Mathematical Biosciences and Engineering最新文献

In confronting the critical challenge of disease outbreak management, health authorities consistently encourage individuals to voluntarily disclose a potential exposure to infection and adhere to self-quarantine protocols by assuring medical care (hospital beds, oxygen, and constant health monitoring) and helplines for severe patients. These have been observed during pandemics; for example, COVID-19 phases in many middle-income countries, such as India, promoted quarantine and reduced stigma. Here, we present a game-theoretic model to elucidate the behavioural interactions in infection disclosure during an outbreak. By employing a fractional derivative approach to model disease propagation, we determine the minimum level of voluntary disclosure required to disrupt the chain of transmission and allow the epidemic to fade. Our findings suggest that higher transmission rates and an increased perceived severity of infection may change the externality of the disclosing strategy, leading to an increase in the proportion of individuals who choose disclosure, and ultimately reducing disease incidence. We estimate the behavioural parameters and transmission rates by fitting the model to COVID-19 hospitalized cases in Chile, South America. The results from our paper underscore the potential for promoting the voluntary disclosure of infection during emerging outbreaks through effective risk communication, thereby emphasizing the severity of the disease and providing accurate information to the public about capacities within hospitals and medical care facilities.

Antimalarial drugs are critical for controlling malaria, but the emergence of drug resistance poses a significant challenge to global eradication efforts. This study explores strategies to minimize resistance prevalence and improve malaria control, particularly through the use of mass drug administration (MDA) in combination with antimalarial drugs. We develop a compartmental mathematical model that incorporates asymptomatic, paucisymptomatic, and clinical states of infection and evaluates the impact of resistance mutations on transmission dynamics. The model includes both treated and untreated states among infected and recovered individuals, with a focus on optimizing control strategies through MDA and antimalarial treatment. A global sensitivity analysis identifies the critical factors that influence malaria dynamics, including MDA coverage, treatment access for different infection states, the probability of mutation from treated sensitive human infections, to treated resistant human infections and the initial prevalence of resistance. The model is extended to include optimal control strategies that provide time-dependent control interventions for treatment and MDA. Intuitively, when the mutation rate is relatively low, the optimal strategy combines the use of antimalarial drugs and MDA, with a gradual decrease in antimalarial drug use over time, ensuring sustainable malaria control. In contrast, at higher mutation rates, the strategy prioritizes broader deployment of MDA while significantly reducing reliance on antimalarial to minimize the risk of resistance developing. Numerical simulations of the optimal control problem reinforce the importance of strategic intervention in mitigating drug resistance. This study contributes to understanding the role of MDA and treatment strategies in the control of malaria, with implications for optimizing malaria control programs in endemic regions.

Although different strategies for mosquito-borne disease prevention can vary significantly in their efficacy and scale of implementation, they all require that individuals comply with their use. Despite this, human behavior is rarely considered in mathematical models of mosquito-borne diseases. Here, we sought to address that gap by establishing general expectations for how different behavioral stimuli and forms of mosquito prevention shape the equilibrium prevalence of disease. To accomplish this, we developed a coupled contagion model tailored to the epidemiology of dengue and preventive behaviors relevant to it. Under our model's parameterization, we found that mosquito biting was the most important driver of behavior uptake. In contrast, encounters with individuals experiencing disease or engaging in preventive behaviors themselves had a smaller influence on behavior uptake. The relative influence of these three stimuli reflected the relative frequency with which individuals encountered them. We also found that two distinct forms of mosquito prevention-namely, personal protection and mosquito density reduction-mediated different influences of behavior on equilibrium disease prevalence. Our results highlight that unique features of coupled contagion models can arise in disease systems with distinct biological features.

We present a general version of Massera's theorems for arbitrary discrete domains, based on a newly introduced definition for both linear and nonlinear equations. For scalar nonlinear equations, we identify sufficient conditions that ensure each u-bounded solution approaches a periodic solution asymptotically. In the case of linear systems, we prove that the presence of a u-bounded solution necessarily leads to a periodic solution. We also provide some examples to show the practical implications of our findings.

A short-term stochastic model of minute-by-minute food intake is formulated, incorporating the interaction of appetite, insulinemia, and glycemia in determining the size and frequency of meals. By assuming a person would maintain his or her eating habit over time, we extend the simulation period to several years and explore scenarios based on food choices (high-fiber vs. high-carbohydrate) or appetite suppression. The model coherently predicts increments or decrements in body weight in the long-term when altering appetite in the short-term. Further, the model shows how food type choice, at the same appetite drive and habitual proposed meal size, induces macroscopic changes in body weight over a very few years. The model is innovative in that it connects the minute-by-minute behavior of the individual with long-term changes in metabolic compensation, in insulin sensitivity, in glycemic variability, and eventually in body size, thus helping to interpret the long-term development of Type 2 diabetes mellitus resulting from an unhealthy lifestyle.

Parametrized problems involve high computational costs when looking for the proper values of their input parameters and solved with classical schemes. Reduced-order models (ROMs) based on the proper orthogonal decomposition act as alternative numerical schemes that speed up computational times while maintaining the accuracy of the solutions. They can be used to obtain solutions in a less expensive way for different values of the input parameters. The samples that compose the training set determine some computational limits on the solution that can be computed by the ROM. It is highly interesting to study what can be done to overcome these limits. In this article, the possibilities to obtain solutions to parametrized problems are explored and illustrated with several numerical cases using the two-dimensional (2D) advection-diffusion-reaction equation and the 2D wildfire propagation model.

Balancing economic prosperity with environmental conservation is crucial in managing renewable bioeconomic resources. We explored a predator-prey fishery model that incorporates tourism, dynamic harvesting, and pricing strategies. Our analysis showed that increased fishing taxes reduce fishing efforts, enabling fish populations to recover. Furthermore, higher entrance fees for ecotourism support the predator population's growth. Bifurcation analysis revealed key dynamic transitions, including transcritical and Hopf bifurcations. A deeper look into coupled parameter bifurcation uncovered a transcritical bifurcation of the limit cycle, emphasizing the system's complexity. Using Pontryagin's maximum principle, we optimized fishing taxes and ecotourism entrance fees to achieve sustainable trade-offs between ecosystem health and societal revenue. The results highlighted that societal revenue peaked at an intermediate level of entrance fees, suggesting diminishing returns beyond a certain point. Revenue landscape analysis further showed that centralized, two-parameter optimization strategies outperform decentralized, single-parameter approaches. These insights provide policymakers with effective tools to design regulations that promote ecological resilience and economic viability through balanced fishing and tourism practices.

The spread of diseases poses significant threats to human health globally. The dynamic nature of infectious diseases, especially those that also rely on carriers (e.g., house flies) for transmission, requires innovative strategies to control their spread, as environmental conditions such as temperature, humidity, etc., affect the rate of growth of the carrier population. This study introduces a mathematical model to assess the effect of increasing global average temperature rise caused by carbon dioxide emissions and chemical control strategies on the dynamics of such diseases. The stability properties of feasible equilibrium solutions were discussed. Sensitivity analysis was also performed to highlight the key parameters that may help to design effective intervention strategies to control disease transmission. The model was further analyzed for an optimal control problem by incorporating a control measure on the application rate of chemical insecticides to reduce the carrier population. Through the combination of analytical techniques and numerical simulations, we have evaluated the effectiveness of chemical control strategies under varying epidemiological parameters. The model also explored the critical thresholds necessary for achieving disease control and eradication. Our results are valuable to public health officials and policymakers in designing effective interventions against carrier-dependent infectious diseases.

We propose several spatial-temporal epidemiological mathematical models to study their suitability to approximate the dynamics of the early phase of the COVID-19 pandemic in Chile. The model considers the population density of susceptible, infected, and recovered individuals. The models are based on a system of partial differential equations. The first model considers a space-invariant transmission rate, and the second modeling approach is based on different space-variant transmission rates. The third modeling approach, which is more complex, uses a transmission rate that varies with space and time. One main aim of this study is to present the advantages and drawbacks of the mathematical approaches proposed to describe the COVID-19 pandemic in Chile. We show that the calibration of the models is challenging. The results of the model's calibration suggest that the spread of SARS-CoV-2 in the regions of Chile was different. Moreover, this study provides additional insight since few studies have explored similar mathematical modeling approaches with real-world data.

Chimeric antigen receptor (CAR) T-cell therapy is a personalized immunotherapy approach in which a patient's T cells are genetically engineered to express synthetic receptors that specifically recognize and target tumor-associated antigens. This approach has demonstrated remarkable success in treating B-cell malignancies by directing CAR-T cells against the CD19 protein. However, treatment efficacy is influenced by the composition and distribution of CAR-T cell subsets administered to the patient. To investigate the impact of different CAR-T cell subtypes and infusion strategies, we developed a mathematical model that captures the dynamic interactions between tumor cells and CAR-T cells within the tumor immune microenvironment. Through computational simulations, we explored how varying the dosage and subtype proportions of infused CAR-T cells affects tumor dynamics and therapeutic outcomes. Our findings highlight the critical role of CAR-T cell subset composition in optimizing treatment efficacy, underscoring the necessity of precise dosing control and tailored infused strategies to maximize therapeutic success.