Communication in Biomathematical Sciences

Clifford-algebraic framework for intraoperative blood management

HICHAM Banouh

We develop a Clifford-algebraic framework for modeling blood transport and intraoperative blood management in the low-Reynolds-number regime relevant to surgical microvasculature. By encoding the scalar hematocrit field together with the vectorial blood velocity into a single Clifford paravector $X = H + \mathbf{U}$, we define a Clifford transport operator whose grade projections yield a coupled system of partial differential equations. The scalar projection recovers a hematocrit diffusion-reaction equation, while the vector projection recovers a modified Stokes momentum equation augmented by a hematocrit-gradient forcing term $\kappa\rho\nabla H$ that arises intrinsically from the Clifford symmetric product and encodes the physical effect of hematocrit gradients on microvascular blood flow. The pressure is treated as a Lagrange multiplier outside the paravector, preserving the correct mathematical structure of the Stokes system. We derive a two-tier formulation: a Tier-1 linear Clifford system valid in the diffusion-dominated regime, and a Tier-2 extension that recovers advective transport via the Clifford product. A mathematically rigorous bleeding operator with regularized spatial localization is introduced. An optimal control problem is formulated with infusion and transfusion rates as controls; the resulting adjoint system decouples under incompressibility, yielding a single backward parabolic equation for the adjoint hematocrit and explicit pointwise Pontryagin-type optimality conditions. We prove well-posedness of the state system and existence of optimal controls, and we demonstrate that the Clifford framework provides genuine analytical advantages-unified Clifford-Green identities, grade-based Helmholtz decomposition, and coupled spectral modes-that streamline the analysis of the coupled hematocrit-velocity system.

Least-Cost Habitat Connectivity and Critical Patches in Kerinci Seblat National Park

Ahmad Shulhany, Agus Yodi Gunawan, Hilda Assiyatun, Iding Achmad Haidir

Habitat connectivity depends on habitat quality, spatial configuration, and the movement scale used to
translate inter-patch separation into connection probability. We develop a quality-weighted graph framework
for ten focal terrestrial mammals in Kerinci Seblat National Park (KSNP), Sumatra, using 8,648 camera-trap
detections. Habitat-suitability models were evaluated by five-fold cross-validation, upper-decile suitability was
used to delineate core habitat, and the resulting patches were linked through a resistance-based least-cost
graph. Patch capacity was defined as ai = Ai HSIi , while landscape connectivity and patch criticality were
quantified by the Probability of Connectivity (PC) and node-removal delta Probability of Connectivity (dPC).
Random Forest outperformed the Generalized Linear Model for all species, increasing mean AUC from 0.747
to 0.925. Core-habitat structure varied strongly among species, with 384–4,178 patches and a strong negative
association between patch number and mean patch area (Spearman ρ = −0.976, p < 0.001). The canonical
baseline contained 1,048,574 nonduplicated least-cost connections. In the pooled network, dPC was highly
concentrated: the maximum was 14.88%, whereas the median was 0.0033%. Patch capacity correlated strongly
with dPC (ρ = 0.750), yet the highest-dPC patch differed from the maximum-capacity patch in nine of ten
species-specific networks. A targeted movement-scale sensitivity analysis of the 20 baseline-priority patches
showed high rank concordance across d 50 = 1.5, 3, and 6 km (ρ = 0.910–0.977), with top-10 Jaccard overlap
of 0.818–1.000. Spatial visualization of core patches and the minimum-spanning forest further localized high-
dPC nodes within the landscape backbone. The results show that habitat capacity and network criticality are
complementary rather than interchangeable, and that the upper tail of conservation priorities is relatively robust
although exact rankings remain movement-scale dependent.

Mathematical Model Analysis of Listeriosis Disease Specially Emphasized on Time Delay, Environmental Noise and Spatial Diffussion

Kalyan Das

In order to comprehend the combined impacts of contaminated food products, bacterial growth, environmental perturbations, and spatial diffusion on disease propagation, a delayed mathematical model for the transmission dynamics of Listeriosis infection is constructed and examined in this work. The model includes environmental bacterial populations, contaminated food compartments, vulnerable humans, infected humans, and recovered humans. To guarantee the model’s biological viability, fundamental characteristics of the system, such as positivity, boundedness, and permanence of solutions, are carefully proven. The equilibrium analysis of the system is carried out by determining the disease-free and endemic steady states. The next-generation matrix approach is used to generate the basic reproduction number (R0), and its epidemiological importance is examined. The Jacobian matrix and characteristic equations are used to analyze the equilibria’s local stability, and LaSalle’s invariance principle and appropriately constructed Lyapunov functions are used to determine the global stability of both disease-free and endemic steady states. A stochastic variant of the model is developed by adding white noise to the transmission dynamics in order to account for environmental variability and random perturbations. The stochastic analysis shows that long-term system behavior and disease persistence are strongly impacted by environmental changes. Increasing noise intensity may produce oscillatory and irregular illness patterns while maintaining the boundedness of the solutions, according to numerical simulations. Additionally, to study the spread of the disease in space, a reaction-diffusion version of the delayed Listeriosis model is created. Turing pattern creation and diffusion-driven instability conditions are derived analytically in terms of the diffusion coefficients. According to the analysis, the homogeneous equilibrium might be upset and regional heterogeneity in the distribution of disease can result from differential diffusion rates of contaminated food products and diseased persons. The theoretical results, such as deterministic dynamics, stochastic trajectories, delay-induced oscillations, phase portraits, and diffusion-driven spatial patterns, are demonstrated numerically using MATLAB. The simulation results support the analytical findings and highlight the critical roles that environmental noise, bacterial diffusion, delay, and contaminated food transportation play in the persistence and spread of Listeriosis infection

A Three-Dimensional Geometric Model of the Honeybee Comb Cell: Variational Derivation of the Maraldi Angle and the Limits of the Optimality Claim

Fahril Irkham, Distya Rizqi Aliffa

The honeybee comb is a standard example of structural efficiency, yet accounts of its hexago-
nal form remain split between mathematical optimality, the physics of wax flow, and construction
behaviour, and most stop at the two-dimensional cross-section. We develop a parametric three-
dimensional model of the comb cell whose parameters are drawn from published measurements
and labelled by epistemic status. Treating the√basal amplitude as a free variable and minimising
wall area at constant volume gives a∗ = R/(2 2), so the Maraldi angle of 109.4712◦ emerges as
the solution of an optimisation problem rather than as a model input. The derived angle departs by
16′′ from Maraldi’s 1712 measurement, and the surface-area formulation agrees with a published
one to machine precision; that equivalence test also exposed a stationary point described in the liter-
ature as a maximum which is in fact a minimum. The optimum is shallow: displacing the amplitude
by 20 % costs only 0.06 % more wax, so agreement between a measured and an ideal angle is weak
evidence for optimality. At equal relative density the hexagon is the most compliant tiling in plane,
although it lies only 5.01 % above the isoperimetric bound. The comb optimises material economy,
not stiffness.