Mathematical biosciences最新文献

An epidemiological model with a minimal number of parameters is introduced and its structural and practical identifiabity is investigated both analytically and numerically. The model is useful when a high percentage of unreported cases is suspected, hence only hospitalization data are used to fit the model parameters and calculate the basic reproductive number R₀ and the effective reproductive number R_e. As a case study, the model is used to study the initial surge and the Omicron wave of the COVID-19 epidemic in Belgium. It was found that the reported cases largely underestimate the actual cases, and the estimated values of R₀ are consistent with other studies. The exact number of people initially in each epidemiological class is also considered unknown and was estimated directly and not considered as additional parameters to be fitted. Furthermore, the parameter fitting was performed with two different available data sets, in order to improve confidence. The methodology presented here can be easily modified to study outbreaks of diseases for which little information on confirmed cases is known a priori or when the available information is largely unreliable.

One of the main drivers of fibrotic diseases is epithelial-mesenchymal transition (EMT): a transdifferentiation process in which cells undergo a phenotypic change from an epithelial state to a pro-migratory state. The cytokine transforming growth factor-β1 (TGF-β1) has been previously shown to regulate EMT. TGF-β1 binds to fibronectin (FN) fibrils, which are the primary extracellular matrix (ECM) component in renal fibrosis. We have previously demonstrated experimentally that inhibition of FN fibrillogenesis and/or TGF-β1 tethering to FN inhibits EMT. However, these studies have only been conducted on 2-D cell monolayers, and the role of TGF-β1-FN tethering in 3-D cellular environments is not clear. As such, we sought to develop a 3-D computational model of epithelial spheroids that captured both EMT signaling dynamics and TGF-β1-FN tethering dynamics. We have incorporated the bi-stable EMT switch model developed by Tian et al. (2013) into a 3-D multicellular model to capture both temporal and spatial TGF-β1 signaling dynamics. We showed that the addition of increasing concentrations of exogeneous TGF-β1 led to faster EMT progression, indicated by increased expression of mesenchymal markers, decreased cell proliferation and increased migration. We then incorporated TGF-β1-FN fibril tethering by locally reducing the TGF-β1 diffusion coefficient as a function of EMT to simulate the reduced movement of TGF-β1 when tethered to FN fibrils during fibrosis. We showed that incorporation of TGF-β1 tethering to FN fibrils promoted a partial EMT state, independent of exogenous TGF-β1 concentration, indicating a mechanism by which fibrotic ECM can promote a partial EMT state.

Hemorrhagic fever with renal syndrome (HFRS) caused by hantavirus is prevalent across China and causes a significant number of deaths every year. This study aims to examine the transmission dynamics of hantavirus and to suggest effective control measures. We extend a periodic model of HFRS infection including house/field mice, contaminated environments, and the human population by introducing nonlinear pulses used to describe impulsive interventions. In our model, the systemic period determined by natural factors may be inconsistent with the periods of control strategies for the two kinds of mice. We prove that the model is uniformly and ultimately bounded and discuss the existence and uniqueness of the disease-free periodic solution. We calculate the basic reproduction number for the house/field mouse subsystem denoted by R₀₁/R₀₂. We then examine the threshold dynamics and analyze the conditions for global asymptotic stability of the disease-free periodic solution. Additionally, we determine that the HFRS infection uniformly persists in the human population when max{R₀₁,R₀₂}>1. Further, the existence of nontrivial periodic solutions for subsystems is examined via bifurcation theory. In particular, we observe complicated dynamics in the proposed model with multiple periods and nonlinear pulses. By fitting data on HFRS cases, we estimate the unknown parameters and predict the trend of HFRS infection in the human population. Numerical simulations show that enhancing the intensity and frequency of culling mice could curb the spread of hantavirus. Our findings suggest that improving the vaccination rate and decreasing the number of rodents, especially wild mice, are crucial in reducing HFRS infection.

Amphibian decline and extinction have been observed on a global scale, highlighting the urgency of identifying the underlying factors. This issue has long been recognized as a critical concern in conservation ecology and continues to receive significant attention. Pathogen infection, in particular the chytrid fungus Batrachochytrium dendrobatidis, is postulated as a key factor contributing to the decline of certain species within specific regions. In this paper, we focus on identifying the pathogen characteristics that can drive host species extinction. Both deterministic and stochastic modeling frameworks based on a susceptible-infectious-pathogen epidemic model are proposed, to assess the influence of pathogen infection on species decline and extinction. Various indices, including the reproduction numbers of the host species, the replication of the pathogen, and the transmission of the pathogen are derived. Theoretical analysis includes the stability of equilibria, the extinction and persistence of host species in the deterministic model, and the evaluation of extinction probability and average extinction time in the stochastic model. Additionally, numerical simulations are conducted to quantify the effects of various factors on host decline and extinction, as well as the probabilities of extinction. We find two crucial conditions for a pathogen to drive host extinction: (i) the pathogen's self-reproduction capacity in the environment, and (ii) the pathogen's impact on the fecundity and survival of the infected host. These findings provide insights that could aid in the design and implementation of effective conservation strategies for amphibians.

We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are described by a system of ordinary differential equations associated with the epidemiological SIRD model. Applying an optimise-then-discretise approach, we examine properties of the solution operator and determine existence of optimal parameters for the problem considered. Further, first-order optimality conditions are derived, the solution of which provides a certificate of goodness of fit, which is not always guaranteed with parameter tuning techniques. We then propose strategies for the numerical solution of such problems, based on projected gradient descent, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), nonmonotone Accelerated Proximal Gradient (nmAPG), and limited memory BFGS trust region approaches. We carry out a thorough computational study for a range of problems of interest, determining the relative performance of these numerical methods. Our results provide insights into the effectiveness of these strategies, contributing to ongoing research into optimising parameters for accurate and reliable disease spread modelling. Moreover, our approach paves the way for calibration of more intricate compartmental models.

Foraging strategies are shaped by interactions with the environment, and evolve under metabolic constraints. Optimal strategies for isolated and competing organisms have been studied extensively in the absence of evolution. Much less is understood about how metabolic constraints shape the evolution of an organism's ability to detect and reach food. To address this question, we introduce a minimal agent-based model of the coevolution of two phenotypic attributes critical for successful foraging in crowded environments: movement speed and perceptual acuity. Under competition higher speed and acuity lead to better foraging success, but at higher metabolic cost. We derive the optimal foraging strategy for a single agent, and show that this strategy is no longer optimal for foragers in a group. We show that mutation and selection can lead to the coexistence of two strategies: A metabolically costly strategy with high acuity and velocity, and a metabolically cheap strategy. Generally, in evolving populations speed and acuity co-vary. Therefore, even under metabolic constraints, trade-offs between metabolically expensive traits are not guaranteed.

This article uses a compartmental model describing the dynamic of the chikungunya virus in populations of humans and mosquitoes with parameters fitted to the incidence in Brazil to estimate the economic trade-off of vaccination against the virus infection. The model uses time-dependent parameters to incorporate fluctuations in the transmission and the mosquito population across the years. Using the model predictions of symptomatic infections and literature data concerning the proportions of post-acute and chronic cases, the vaccination cost is compared with the disease cost. Numerical results considering different scenarios indicate that vaccination has a limited impact on reducing the disease cost assuming that vaccination is applied uniformly countrywide. We do not consider regional targets. In some scenarios, vaccinating about 10% of the population as early as possible can reduce the disease cost and is more economically efficient. Larger proportions make vaccination not viable.

The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates asymptomatic and super-spreader individuals in a single compartmental model. We highlight the advantages of utilizing incommensurate fractional order derivatives in ordinary differential equations, including increased flexibility in capturing disease dynamics and refined memory effects in the transmission process. We conduct a qualitative analysis of our proposed model, which involves determining the basic reproduction number and analysing the disease-free equilibrium's stability. By fitting the proposed model with real data from Portugal and comparing it with existing models, we demonstrate that the incorporation of supplementary population classes and fractional derivatives significantly improves the model's goodness of fit. Sensitivity analysis further provides valuable insights for designing effective strategies to mitigate the spread of the virus.

Experimental research suggests that local patterns in DNA sequences can result in stiffer or more curved structures, potentially impacting chromatin formation, transcription regulation, and other processes. However, the effect of sequence variation on DNA geometry and mechanics remains relatively underexplored. Using rigid base pair models to aid rapid computation, we investigated the sample space of 100 bp DNA sequences to identify mechanical extrema based on metrics such as static persistence length, global bend, or angular deviation. Our results show that repetitive DNA motifs are overrepresented in these extrema. We identified specific extremal motifs and demonstrated that their geometric and mechanical properties significantly differ from standard DNA through hierarchical clustering. We provide a mathematical argument supporting the presence of DNA repeats in extremizing sequences. Finally, we find that repetitive DNA motifs with extreme mechanical properties are prevalent in genetic databases and hypothesize that their unique mechanical properties could contribute to this abundance.

Public health interventions reduce infection risk, while imposing significant costs on both individuals and the society. Interventions can also lead to behavioral changes, as individuals weigh the cost and benefits of avoiding infection. Aggregate epidemiological models typically focus on the population-level consequences of interventions, often not incorporating the mechanisms driving behavioral adaptations associated with interventions compliance. In this study, we use a behavior-epidemic model to analyze the consequences of detrimental behavioral responses driven by risk compensation. We analyze scenarios with varying levels of vaccine-acquired immunity and study the trade-off between risk compensation behaviors and reduced susceptibility. Our results reveal a trade-off between imperfect vaccine-acquired immunity and the potential risk compensation behavior of vaccinated individuals. We find that the impact of vaccination is ultimately influenced by the risk compensation behaviors of vaccinated individuals, which can either increase or decrease the size of the epidemic depending on the vaccine effectiveness. Moreover, we show that the behavioral response of the susceptible population modulates the impact of compensation behaviors by vaccinated individuals. Our results highlight that the distribution of highly protective vaccines can mitigate the observed effect. Additionally, they emphasize the importance of concurrently implementing non-pharmaceutical interventions in scenarios wherein vaccines have low efficacy. We extend our model by incorporating a model of disease surveillance, which drives a realistic operational course of action based on testing, analysis and response. Our results highlight the importance of robust surveillance systems in providing early warnings of disease outbreaks, which trigger early behavioral responses and timely interventions.