Mathematical Biosciences and Engineering最新文献

A spatio-temporal prey-predator (quokka and red fox interaction) model with the fear effect, Holling type Ⅱ functional response, and a generalist predator is proposed. The existence of equilibrium points and their corresponding stability are analyzed under certain conditions to explore the system's dynamics. The occurrence of a Hopf bifurcation, a saddle-node bifurcation, and a Bogdanov-Takens bifurcation are confirmed. The partial rank correlation coefficient method is performed for the sensitivity analysis. Furthermore, the cross-diffusion is incorporated in the formulated model system to identify the spatio-temporal dynamics of the system. All theoretical results are validated through a numerical simulation. The outcome of the temporal model shows a decrease in the fear effect due to the predation by the red fox helps to increase the quokka population. The spatio-temporal model indicates that as the diffusion coefficient and fear parameters vary, the pattern changes from isolated spots to stripes, and again from stripes to spots. This represents the variation in spatial interactions and aggregation. The dispersion of predators and prey increases with an increased diffusion; however, the group formation is restricted by a stronger fear effect that scatters prey.

Conservation efforts are under constant threat of failure due to poaching. Efforts to combat poaching may take a number of forms, but access to each form depends on resources, and access to these resources may depend on the success of previous efforts (e.g., monetary donations from supporters could directly combat poaching, but may be more effective if partially spent on recruiting additional supporters who then also donate). We adopted a mathematical framework with inspiration from the famous colonel blotto game to model the ongoing battle between conservationists and poachers. Focusing on a marine setting as a case study, players have budgets consisting of three types of resources: monetary, non-monetary, and supporters. The heterogeneous battlefields (laws, marine reserves, and community) reflect commonly employed conservation tactics meant to limit poaching. conservationists allocate resources to limit the success of poachers, while poachers allocate resources to overcome barriers implemented by conservationists. We assumed that no action can succeed without supporters, and thus whichever player wins over all the supporters in the community (i.e., the community battlefield), wins the game. We analyzed battlefield payoffs and player budget distributions to determine overall player success. We demonstrated how initially disadvantaged players may have an opportunity to win the game, although, we found that success in the first round can be most critical under certain scenarios. By framing the question in this way, we hope to provide additional tools for decision support to guide resource allocation, improving the efficacy of conservation efforts.

In this review, we explore the advances, setbacks, and future possibilities of directed acyclic graphs (DAGs) as conceptual and analytical tools in applied and theoretical epidemiology. DAGs are literal, theoretical or speculative, and diagrammatic representations of known, uncertain, or unknown data generating mechanisms (and dataset generating processes) in which the causal relationships between variables are determined on the basis of two over-riding principles-"directionality" and "acyclicity". Among the many strengths of DAGs are their transparency, simplicity, flexibility, methodological utility, and epistemological credibility. All these strengths can help applied epidemiological studies better mitigate (and acknowledge) the impact of avoidable (and unavoidable) biases in causal inference analyses based on observational/non-experimental data. They can also strengthen the credibility and utility of theoretical studies that use DAGs to identify and explore hitherto hidden sources of analytical and inferential bias. Nonetheless, and despite their apparent simplicity, the application of DAGs has suffered a number of setbacks due to weaknesses in understanding, practice, and reporting. These include a failure to include all possible (conceivable and inconceivable) unmeasured covariates when developing and specifying DAGs; and weaknesses in the reporting of DAGs containing more than a handful of variables and paths, and where the intended application(s) and rationale(s) involved is necessary for appreciating, evaluating, and exploiting any causal insights they might offer. We proposed two additional principles to address these weaknesses and identify a number of opportunities where DAGs might lead to further advancements: The critical appraisal and synthesis of observational studies; the external validity and portability of causality-informed prediction; the identification of novel sources of bias; and the application of DAG-dataset consistency assessment to resolve pervasive uncertainty in the temporal positioning of time-variant and time-invariant exposures, outcomes, and covariates.

The known global dynamics of the classic Leslie logistic model for the dynamics of an age-structured population are extended to a Darwinian dynamic version of the model for a single phenotypic trait (that is subject to natural selection). This is done under the assumption that the speed of evolution does not exceed an upper bound and that the maximum intraspecific competition intensity experienced by an individual occurs when its inherited trait equals that of the population mean trait. An example is given that applies the results to a model in which age-specific birth rates are subject to natural selection and that illustrates conditions under which evolution favors an iteroparous-type or a semelparous-type of life history strategy.

Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria Legionella. It primarily occurs in places with poorly maintained artificial sources of water. There is currently a lack of mathematical models on the dynamics of LD. In this paper, we formulate a novel ordinary differential equation-based susceptible-exposed-infected-recovered (SEIR) model for LD. One issue with LD is the difficulty in its detection, as the majority of countries around the world lack the proper surveillance and diagnosis methods. Thus, there is not much publicly available data or literature on LD. We use parameter estimation for our model with one of the few outbreaks with time series data from Murcia, Spain in 2001. Furthermore, we apply a global sensitivity analysis to understand the contributions of parameters to our model output. To consider managing LD outbreaks, we explore implementing sanitizing individual sources of water by constructing an optimal control problem. Using our fitted model and the optimal control problem, we analyze how different parameters and controls might help manage LD outbreaks in the future.

Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these transitions. We established the existence of global positive solutions for the model and conducted numerical analyses to assess the impact of model parameters on deforestation incentives. To address the challenge of parameter estimation, we proposed a novel deep learning approach that estimates all model parameters from a single sample containing time-series observations of forest and agricultural land proportions. This innovative approach enables us to understand forest transition dynamics and deforestation trends at any future time.

The synergy between radiotherapy and immunotherapy plays a pivotal role in enhancing tumor control and treatment outcomes. To explore the underlying mechanisms of synergy, we investigated a novel treatment approach known as personalized ultra-fractionated stereotactic adaptive radiation (PULSAR) therapy, which emphasizes the impact of radiation timing. Unlike conventional daily treatments, PULSAR delivers high-dose radiation in spaced intervals over weeks or months, enabling tumors to adapt and potentially enhancing synergy with immunotherapy. Drawing on insights from small-animal radiation studies, we developed a discrete-time model based on multiple difference equations to elucidate the temporal dynamics of tumor control driven by both radiation and the adaptive immune response. By accounting for the migration and infiltration of T cells within the tumor microenvironment, we established a quantitative link between radiation therapy and immunotherapy. Model parameters were estimated using a simulated annealing algorithm applied to training data, and our model achieved high accuracy for the test data with a root mean square error of 287 mm³. Notably, our framework replicated the PULSAR effect observed in animal studies, revealing that longer intervals between radiation treatments in the context of immunotherapy yielded enhanced tumor control. Specifically, mice receiving immunotherapy alongside radiation pulses delivered at extended intervals, ten days, showed markedly improved tumor responses, whereas those treated with shorter intervals did not achieve comparable benefits. Moreover, our model offers an in-silico tool for designing future personalized ultra-fractionated stereotactic adaptive radiation trials. Overall, these findings underscore the critical importance of treatment timing in harnessing the synergy between radiotherapy and immunotherapy and highlight the potential of our model to optimize and individualize treatment protocols.

Here, we considered Holling functional responses, a core concept in population dynamics, and discussed their potential interpretation in the context of social epidemiology. Then, we assessed which Holling functional response best represents the vaccination behaviour of individuals when such a behaviour is influenced by information and rumours about the disease. In particular, we used the Holling functionals to represent the information-dependent vaccination rate in a socio-epidemiological model for meningococcal meningitis. As a field case test, we estimated the information-related parameters by using official data from a meningitis outbreak in Nigeria and numerically assessed the impact of the functionals on the solutions of the model. We observed significant inaccuracies on parameter estimates when either Holling type Ⅰ or Holling type Ⅲ functional were used. On the contrary, when the Holling type Ⅱ functional was employed, epidemiological data were well reproduced, and reasonable values of the information parameters were obtained. Given the socio-epidemiological interpretation of the Holling type Ⅱ functional, this means that the rate at which susceptible individuals come into contact with information may be assumed to be constant and that the time needed to handle the available information cannot be neglected.

In this paper, a patchy model in which the migration is induced by the fear effect on the predator was investigated. By applying dynamical theory, the complete study on persistence of the system and the local/global stability of equilibria were discussed. Choosing the diffusion coefficient $ D_1 $ as the bifurcation parameter, transcritical bifurcation occurring near the trivial equilibrium was demonstrated. We concluded that low dispersal is favorable for the coexistence of both species, but large dispersal leads to the extinction of species. There is an optimal diffusion coefficient to make the density of the prey population reach its maximum. In addition, the level of fear effect $ k $ and the maximum fear cost $ eta $ are beneficial to the total population density of prey.

The prediction of bovine infectious diseases is a constant challenge as generally, only laboratory data is available not allowing the study of their relationship with each disease's risk factors. The diseases neosporosis and bovine viral diarrhea, which are present in Colombia, the United States, Mexico, Brazil, and Argentina, cause reproductive problems in cattle and generate economic losses for ranchers. Although there are mathematical models that can evaluate which cattle are susceptible to these diseases, these provide limited information, maintaining the need for a model that provides information on both transmission and mechanisms for controlling the disease. In this article, a machine learning model is presented that combines laboratory data with risk factors in a neural network to predict the presence of bovine neosporosis. The proposed model was implemented with data from previous studies conducted in the municipality of Sotaquirá, Boyacá, Colombia, and obtained an accuracy of 94% in predicting the presence of the disease. It can be concluded that incorporating laboratory data into machine learning algorithms improves the prediction of the presence of these diseases. Furthermore, the proposed system not only predicts but also provides useful information for clinical decision-making, making it a valuable tool in the veterinary field.