arXiv subjects

Maximilian Nguyen

Publications and source records attributed to Maximilian Nguyen.

5 recordsLinked to original sources

arXiv2025

The logarithmic relationship between mean arterial pressure and heart rate

The classic heuristic formula for calculating the mean arterial blood pressure (MAP) in the human cardiac cycle using 1/3 of the systolic pressure (P_S) plus 2/3 of the diastolic pressure (P_D) importantly neglects the nonlinear effect of heart rate (HR) on blood pressure. Regression analysis on blood pressure data from patients experiencing a variety of heart rates captured a logarithmic relationship between mean arterial pressure and heart rate, F_S=0.086 *ln(HR-41.2)+0.079, where F_S is the MAP form factor corresponding to the fraction of time the cardiac cycle spends in ventricular systole. The logarithmic relationship is qualitatively distinct from the linear and exponential relationships previously suggested in the literature yet better aligns with the known human physiology. This heart rate-dependent formula for the mean arterial pressure recapitulates the classic intuition as a special case (HR=60bpm implies F_S =1/3). In addition, the model suggests several other MAP heuristics: HR=45bpm implies F_S = 1/5, HR=50bpm implies F_S = 1/4, HR=175bpm implies F_S = 1/2. A calculator for the MAP can be found at https://mngu265.shinyapps.io/map\_calculator/

q-bio.TO↗

arXiv2024

The Complex Interplay Between Risk Tolerance and the Spread of Infectious Diseases

Risk-driven behavior provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regards to risk tolerance. The interplay between behavior and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioral composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behavior, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the number of risk-averse people in the population, and the duration of intervention usage reduces the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold. Lastly, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse.

physics.soc-ph↗

arXiv2023

Fundamental Bound on Epidemic Overshoot in the SIR Model

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984... occurs at $R_0^*$ = 2.151... . In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with $R_0$ near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

q-bio.PE↗

arXiv2023

Upper Bounds on Overshoot in SIR Models with Nonlinear Incidence

We expand the calculation of the upper bound on epidemic overshoot in SIR models to account for nonlinear incidence. We lay out the general procedure and restrictions to perform the calculation analytically for nonlinear functions in the number of susceptibles. We demonstrate the procedure by working through several examples and also numerically study what happens to the upper bound on overshoot when nonlinear incidence manifests in the form of epidemic dynamics over a contact network. We find that both steeper incidence terms and larger contact heterogeneity can increase the range of communicable diseases at which the overshoot remains a relatively large public health hazard.

q-bio.PE↗

arXiv2020

Early life imprints the hierarchy of T cell clone sizes

The adaptive immune system responds to pathogens by selecting clones of cells with specific receptors. While clonal selection in response to particular antigens has been studied in detail, it is unknown how a lifetime of exposures to many antigens collectively shape the immune repertoire. Here, through mathematical modeling and statistical analyses of T cell receptor sequencing data we demonstrate that clonal expansions during a perinatal time window leave a long-lasting imprint on the human T cell repertoire. We demonstrate how the empirical scaling law relating the rank of the largest clones to their size can emerge from clonal growth during repertoire formation. We statistically identify early founded clones and find that they are indeed highly enriched among the largest clones. This enrichment persists even after decades of human aging, in a way that is quantitatively predicted by a model of fluctuating clonal selection. Our work presents a quantitative theory of human T cell dynamics compatible with the statistical laws of repertoire organization and provides a mechanism for how early clonal dynamics imprint the hierarchy of T cell clone sizes with implications for pathogen defense and autoimmunity.

q-bio.PE↗