Mathematical Biosciences and Engineering最新文献

{"title":"Local epidemic control through mobility restrictions.","authors":"Uvencio José Giménez-Mujica, Oziel Gómez-Martínez, Jorge Velázquez-Castro, Ignacio Barradas, Andrés Fraguela-Collar","doi":"10.3934/mbe.2026012","DOIUrl":"10.3934/mbe.2026012","url":null,"abstract":"<p><p>Epidemic severity indices that incorporate disease information are essential tools for decision-makers, as these indices allow the design and evaluation of possible control strategies in advance of implementation in susceptible populations. In spatially structured settings, indices that consider human mobility provide valuable information on the spread of infectious diseases and the potential impact of mobility restrictions during outbreaks. In this context, the final epidemic size in metapopulation models serves as an effective measure of outbreak severity in geographical terms. However, the existence and uniqueness of the solution to the corresponding equation have only been established in particular cases. In this study, we derived conditions that guarantee the existence and uniqueness of the solution to the final epidemic size equation in a SIR-type metapopulation model. We also conducted a sensitivity analysis in a two-region, unidirectional infection scenario, which allowed us to examine the effects of mobility between an infected region and a susceptible one. Our results indicate that, under relatively simple conditions, restricting mobility can help contain outbreaks. However, we also identified situations in which mobility is not detrimental and may even be beneficial. These findings provide a preliminary framework for assessing the appropriateness of mobility restrictions during infectious disease outbreaks in spatially structured regions.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 2","pages":"291-311"},"PeriodicalIF":2.6,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146087841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cost-performance trade-off analysis of physicochemical phosphorus removal systems for wastewater treatment: A bi-objective optimization approach.","authors":"Florencia Caro, Diego Rossit, Claudia Santiviago, Jimena Ferreira, Sergio Nesmachnow","doi":"10.3934/mbe.2026006","DOIUrl":"https://doi.org/10.3934/mbe.2026006","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"124-147"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling of the 2023 dengue outbreak in the Centre Region of Burkina Faso: Parameter estimation and assessment of control strategies.","authors":"Haoua Tinde, Wenddabo Olivier Sawadogo, Pegdwindé Ousséni Fabrice Ouedraogo, Adama Kiemtore","doi":"10.3934/mbe.2026003","DOIUrl":"10.3934/mbe.2026003","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"40-75"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On models of shared resource competition, coexistence and traveling waves.","authors":"Wei Feng, Xin Lu, Karen Ward","doi":"10.3934/mbe.2026002","DOIUrl":"https://doi.org/10.3934/mbe.2026002","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"22-39"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic modeling, analysis, and simulation of Dengue in Valle del Cauca: A case study.","authors":"Diego Alejandro Becerra-Becerra, Jhonier Rangel, Viswanathan Arunachalam","doi":"10.3934/mbe.2026011","DOIUrl":"10.3934/mbe.2026011","url":null,"abstract":"<p><p>Dengue remains a major public health challenge in Colombia, with Valle del Cauca experiencing recurrent outbreaks characterized by seasonal fluctuations and long-term variability. Understanding the transmission dynamics of Dengue across age groups is critical for targeted interventions. In this study, we developed an age-structured stochastic host-vector model, incorporating a compartmental SIR-SI framework within a stochastic differential equation (SDE) approach. The population is stratified into youths (0-17 years) and adults (18 years and older), enabling analysis of age-specific infection and recovery patterns. Simulations and forecasts were performed using the Euler-Maruyama method, informed by fixed parameters from the literature, estimated disease-specific parameters, and epidemiological data from Colombia's Public Health Surveillance System (SIVIGILA) spanning 2013-2023. Additionally, a Seasonal Autoregressive Integrated Moving Average (SARIMA) model was employed as a complementary approach to capture and forecast monthly Dengue incidence. Our results highlighted distinct epidemic patterns across age groups, the higher infection burden among adults, and the complementary roles of mechanistic SDE modeling and SARIMA forecasting for surveillance and control planning.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 2","pages":"266-290"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146087877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A general multi-stratum model for a nanofunctionalized releasing capsule: An experiment-driven computational study.","authors":"Elia Onofri, Emiliano Cristiani, Andrea Martelli, Piergiorgio Gentile, Joel Girón Hernández, Giuseppe Pontrelli","doi":"10.3934/mbe.2026001","DOIUrl":"10.3934/mbe.2026001","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"1-21"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Behavior-induced oscillations in epidemic outbreaks with distributed memory: Beyond the linear chain trick using numerical methods.","authors":"Alessia Andò, Simone De Reggi, Francesca Scarabel, Rossana Vermiglio, Jianhong Wu","doi":"10.3934/mbe.2026004","DOIUrl":"https://doi.org/10.3934/mbe.2026004","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"76-96"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An IoT-driven predictive analytics framework for dynamic irrigation optimization in tomato cultivation.","authors":"Maung Maung Htwe, Lachezar Filchev, Ekaterina Batchvarova, Sandra Jardim","doi":"10.3934/mbe.2026010","DOIUrl":"https://doi.org/10.3934/mbe.2026010","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"242-265"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear bioheat model for dynamics of hypothermia and frostbite. Ⅰ. Modeling aspects.","authors":"Tyler Fara, Malgorzata Peszynska","doi":"10.3934/mbe.2026009","DOIUrl":"https://doi.org/10.3934/mbe.2026009","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"210-241"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Base state of growing reaction-dilution systems exhibiting Turing patterns.","authors":"Aldo Ledesma-Durán, Consuelo García-Alcántara, Iván Santamaría-Holek","doi":"10.3934/mbe.2026005","DOIUrl":"https://doi.org/10.3934/mbe.2026005","url":null,"abstract":"<p><p>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.</p>","PeriodicalId":49870,"journal":{"name":"Mathematical Biosciences and Engineering","volume":"23 1","pages":"97-123"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145913838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}