Mathematical Biosciences and Engineering最新文献

Mathematical models are valuable tools in the fight against infectious diseases such as dengue. However, their use to guide public health strategies in sub-Saharan Africa, particularly in Burkina Faso, remains limited due to the scarcity of locally calibrated models. Moreover, no study has yet applied the African vulture optimization algorithm (AVOA) for dengue parameters in this context. In this study, we develop a compartmental model to evaluate the impact of control strategies on the 2023 dengue epidemic in the Centre Region of Burkina Faso. The model combines a susceptible-infected (SI) structure for the mosquitoes aquatic phase, a susceptible-exposed-infected (SEI) structure for adult mosquitoes, and a susceptible-exposed-infected-recovered (SEIR) framework for the human population. It incorporates key features, including vertical transmission in mosquitoes and a distinction between clinically detected and undetected human cases. After mathematical analysis, key epidemiological parameters were estimated by calibrating the model against weekly reported case data from June to December 2023 using AVOA. The basic reproduction number ($ mathcal{R}_0 $) was estimated at 2.30, confirming the potential for sustained transmission. Sensitivity analysis identified the mosquito biting rate ($ b $), larval carrying capacity ($ k_A $), mosquito mortality ($ mu_V $), and the recovery rate of undetected cases as the most influential parameters. Finally, numerical simulations assessed the impact of control measures recommended by the Ministry of Health of Burkina Faso. The results show that the effectiveness of dengue control strategies depends critically on their intensity and, most importantly, their duration, highlighting the need for integrated, intensive, and sustained vector control measures combined with individual protective actions for effective and long-term management of dengue transmission.

In an increasingly competitive world, industries face growing pressure to improve efficiency while meeting strict environmental and social standards. Wastewater treatment plants (WWTPs) play a key role in reducing the environmental impact of water use across industrial, agricultural, and domestic activities. This study presents a bi-objective optimization framework to support chemical dosing decisions in physicochemical phosphorus removal (PPR) systems. Using an edible-oil WWTP as a case study, two common metal salts (aluminum sulfate and ferric chloride) are compared, considering operational cost and phosphorus removal efficiency as conflicting objectives. Polynomial surrogate models enabled the integration of BioWin PPR models into the optimization problem, and the weighted sum and $ varepsilon $-constraint methods were used to estimate the Pareto fronts, yielding complementary solutions. The proposed framework provides a practical decision-support tool for WWTPs by revealing cost-performance trade-offs. Results show that costs escalate disproportionately: reducing effluent P from 3.0 to 1.0 mg-P/L increased costs by 114% with aluminum sulfate and 355% with ferric chloride. The framework is adaptable to different PPR systems and influent conditions.

We investigate a two-species competition model in which both populations exploit a common standing resource. The dynamics are governed by a system of nonlinear differential equations admitting three equilibrium classes: extinction, competitive exclusion, and coexistence. Analytical conditions on the biological parameters ensuring the existence and asymptotic stability of these equilibria are derived, with particular emphasis on the coexistence equilibrium, representing the stable persistence of both species under shared-resource competition. In the corresponding reaction-diffusion model posed on an unbounded spatial domain, we further examine the stability of the coexistence equilibrium via traveling wavefronts. Using the upper-lower solution method, we establish the existence of traveling wave solutions connecting the extinction or single-dominance states to the coexistence state for a continuum of wave speeds exceeding a biologically determined minimal value, which depends explicitly on equilibrium magnitudes and other key parameters. Numerical simulations are provided to corroborate the theoretical results and to illustrate dynamic transitions from dominance to stable coexistence.

Releasing capsules are widely employed in biomedical applications as smart carriers of therapeutic agents, including drugs and bioactive compounds. Such delivery vehicles typically consist of a loaded core, enclosed by one or multiple concentric coating strata. In this work, we extended existing mechanistic models to account for such multi-strata structures, including possible concurrent erosion of the capsule itself, and we characterized the release kinetics of the active substance into the surrounding medium. We presented a computational study of drug release from a spherical microcapsule, modeled through a non-linear diffusion equation incorporating radial asymmetric diffusion and space- and time-discontinuous coefficients, as suggested by the experimental data specifically collected for this study. The problem was solved numerically using a finite volume scheme on a grid with adaptive spatial and temporal resolution. Analytical expressions for concentration and cumulative release were derived for all strata, enabling the exploration of parameter sensitivity-such as coating permeability and internal diffusivity-on the overall release profile. The resulting release curves provide mechanistic insight into the transport processes and offer design criteria for achieving controlled release. Model predictions were benchmarked against in vitro experimental data obtained under physiologically relevant conditions, showing good agreement and validating the key features of the model. The proposed model thus serves as a practical tool for predicting the behavior of composite coated particles, supporting performance evaluation and the rational design of next-generation drug delivery systems with reduced experimental effort.

We considered a model for an infectious disease outbreak, when the depletion of susceptible individuals is negligible, and assumed that individuals adapt their behavior according to the information they receive about new cases. In line with the information index approach, we supposed that individuals react to past information according to a memory kernel that is continuously distributed in the past. We analyzed equilibria and their stability, with analytical results for selected cases. Thanks to the recently developed pseudospectral approximation of delay equations, we studied numerically the long-term dynamics of the model for memory kernels defined by gamma distributions with a general non-integer shape parameter, extending the analysis beyond what is allowed by the linear chain trick. In agreement with previous studies, we showed that behavior adaptation alone can cause sustained waves of infections even in an outbreak scenario, and notably in the absence of other processes like demographic turnover, seasonality, or waning immunity. Our analysis gives a more general insight into how the period and peak of epidemic waves depend on the shape of the memory kernel and how the level of minimal contact impacts the stability of the behavior-induced positive equilibrium.

Addressing the critical challenges of global food security and water scarcity, we introduced an Internet of Things (IoT)-driven predictive analytics framework for dynamic irrigation optimization in tomato cultivation. Our primary objective was to develop a robust model that accurately estimates daily water requirements, with the aim of minimizing water consumption while concurrently maintaining optimal soil health. This framework leverages a uniquely comprehensive, experimentally controlled dataset from multi-sensor IoT deployments, covering environmental conditions (air temperature, humidity, CO₂, pressure) and key soil parameters (humidity, temperature, electrical conductivity). Through a rigorous data preprocessing pipeline and a tailored feature engineering approach, critical temporal patterns, inter-variable relationships, and insights from agronomic indicators like Growing Degree Days (GDD), alongside other dynamically derived features, were extracted. A two-part eXtreme Gradient Boosting (XGBoost) regression model, combining classification and regression, was developed and validated to precisely predict the daily water volume needed per hectare. The innovation of this work lies in its ability to harness complex historical IoT data to build a sophisticated intelligence layer for irrigation scheduling. By demonstrating the model's accuracy in identifying optimal water levels under varying conditions and achieving significant water savings in a simulated dynamic optimization, this research provides foundational data-driven insights that can inform highly effective precision irrigation strategies. The model achieved a high R² of 0.9476 and yielded a potential water saving of 50.84% in a simulated dynamic optimization compared to the model's raw prediction. Such intelligence empowers farmers to significantly reduce water waste and prevent harmful over-irrigation, leading to more sustainable and efficient smart agriculture, which is critical for enhancing crop resilience and resource efficiency in a changing climate.

We propose a new bioheat model for thermoregulation in the human body in response to cold environments, with emphasis on hypothermia and frostbite in exposed extremities. The model couples the bioheat transfer equation in the extremity with a differential equation that describes the core temperature. We used simulations to illustrate the connection between microscale vascular exchange and the effective perfusion term in the bioheat transfer equation. The nonlinear coupling proposed here incorporates physiologically motivated feedback laws for local and reflex vasoconstriction, as well as heat exchange with the environment. We illustrated the model numerically with realistic scenarios of thermoregulation regarding the thermal response of the body, which involves preservation of core temperature despite an increased frostbite risk. The model provides a robust framework for predictive studies of cold-induced injuries.

Turing pattern formation in growing domains depends on a steady state that balances reaction rates and local volume changes, leading to more complex patterning conditions than in fixed domains. We analyzed the effects of domain growth and shrinkage on spatially homogeneous concentrations and their stability, demonstrating that long-term behavior depends on the growth type: exponential growth causes asymptotic deviations, linear and quadratic growth enable gradual recovery of the fixed-domain state, and oscillatory growth induces concentration oscillations. Using a linear approximation for the base state, we derived an analytic expression that accurately predicts these effects for slow domain variations. Our theoretical model shows that dilution-induced steady states evolve proportionally to the chemical fixed-point concentration, a result validated through extensive numerical simulations of the Brusselator and BVAM reactions. Additionally, we proposed an approximate framework for evaluating the stability of spatially homogeneous perturbations, interpreting it as a balance between reaction rates and dilution. This yielded an analytical criterion for determining stability in the absence of diffusion, offering an alternative to previously exclusive numerical approaches for identifying the first Turing condition for pattern formation.

Over 140 million people worldwide and over 45 million people in the United States wear contact lenses; it is estimated that - contact lens users stop wearing them due to discomfort. Contact lens mechanical interactions with the ocular surface have been found to affect the ocular surface itself. These mechanical interactions are difficult to measure and calculate in a clinical setting, and the research in this field is limited. This paper presents the first mathematical model that captures the interactions between the contact lens and the open eye, where the contact lens configuration, the contact lens suction pressure, and the deformed ocular shape are all emergent properties of the model. The non-linear coupling between the contact lens and the eye is achieved by assuming that the suction pressure under the lens is applied directly to the ocular surface through the post-lens tear film layer. The contact lens mechanics are modeled using a previous published model. We consider homogeneous and heterogeneous linear elastic eye models, different ocular shapes, different lens shapes and thickness profiles, and extract lens deformations, suction pressure profiles, and ocular deformations and stresses for all the considered scenarios. The model predicts higher ocular deformations and stresses at the center of the eye and in the limbal/scleral regions. Accounting for heterogeneous material eye parameters increases the magnitude of such deformations and stresses. The ocular displacements and stresses non-linearly increase as we increase the stiffness of the contact lens. Inserting a steeper contact lens on the eye results in a reduction of the ocular displacement at the center of the eye and a larger displacement at the edge of the contact lens. The model predictions are compared with experimental data and previously developed mathematical models.

During epidemics, individuals may adjust their social behavior in response to the threat. This may affect the course of the epidemic, and, in turn, again modify people's behavior. Game theoretically, the system may end up in a Nash equilibrium, where no member of the population can benefit by unilaterally changing their behavior. Compartmentalized epidemic models can incorporate such endogenous decision making, where individuals try to optimize a utility function via their behavior. Typically, such models can only be solved numerically. Here, we extend a recently discovered analytic solution for time-dependent social distancing and the corresponding epidemic dynamics: now, the probability of an infection taking place can depend on both the susceptible and infectious individual behaviors. We show that the more effectively the susceptible individual can reduce the probability of infection, the more self-organized social distancing is expected to occur. The previously identified heuristic that the strength of rational social distancing is proportional to both the perceived infection cost and prevalence is found to also hold in the generalized model.