Communication in Biomathematical Sciences

Mathematical Modelling of an Oscillatory Flow of Jeffrey Fluid in an elastic channel

2026-06-02T18:00:23+07:00

This study investigates the effects of the Womersley parameter, Jeffrey parameter, and elasticity parameter on the oscillatory flow of a Jeffrey fluid within an elastic channel. The perturbation method is employed to derive analytical solutions for the flow characteristics. The Runge-Kutta fourth-order method is used to solve the differential equation for the pressure numerically along with the prescribed initial conditions. The graphs illustrate how the Womersley, elasticity, and Jeffrey parameters affect the mean pressure drop and modulus of wall shear stress. The results shown that increasing of the Womersley and elasticity parameters raises the modulus of wall shear stress in rigid and elastic channels.

Topological Entropy and Chaos-Based Modeling of Microbial Quorum-Sensing Synchronization in Antibiotic-Stressed Biofilm Ecosystems

2026-06-01T23:20:53+07:00

Microbial quorum sensing (QS) is a population-density-dependent signaling mechanism that governs biofilm formation and collective bacterial behavior. Under antibiotic stress, QS networks undergo nonlinear perturbations whose dynamical complexity has not been rigorously characterized in the chaos-theoretic framework. Here, we introduce a mathematical approach that integrates topological entropy, Lyapunov exponent analysis, and bifurcation theory to model QS synchronization dynamics in Pseudomonas aeruginosa biofilms exposed to sub-inhibitory concentrations of ciprofloxacin. We reconstructed the QS gene regulatory network from STRING protein-protein interaction data, mapped pathway nodes via KEGG metabolic pathway analysis (ko02020, ko02024), and leveraged transcriptomic time-series from GEO datasets (GSE59748, GSE116575) to parameterize a four-dimensional autonomous ODE system incorporating autoinducer production, receptor binding, gene activation, and biofilm matrix secretion. This system undergoes period-doubling bifurcations leading to chaos at critical antibiotic concentrations. Topological entropy of the QS attractor increases monotonically with antibiotic dose (h_top ∈ [0.12, 1.87] nats h⁻¹), suggesting entropy as a predictive biomarker of resistance transition. Coupled colony simulations reveal chimera-like states where subpopulations achieve partial phase-locking, providing a mathematical model for biofilm phenotypic heterogeneity. Model predictions are validated against GEO transcriptomic data with Pearson r = 0.847.

Nonlinear host -vector model taking into account Vector aggregation and host preference

2026-05-31T22:16:34+07:00

This study presents a mathematical model for the horizontal transmission of
Tomato Yellow Leaf Curl Virus (TYLCV), incorporating two key features: vector
aggregation (Bemisia tabaci) and a nonlinear incidence rate. Theoretical analysis demonstrates that the disease-free equilibrium is globally asymptotically stable
when the basic reproduction number R
0
< 1, whereas the endemic equilibrium
becomes globally asymptotically stable when R
0
> 1, indicating disease persistence. Sensitivity analysis reveals that vector aggregation substantially influences
transmission dynamics, highlighting its critical role in epidemic behavior. Numerical simulations corroborate the analytical results and provide quantitative insights
into the impact of vector behavior on virus spread. These findings offer a robust
framework for predicting TYLCV outbreaks and inform the development of more
effective management strategies in tomato cultivation.

Reproduction Numbers and Backward Bifurcation in Nonlocal Epidemic Systems

2026-05-27T17:46:02+07:00

We investigate a class of nonlocal reaction--diffusion epidemic systems with finite-range interactions and aggregation-driven transmission mechanisms. Extending the classical next-generation operator framework to infinite-dimensional heterogeneous settings, we formulate a generalized nonlocal reproduction operator in Banach spaces incorporating nonlocal dispersal and finite sensing kernels. We characterize the basic reproduction number as the spectral radius of a compact positive operator and establish threshold conditions for disease extinction and persistence. Using semigroup theory, spectral analysis, and center manifold reduction, we prove the existence of endemic equilibria and identify conditions leading to backward bifurcation and kernel-induced spatial instability. We further show that finite-range interactions may destabilize homogeneous endemic states and generate nontrivial spatial patterns. Numerical simulations illustrate the effects of sensing radius and aggregation strength on epidemic persistence and spatial organization.