of the scene. The first occluder model proposed to represent CIE human FOV was enumerated in terms of: the CIE definition; the radius of the occluder; and, the radius of the light sensor disc. We present a simpler model based only on the CIE definition and the occluder radius. Both models were tested using a virtual goniophotometer. Various sensor response functions describing the spatial sensitivity across the sensor disc, including several we characterized through laboratory measurements, were included in the test. For all functions considered, the performance of the simpler occluder model was equivalent to or better than the model first proposed.

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

We present a quantum-enhanced version of the classic k-Nearest Neighbors (kNN) classification algorithm, applied to the prediction of arterial hypertension. The traditional Euclidean distance metric of the kNN algorithm is replaced with a Fidelity-derived quantum dissimilarity measure to evaluate the similarity between data samples. We map classical real-world clinical and ECG-derived data features into quantum states via the Dense-Angle Encoding, which efficiently utilizes parameterized rotation gates to pack multiple features into minimal qubits while maintaining pure states. We evaluate the performance of the dissimilarity measure using both the noiseless state vector Simulator and the IBM Qiskit Estimator primitives. The quantum circuit demonstrates robust predictive capabilities comparable to the classical model. While it does not claim computational supremacy over the classical baseline, the framework proves that fidelity-based similarity is a physically meaningful and efficient approach for hybrid quantum classical classification.

Malaria is still one of the most dangerous causes of morbidity and mortality in tropical and subtropical regions even though it has been actively combated for many years. In 2023, there were approximately 263 million malaria cases and 597,000 deaths from this disease on a global scale, with sub-Saharan Africa being the region most affected by it [24]. Climate factors affect mosquito biology, including their abundance, survival, and biting rates, as well as parasite development, while human awareness plays a crucial role in adopting preventive measures and effective treatments. Despite the progress in both climate- and awareness-based malaria modelings, few studies integrate these factors in one comprehensive model that involves the detailed mechanisms of transmission processes. The current study develops a deterministic climate-driven SEAIR-SEI malaria transmission model that includes the impact of temperature, rainfall, and humidity on mosquito biology and endogenous community awareness. The model was proven to be well-posed by showing the positivity and boundedness of its solution and through the demonstration of the existence and uniqueness of its solution. The malaria-free equilibrium was determined, and the basic reproduction number was calculated using the next-generation matrix method. The model underwent local and global stability analyses to characterise the diseases persistence in the population. Additionally, a normalized forward sensitivity analysis was conducted, revealing the mosquito biting rate as the key force driving malaria transmission. Four time-dependent malaria interventions, namely, long-lasting insecticidal nets, community awareness campaigns, indoor residual spraying, and prompt treatment, were included in the model through optimal control theory and analysed using Pontryagins Maximum Principle. The numerical results for the optimal control problem showed that employing all four interventions leads to the best outcome by decreasing the objective functional value by 88.17%, reducing the total number of infected humans by 92.49%, and minimizing the total number of infectious mosquitoes by 93.87%. Interestingly, combining two interventions, indoor residual spraying, and prompt treatment, also yielded nearly optimal results. Therefore, the designed control strategy can serve as an efficient and affordable framework for malaria control in sub-Saharan Africa.

Human Papillomavirus (HPV) infection among men who have sex with men (MSM) has become a significant public health concern, particularly in countries where male vaccination is unavailable. Given the high susceptibility of MSM to HPV and anal cancer, and the unavailability of HPV vaccination for males in low- and middle-income countries (LMICs), there is a need to identify alternative interventions for reducing disease transmission and burden in this population. The novel mathematical model presented in this article couples smoking behavior dynamics with HPV transmission and anal cancer progression among MSM. Smoking reduction is introduced as an intervention to assess its effects on disease transmission and burden. The basic reproduction number (R0) is derived using the next-generation matrix method, and a global sensitivity analysis is performed using partial rank correlation coefficients (PRCC) to identify the influence of model parameters on RR0. Further, the theoretical analysis of the model reveals a backward bifurcation, implying that RR0 < 1 is necessary but not sufficient to eradicate the disease. The study finds that smoking reduction among MSM reduces HPV infection and anal cancer burden relative to baseline projections without intervention. The joint effect of smoking reduction and vaccination shows that the critical vaccination coverage needed to achieve RR0 <1 decreases as the level of smoking reduction increases. A similar outcome is observed for contact reduction. These findings highlight the importance of concurrent interventions, which can significantly curtail the spread of HPV and reduce disease burden in both the high-risk group and the general population.

Neural temporal point processes (NTPPs) are powerful tools for modeling sequences of timestamped events with statistical temporal structure. Density-based NTPPs, in particular, are an interesting opportunity to merge the universal function approximation capability of neural networks with a defined statistical model in a way that has many potential applications. We demonstrate one such application to heartbeat dynamics, a physiologic point process. We specifically apply a lognormal mixture NTPP to compute instantaneous estimates of the mean and standard deviation of beat-to-beat intervals. We compare our results to the state of art (Barbieri et al.) point process model for heartbeat dynamics, which uses a more physiologically rigorous inverse Gaussian model. We find that the NTPP model maintains reasonable accuracy while improving upon robustness to noise.

Machine learning (ML) has emerged as a transformative technology across biomedical and life science sectors, with applications spanning drug discovery, medical imaging, genomics, and clinical decision support (Goecks et al., 2020; Patel et al., 2020). Despite exponential growth in ML-related publications, from fewer than 100 articles in 2003 to nearly 25,000 by 2021 (NCBI, 2022), adoption among industry professionals remains uneven and sector-dependent. Understanding what drives or inhibits this adoption is critical for organisations seeking to leverage ML capabilities in research and clinical practice. Technology adoption in organisational contexts has been extensively studied through the Technology Acceptance Model (TAM), originally proposed by Davis (1989) and subsequently extended to incorporate external variables influencing perceived usefulness (PU) and perceived ease of use (PEU) (Venkatesh & Davis, 1996). While TAM has been applied across multiple industries, its application within biomedical and life science contexts remains limited, and the industry-specific factors that shape ML acceptance in this sector have not been systematically examined. Two external variables are particularly relevant to life science professionals. First, the bibliometric journal impact factor (JIF) functions as a cognitive signal of scientific credibility, a sector where evidence-based decision-making is culturally embedded, and publication quality serves as a proxy for technological legitimacy (Garfield, 1996). Second, technology hype, operationalised through the Gartner Hype Cycle framework, represents a social influence variable that shapes organisational expectations and investment decisions around emerging technologies (Gartner Inc., 2018). Whether these variables influence ML acceptance among life science professionals, alongside individual knowledge and experience, has not been empirically tested. This study addresses that gap by investigating ML technology acceptance among 213 biomedical and life science professionals across EMEA, LATAM, and North America, using a cross-sectional quantitative survey and PLS-SEM analysis. The TAM model is extended with three external variables, JIF, technology hype, and prior knowledge and experience, to test their influence on PU and PEU in this specific professional context. Additionally, the study examines demographic and regional differences in ML acceptance, with particular attention to variation between academic researchers and healthcare professionals. The findings contribute a validated, sector-specific extension of TAM for life sciences, provide actionable insights for organisations seeking to accelerate ML implementation, and establish a framework for future subsector-specific research.

Length and time constants are foundational to the study of conduction in neurons and other biological cables but are exactly defined only for passive membranes. Here we define and derive exact length and time constants for propagating action potentials in unmyelinated axons. This derivation exploits specific instants during action potential conduction when the net transmembrane ionic current is zero, but axial current remains non-zero. At these instants, we define a curvature parameter,{kappa} , explore its determinants using computer modelling, demonstrate that it is the local real Laplace exponent of the action potential upstroke, and suggest practical approaches for its experimental measurement. From{kappa} , we define action potential length and time constants, {lambda}AP = 1/{surd}({kappa}racm) and {tau}AP = 1/{kappa}, and show that action potential propagation velocity is exactly {lambda}AP/{tau}AP.

Coronary flow waveforms have a distinct diastolic-dominant shape with periods of low or retrograde flow during systole. While the general waveform shape has been attributed to complex interactions between cardiac and vascular mechanics, there is limited research into the variability in coronary flow waveforms and what this variability may reveal about cardiac function. This work presents a shape analysis of left anterior descending artery (LAD) flow waveforms using Fourier transforms and Singular Value Decomposition (SVD) performed on baseline data collected from 32 pigs. Pigs included in the study reflect two breeds (Ossabaw and Yorkshire) and three different experimental conditions (lean-control, lean-paced, and obese-paced). Fourier transforms were used to decompose the waveforms into 15 harmonics for each pig. An SVD analysis is then used to extract temporal patterns of the waveforms. Correlations between pig-specific coefficients for the SVD modes and clinical metrics were used to investigate physiological explanations of LAD waveform variability. Temporal LAD flow patterns of the second SVD mode are significantly correlated with heart rate. The third SVD mode significantly correlates with mean blood pressure and maximum hyperemic flow. Furthermore, the fourth SVD mode is weakly correlated with left-ventricular end diastolic pressure and endocardial-epicardial flow ratios. This work demonstrates that LAD flow waveforms can be broken down into temporal patterns that correlate with physiological features. Furthermore, this shape-analysis method allows for waveform reconstruction and simplifies visualization of the temporal patterns identified using SVD, an advantage over existing methods that focus on characterizing flow waveforms by points of interest.

Background and ObjectiveAccurately parameterizing dynamic, time-varying interactions in physiological systems is a methodological challenge, as global causal discovery methods may obscure transient, local fluctuations. This study introduces tempord, an open-source Python library designed to estimate local temporal orders and evaluate the short-term stability, directionality, and strength of causal links in non-stationary biological signals. MethodsThe algorithm estimates temporal relationships by keeping one signal stationary while iteratively shifting another one within a sliding window. To parameterize optimal inter-signal shifts (causal vector, CV), the framework utilizes linear modeling or time series distance metrics. The methodology was validated through a simulation study on synthetic bivariate signals with mathematically imposed dynamic phase delays, under both deterministic and noisy conditions. Furthermore, in-vivo capabilities were demonstrated by evaluating cardiorespiratory coupling dynamics across spontaneous and music-induced relaxation breathing states. ResultsThe simulation study demonstrated that the extracted CV trajectories precisely aligned with ground-truth temporal delays, assessed using mean absolute error and root mean square error for both noise-free and noisy synthetic data. In-vivo application demonstrated dynamic temporal stability and the detection of minor step changes during autonomic nervous system state transitions. ConclusionsThe tempord Python package bridges the gap between global causal discovery and local beat-by-beat statistical parameterization. It provides a robust "bottom-up" analytical instrument for investigating the transient mechanisms governing complex biological networks.

Background: Globally and in Bangladesh, high-risk fertility behaviour (HRFB) continues to be a significant public health issue, contributing to negative health outcomes for both mothers and children. So, this study aimed to evaluate the trends, prevalence, determinants, and socio-economic inequalities associated with HRFB among presently married women of reproductive age by utilising data from the Bangladesh Demographic and Health Survey (BDHS). Methods: We analysed data from 19,060 currently married women aged 15-49 years. HRFB was defined as the presence of any of the following: maternal age (<18 or >34 years), short birth intervals (<24 months), or high birth order ([&ge;]4). Two outcome variables were constructed: a binary indicator for any HRFB (yes/no) and a three-category variable indicating no, single, or multiple HRFBs. Bivariate analysis was conducted to determine the prevalence of HRFB, and multilevel mixed-effect logistic and multinomial regression models were applied to identify determinants, accounting for the complex survey design. Socioeconomic inequalities were examined using concentration indices and concentration curves. Results: Overall, 58% of women experienced at least one HRFB, with 33% exhibiting a single HRFB and 25% multiple HRFBs. Women who married after age 18 years, had higher education, were exposed to media, or had educated husbands were significantly less likely to experience HRFB. Higher odds of HRFB were associated with rural residence, lower household wealth, and regions such as Mymensingh, Barishal, and Chattogram. Significant inequalities were observed, with HRFB disproportionately concentrated among women with lower wealth (CIX = -0.427, p<0.001) and no education (CIX = -0.268, p<0.001). Conclusion: In Bangladesh, HRFB remains prevalent and is unevenly distributed across socio-economic and geographic groups. Targeted interventions aimed at delaying early marriage, improving educational attainment for women and their partners, expanding mass media outreach, and increasing access to reproductive healthcare- especially among disadvantaged and rural populations- are essential for reducing HRFB and improving maternal health outcomes.

Stochastic epidemic models are a cornerstone of infectious disease epidemiology and are often used to study intervention scenarios. However, large run-to-run variability can make intervention effects difficult to estimate precisely. We revisit the epidemic Sellke construction, which assigns each individual an infection threshold for the cumulative infection hazard such that, conditional on the thresholds, the epidemic trajectory becomes deterministic. This enables coupling of simulations with and without an intervention, yielding low-variance effect estimates even when outcomes such as final size or peak incidence vary widely between runs. We develop an exact, event-driven implementation that maintains infection and recovery events in priority queues. Cumulative infection-hazard updates require O(log N) time per event, yielding overall complexity O(Elog N) for E events in a population of size N. The implementation achieves computational performance comparable to the classical Gillespie algorithm while naturally accommodating non-Markovian infectious periods and complex infectiousness profiles. We illustrate the approach using distance-dependent spread of avian influenza between poultry farms in the Netherlands and a multilayer population with households, schools, and workplaces. In both examples, coupling enables efficient within-run comparisons of intervention scenarios across stochastic realisations.

The initial response of populations to the SARS-CoV-2 virus reduced the incidence of COVID-19 cases. However, this success was shorted lived once most populations relaxed most restrictions, resulting in an increase in infections. This feedback contributed to additional pandemic waves. The temporal unfolding of behavioural changes in populations present a challenge to mathematical models for disease dynamics. Coupled behaviour-disease models with varying levels of complexity accounting for several factors have been used to capture behavioural dynamics and SARS-CoV-2 transmission, with varying results. To study the impact of model complexity on the predictive power of models, here we formulate five coupled behaviour-disease models with varying structure and number of parameters. We fit the models to SARS-CoV-2 infection incidence and stringency of control interventions from five European countries in the first wave, and study how well these fitted models predict the second wave. We show that models with more parameters do not necessarily have a greater ability to explain and predict key features of a pandemic wave. Hence, our results show that a relatively simple coupled behaviour-disease model with important parameters can do an adequate job of providing information about the pandemic wave. Additionally, our findings show that complex models can be country-specific, working better for some countries and poorly for others. We conclude that modellers should not always opt for the most complicated possible models, if the data do not support their use.

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

Our study is an assessment of the knowledge, personal coverage, and related determinants of private health insurance as revealed by healthcare professionals in Freetown, the urban capital of Sierra Leone. This study stands as a precursor for Low- and Middle-Income Countries (LMICs), like Sierra Leone, seeking to establish Universal Health Coverage (UHC) to provide healthcare access and coverage through publicly arranged risk pooling, designed to help protect against unmanageable medical costs. In parallel, such countries face significant challenges with achieving sustainable universal coverage due to limited public resources, inefficient allocation systems, uneasy reliance on out-of-pocket payments, and large struggling populations. Our research sheds particular light on how healthcare professionals view their own participation with private healthcare options. A cross-sectional, analytical study was conducted, openly recruiting individuals from various facilities in Freetown. Using the Yamane Formula, a sample size of 109 participants was calculated. STATA 14.0 was used for data analysis. Our findings revealed that 96 (88.9%) participants did not have private health insurance, while 12 (11.1%) did have private coverage. However, 105 (97.2%) reported other modes of health insurance, with only 3 (2.8%) uninsured. Notably, 97.2% expressed willingness to join a private health insurance scheme. Our study found no statistically significant associations between selected indicators (demographic or socioeconomic fac tors) and current insurance coverage among study participants. These results highlight a low prevalence and understanding of private health insurance among healthcare professionals in a representative urban center in Sub-Saharan Africa (SSA), while acknowledging high willingness to enroll. The lack of any significant determinants suggests other unexamined factors, such as cost, accessibility, or awareness, capable of influencing the adoption and implementation of a universal health program.

Patients suffering from sepsis need to be treated with an effective antibiotic therapy within the first hour after sepsis onset to decrease their risk of death. Microbiological data that provide information about the suitability of antibiotic therapies, however, is usually available only after 72 hours. Consequently, the treating physicians need to judge a therapy's effectiveness based on the patients' measured health records and their general health condition. This medical assessment is complex and requires years of experience. In our study, we investigate how statistical modeling can contribute to assessing the effectiveness of antibiotic therapies. To that purpose, we describe the effectiveness of antibiotic therapies by modeling sepsis patients' health conditions using a three-state continuous-time hidden Markov model (ctHMM). In literature, procalcitonin (PCT) and lactate have proven to be helpful for deriving the health condition in this context. The state probabilities obtained by the ctHMM are subsequently used to quantify the effectiveness of antibiotic therapies. To this end, we apply two different approaches, namely (i) averaging of the state probabilities and (ii) a logistic regression model. For (i), we calculate the average of the state probabilities for the state indicating a sepsis-free condition over an antibiotic administration period of 48 hours. For (ii), we use the information about antibiotic susceptibility testings as dependent variable in the logistic regression model; as independent variables, we calculate the difference between state probabilities at the start of antibiotic administration and 48 hours later. With this work, we are able to better understand the relationship between laboratory values, in particular PCT and lactate, and the patients' health condition. We further provide approaches for quantifying the effectiveness. Therefore, our work contributes to developing a clinical decision support system which helps physicians assess the effectiveness of antibiotic therapies in patients with sepsis. Supported by such a system, a physician is able to quickly adjust an ineffective therapy which avoids antibiotic resistances and increases a patient's chance to survive a sepsis.

Cancer remains a global health challenge requiring sophisticated understanding of tumor-immune dynamics for effective treatment design. Mathematical oncology has emerged as a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. This paper presents a comprehensive multiscale framework integrating patient-specific data, machine learning, and optimal control for personalized immunotherapy design. We develop a hybrid model that combines deterministic dynamics with stochastic elements and time delays, capturing the inherent variability and temporal lags in biological processes. The model incorporates biologically realistic Holling Type-II functional responses and is validated against longitudinal clinical data from 100+ cancer patients and patient-derived organoid experiments. Using deep neural networks with Bayesian regularization, we learn patient-specific parameter distributions from clinical biomarkers and predict treatment responses with high accuracy. Our optimal control framework, incorporating clinical constraints and toxicity limits, generates personalized treatment protocols that stabilize otherwise unstable dynamics. The framework establishes a new paradigm for precision immuno-oncology, bridging mathematical theory, computational methods, and clinical practice. Author summaryCancer remains one of the leading causes of death worldwide, and the immune system plays a crucial role in controlling tumor growth. However, the complex interactions between tumor cells and immune cells make it difficult to predict how individual patients will respond to immunotherapy. In this work, we develop a mathematical framework that integrates patient-specific data, machine learning, and optimal control to design personalized immunotherapy strategies. Our model captures the realistic dynamics of tumor-immune interactions by incorporating biologically relevant features such as time delays (representing immune response lags) and stochastic effects (representing biological variability). Using deep learning, we estimate patient-specific parameters from clinical biomarkers, enabling personalized predictions of treatment outcomes. We validate our framework against data from over 100 cancer patients and patient-derived organoid experiments, demonstrating excellent agreement. Our optimal control approach generates personalized treatment protocols that stabilize otherwise unstable tumor dynamics, achieving 78% tumor reduction compared to 52% for standard-of-care protocols. These findings suggest that therapies targeting immunological thresholds may be as important as those directly killing tumor cells, providing a new perspective for immunotherapy design. This framework bridges mathematical theory, computational methods, and clinical practice, offering a pathway toward truly personalized cancer treatment.

Tumors consist of heterogeneous phenotypic cells, such as normoxic cells, which are highly proliferative, and hypoxic cells, which are less proliferative. Their phenotypic switching depends on tumor microenvironmental factors, such as oxygen and nutrient concentrations supplied by local blood vessels. However, during ongoing angiogenesis, the process of sprouting new blood vessels at the tumor site from pre-existing blood vessels, and how this phenotypic switching affects and impacts tumor growth, remains poorly understood. In this article, we formulate a mathematical model to elucidate the crosstalk between vasculature and tumor cellular heterogeneity during tumor progression. The model results show a strong agreement with the experimental data. Our simulation results demonstrate that ongoing angiogenesis increases tumor growth rate. In addition, we observe that the influence of hypoxic cells on phenotypic switching from normoxic to hypoxic is more pronounced than their influence on the transition from hypoxic to normoxic. Furthermore, we perform a global sensitivity analysis using the Sobol's method to assess the importance of the model's parameters. It highlights that the volume at which blood vessels attain half-maximal rate has the maximum effect on the model.