Mathematical Biosciences最新文献

{"title":"Exploring trade-offs in drug administration for cancer treatment: A multi-criteria optimisation approach","authors":"Maicon de Paiva Torres ,&nbsp;Fran Sérgio Lobato ,&nbsp;Gustavo Barbosa Libotte","doi":"10.1016/j.mbs.2025.109404","DOIUrl":"10.1016/j.mbs.2025.109404","url":null,"abstract":"<div><div>This study addresses the combination of immunotherapy and chemotherapy in cancer treatment, recognising its promising effectiveness but highlighting the challenges of complex interactions between these therapeutic modalities. The central objective is to determine guidelines for the optimal administration of drugs, using an optimal control model that considers interactions in tumour dynamics, including cancer cells, the immune system, and therapeutic agents. The optimal control model is transformed into a multi-objective optimisation problem with treatment constraints. This is achieved by introducing adjustable trade-offs, allowing personalised adaptations in drug administration to achieve an optimal balance between established objectives. Various optimisation problems are addressed, considering two and three simultaneous objectives, such as optimising the number of cancer cells and the density of effector cells at the final treatment time. The diverse combinations presented reflect the model’s flexibility in the face of multi-objective optimisation, providing a range of approaches to meet specific medical needs. The analysis of Pareto optimal fronts in <em>in silico</em> investigation offers an additional resource for decision-makers, enabling a more effective determination of the optimal administration of cytotoxic and immunotherapeutic agents. By leveraging an optimal control model, we have demonstrated the effectiveness of considering interactions in tumour dynamics, including the integration of immunotherapy and chemotherapy. Our findings underscore the importance of tailored treatment plans to achieve optimal outcomes, showcasing the versatility of our approach in addressing individual patient needs. The insights gained from our analysis offer valuable guidance for future research and clinical practice, paving the way for more effective and personalised cancer therapies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109404"},"PeriodicalIF":1.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"How environmental stochasticity can destroy the persistence of macroalgae in a coral reefs ecosystem","authors":"Chaoqun Xu,&nbsp;Qiucun Chen","doi":"10.1016/j.mbs.2025.109402","DOIUrl":"10.1016/j.mbs.2025.109402","url":null,"abstract":"<div><div>In this study, we mainly investigate how environmental stochasticity can destroy the persistence of macroalgae in a coral reefs ecosystem by analyzing the noise-induced tipping behavior. Firstly, detailed mathematical analysis for all feasible system parameters shows that the deterministic system has rich dynamics, including two types of bifurcations and two types of bistabilities. This also reveals that the dynamic behavior of coral reefs ecosystem could be highly sensitive to the system parameters and initial values. For the stochastic system, two kinds of noise-induced tipping behaviors are numerically found: Transition from coral-free state to macroalgae-free state; transition from coexistence state to macroalgae-free state. We then mainly analyze the impacts of noise intensity on the probability and time that coral reef ecosystem tips between different states, evaluate the extinction risk of macroalgae for different initial values, and eventually assign extinction warning levels to these values. Our analysis reveals that as a fragile marine ecosystem, the evolution trend of the coral reefs depends not only on the system parameters and initial values, but also on the intensity of the stochasticity experienced by the system.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109402"},"PeriodicalIF":1.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of periodic solution for a free boundary problem modeling small plaques","authors":"Jingyi Liu,&nbsp;Bei Hu","doi":"10.1016/j.mbs.2025.109397","DOIUrl":"10.1016/j.mbs.2025.109397","url":null,"abstract":"<div><div>Mathematical models describing the growth of plaque in the arteries (e.g., Friedman and Hao (2015), Friedman et al. (2015), Hao and Friedman (2014), McKay et al. (2005) and Mukherjee et al. (2019)) were introduced. All of these models include the interaction of the “bad” cholesterols, low-density lipoprotein (LDL), and the “good” cholesterols, high-density lipoprotein (HDL), in triggering whether plaque will grow or shrink.</div><div>Because the blood vessels tend to be circular, 2D cross-section model is a good approximation, and the 2D models are studied in Friedman et al. (2015), Zhang et al. (2023) and Zhao and Hu (2022). A bifurcation into a 3D plaque was recently studied in Huang and Hu (2022). All of these models assume a constant supply of LDL and HDL from the blood vessel.</div><div>In reality, nutrient concentration changes with the intake of food, which happens very often in a periodic manner. When the LDL and HDL supplies from the blood vessel are periodic and are not too far away from the prevalent values, a periodic solution was obtained in Huang and Hu (2023). In this paper, we carry out the linear stability analysis of this periodic solution and provide simulation results to confirm our analysis.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109397"},"PeriodicalIF":1.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infection propagation in a tissue with resident macrophages","authors":"M. Bouzari ,&nbsp;L. Ait Mahiout ,&nbsp;A. Mozokhina ,&nbsp;V. Volpert","doi":"10.1016/j.mbs.2025.109399","DOIUrl":"10.1016/j.mbs.2025.109399","url":null,"abstract":"<div><div>The progression of viral infection within the human body is governed by a complex interplay between the pathogen and the immune response. The initial phase of the innate immune response is driven by inflammatory cytokines and interferons produced by infected target cells and tissue-resident macrophages. These inflammatory cytokines not only amplify the immune response but also initiate programmed cell death, which helps slow the spread of the infection. The propagation of the infection within tissues can be modeled as a reaction–diffusion wave, where the speed of this wave is linked to the virus virulence, and the overall viral load determines its infectivity. In this study, we demonstrate that inflammation reduces both the speed and viral load of the infection wave, and we establish the conditions necessary to halt the spread of the infection. Depending on the relative strength of the infection and the immune response, there are three possible outcomes of infection progression. If the virus replication number is sufficiently low, the infection does not develop. For intermediate values of this parameter, the infection spreads within the affected tissue at a decreasing speed and amplitude before ultimately being eliminated. However, if the virus replication number is high, the infection propagates as a reaction–diffusion wave with a constant speed and amplitude. These findings are derived using analytical methods and are corroborated by numerical simulations. Additionally, we explore viral diffusion, comparing the conventional parabolic diffusion model with the hyperbolic diffusion model, which is introduced to address the limitation of infinite propagation speed. Our results show that while the viral load remains the same across both models, the wave speed in the hyperbolic model is smaller and approaches that of the parabolic model as the relaxation time decreases.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109399"},"PeriodicalIF":1.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stretch-induced recruitment of myosin into transversal actin rings stabilises axonal large cargo transport","authors":"Nizhum Rahman ,&nbsp;Dietmar B. Oelz","doi":"10.1016/j.mbs.2025.109400","DOIUrl":"10.1016/j.mbs.2025.109400","url":null,"abstract":"<div><div>We study the axonal transport of large cargo vesicles and its feedback with contractile transversal actomyosin rings in axons through modelling and simulation. To this end, we simulate a mathematical model that integrates forces generated by the molecular motors and forces exerted by transversal actin rings. Our results predict that cargo vesicles exhibit bidirectional movement along with pauses in agreement with observations. It has been observed that during predominantly retrograde axonal cargo transport, blebbistatin treatment prolongs the periods spent by the cargo in anterograde transport. Our simulations show that this can be explained by mechanotransductive stretch-induced recruitment of myosin motors into transversal actin rings. These findings offer valuable insights into the complex dynamics of axonal cargo transport and propose potential avenues for further experimental research.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109400"},"PeriodicalIF":1.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hybrid analysis with phylogeny and population modeling to estimate the recent founding date of a population: A case study in the origins of COVID-19 illustrates how a branching process approximation can simplify a hybrid analysis","authors":"John L. Spouge","doi":"10.1016/j.mbs.2025.109401","DOIUrl":"10.1016/j.mbs.2025.109401","url":null,"abstract":"<div><div>The exact date of the primary infection in COVID-19 remains unknown. One influential article (Pekar et al. (2021)) estimated the date with a hybrid analysis combining epidemiological and phylogenetic methods. The phylogenetic methods analyzed 583 SARS-COV-2 complete genomes to estimate the sample tMRCA (time of the most recent common ancestor). Before igniting as an epidemic, however, COVID-19 may have had several population bottlenecks with only a single infected person, so the MRCA merely represents the last such bottleneck. Pekar et al. (2021) therefore used epidemiological methods to estimate the time from the primary infection to the sample MRCA. The hybrid method involved several arbitrary decisions, however, reflecting the fact that the epidemiological and phylogenetic analyses overlap at the sample MRCA and are generally probabilistically dependent. Towards removing the dependence, note that the start of an epidemic has a branching process approximation. Let the branching process have a single ancestor. If the branching process does not go extinct, define skeleton particles (individuals) to be particles whose lineages do not go extinct, and define the long-time MRCA as the earliest skeleton particle with at least two skeleton offspring. A linear phylogeny of skeleton particles therefore separates the ancestor from the long-time MRCA. Probabilistically, the linear phylogeny is a defective renewal process of skeleton particles, making the generation count geometrically distributed. Moreover, the terminology “long-time MRCA” is apt, because as time becomes arbitrarily large, the MRCA of the corresponding extant population approaches the long-time MRCA. Effectively, the focus on the long-time MRCA makes the forward epidemiological and backward phylogenetic analyses probabilistically independent. The present article can therefore confirm most of the epidemiological conclusions of the hybrid analysis of Pekar et al. (2021). Its use of branching process approximations also points the way to noticeable simplifications in the hybrid method.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109401"},"PeriodicalIF":1.9,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143416645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A conceptual framework for modeling a latching mechanism for cell cycle regulation","authors":"Punit Gandhi ,&nbsp;Yangyang Wang","doi":"10.1016/j.mbs.2025.109396","DOIUrl":"10.1016/j.mbs.2025.109396","url":null,"abstract":"<div><div>Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"382 ","pages":"Article 109396"},"PeriodicalIF":1.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143411670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equilibrium analysis of discrete stochastic population models with gamma distribution","authors":"Haiyan Wang","doi":"10.1016/j.mbs.2025.109398","DOIUrl":"10.1016/j.mbs.2025.109398","url":null,"abstract":"<div><div>This paper analyzes the stochastic logistic and Ricker difference equations at equilibrium with the gamma distribution. We identify mathematical relationships among the intrinsic growth rate in the stochastic equations, the parameters of the gamma distribution and a small stochastic perturbation. The mathematical relations reveal that there are two branches of the intrinsic growth rate, representing alternative stable states corresponding to higher and lower growth rates. This duality provides deeper insights into population stability and resilience under stochastic conditions. We present the biological significance of these relationships, emphasizing how the stochastic perturbation and shape parameter of the gamma distribution influence population dynamics at equilibrium.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109398"},"PeriodicalIF":1.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of phase tumbling and the reentrainment of circadian oscillators","authors":"Guangyuan Liao ,&nbsp;Casey O. Diekman ,&nbsp;Amitabha Bose","doi":"10.1016/j.mbs.2025.109381","DOIUrl":"10.1016/j.mbs.2025.109381","url":null,"abstract":"<div><div>Circadian clocks are comprised of networks of cellular oscillators that synchronize to produce endogenous daily rhythms in gene expression and protein abundance. These clocks have evolved to align the physiology and behavior of organisms to the 24-h environmental cycles arising from Earth’s rotation. Rapid travel across time zones causes misalignment between an organism’s circadian rhythms and its environment, leading to sleep problems and other jet lag symptoms until the circadian system entrains to the external cycles of the new time zone. Experimental and modeling work has shown that phase tumbling, defined as desynchronizing networks of circadian oscillators prior to an abrupt phase shift of the light-dark cycle, can speed up the process of reentrainment. Here, we use a mathematical model of circadian oscillators and 2-D entrainment maps to analyze the conditions under which phase tumbling has a positive, neutral, or negative effect on reentrainment time. We find that whether or not phase tumbling is beneficial depends on the size of the external phase shift and the location of the perturbed oscillator with respect to the fixed points and invariant manifolds of the entrainment map.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109381"},"PeriodicalIF":1.9,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143392893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal control of species augmentation in a competition model","authors":"Munkaila Dasumani ,&nbsp;Suzanne Lenhart ,&nbsp;Gladys K. Onyambu ,&nbsp;Stephen E. Moore","doi":"10.1016/j.mbs.2025.109394","DOIUrl":"10.1016/j.mbs.2025.109394","url":null,"abstract":"<div><div>Mathematical models of endangered competitive interactions incorporating the Allee effect with augmentation strategies have not been studied extensively. This area is however critical to ecologists since it relates to ways species can become endangered and possibly go extinct due to competition for limited resources. More importantly, the climatic change with its adverse effects has not only affected green forests but has also caused the extinction of some species. Thus, there is a need for critical augmentation strategies to safeguard such species. This paper, therefore, presents an optimal control strategy for a continuous time competition interaction model with strong Allee effects. We seek to maximize the target species at the end of each final time. We consider two objective functionals involving the populations and the cost of the controls. Using Pontryagin’s Maximum Principle, we obtain the optimal control characterizations. We perform numerical simulations using the forward–backward sweep method and the approximate solutions are presented and discussed. Since there is a cost involved in the translocation of the reserve species, we adopt a minimization cost strategy. In addition, we compute the objective functional values for each simulation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109394"},"PeriodicalIF":1.9,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143392896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}