JournalTOCs

Frontiers in Applied Mathematics and Statistics
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This is an Open Access Journal

Open Access journal
ISSN (Online) 2297-4687
Published by Frontiers Media

[96 journals]

A hybrid individual-based mathematical model to study bladder
infections|Introduction|Methods|Results|Conclusions
- Authors: Anas Lasri Doukkali, Tommaso Lorenzi, Benjamin J. Parcell, Jennifer L. Rohn, Ruth Bowness
  Abstract: IntroductionBladder infections are common, affecting millions each year, and are often recurrent problems.MethodsWe have developed a spatial mathematical framework consisting of a hybrid individual-based model to simulate these infections in order to understand more about the bacterial mechanisms and immune dynamics. We integrate a varying bacterial replication rate and model bacterial shedding as an immune mechanism.ResultsWe investigate the effect that varying the initial bacterial load has on infection outcome, where we find that higher bacterial burden leads to poorer outcomes, but also find that only a single bacterium is needed to establish infection in some cases. We also simulate an immunocompromised environment, confirming the intuitive result that bacterial spread typically progresses at a higher rate.ConclusionsWith future model developments, this framework is capable of providing new clinical insight into bladder infections.
  PubDate: 2023-02-03T00:00:00Z
The value of being the decisive voter: Exploratory evidence from a hedonic
model
- Authors: Ethan Peters, Joshua C. Hall
  Abstract: In the field of public economics, there is a literature on calculating the probability of being a decisive voter. The raison d'etre of this literature is to explain voter turnout. In this short empirical paper, we look at the question from a different angle. Heterogeneity in voting preferences means that some individuals vote rationally, others instrumentally, and some individuals are marginal and respond to changes in the probability of being decisive. Individuals with a preference for instrumental voting might be willing to pay more to live in an area with a greater probability of being a decisive voter. If this is the case, housing prices should reflect this higher willingness to pay. We test our theory using hedonic data from Columbus Ohio and find suggestive evidence that voters are willing to pay for a greater likelihood of being a decisive voter. Our results, however, cannot rule out other interpretations.
  PubDate: 2023-02-03T00:00:00Z
A toy model of food production in a connected landscape
- Authors: Anthony O'Hare
  Abstract: The drive to maximize food production in a sustainable manner is a paramount concern for farmers and governments. The aim of food producers is to maximize their production yield employing actions such as application of fertilizer or pesticide they believe help to achieve this aim. However, farms do not exist in isolation, but rather share a landscape with neighbors forming networks where any action taken by any one farmer affects their neighbors who are forced to take mitigating actions creating a complicated set of interactions. Understanding these [non-]cooperative interactions and their effect on the shared ecosystem is important to develop food security strategies while protecting the environment and allowing farmers to make a living. We introduce a simple competitive agent based model in which agents produce food that is sold at a fixed price (we ignore market dynamics and do not include explicit punishment on any agent). We analyzed agent's profits in several simple scenarios allowing us to identify the most advantageous set of actions for maximizing the yield (and thus profit) for each farmer. We show that the effect of the structure of the network on each farm has implications on the actions taken by agents. These results have implications for the understanding of the effects of farming practices on the environment and how different levels of cooperation between farmers, taking into account the local terrain, can be used to incentivise producers to minimise the effects on the environment while maximizing yields.
  PubDate: 2023-02-02T00:00:00Z
COVID-19 and syphilis co-dynamic analysis using mathematical modeling
approach
- Authors: Shewafera Wondimagegnhu Teklu, Birhanu Baye Terefe
  Abstract: In this study, we have proposed and analyzed a new COVID-19 and syphilis co-infection mathematical model with 10 distinct classes of the human population (COVID-19 protected, syphilis protected, susceptible, COVID-19 infected, COVID-19 isolated with treatment, syphilis asymptomatic infected, syphilis symptomatic infected, syphilis treated, COVID-19 and syphilis co-infected, and COVID-19 and syphilis treated) that describes COVID-19 and syphilis co-dynamics. We have calculated all the disease-free and endemic equilibrium points of single infection and co-infection models. The basic reproduction numbers of COVID-19, syphilis, and COVID-19 and syphilis co-infection models were determined. The results of the model analyses show that the COVID-19 and syphilis co-infection spread is under control whenever its basic reproduction number is less than unity. Moreover, whenever the co-infection basic reproduction number is greater than unity, COVID-19 and syphilis co-infection propagates throughout the community. The numerical simulations performed by MATLAB code using the ode45 solver justified the qualitative results of the proposed model. Moreover, both the qualitative and numerical analysis findings of the study have shown that protections and treatments have fundamental effects on COVID-19 and syphilis co-dynamic disease transmission prevention and control in the community.
  PubDate: 2023-02-01T00:00:00Z
High-speed predictions of post-burn contraction using a neural network
trained on 2D-finite element simulations
- Authors: Ginger Egberts, Fred Vermolen, Paul van Zuijlen
  Abstract: Severe burn injuries often lead to skin contraction, leading to stresses in and around the damaged skin region. If this contraction leads to impaired joint mobility, one speaks of contracture. To optimize treatment, a mathematical model, that is based on finite element methods, is developed. Since the finite element-based simulation of skin contraction can be expensive from a computational point of view, we use machine learning to replace these simulations such that we have a cheap alternative. The current study deals with a feed-forward neural network that we trained with 2D finite element simulations based on morphoelasticity. We focus on the evolution of the scar shape, wound area, and total strain energy, a measure of discomfort, over time. The results show average goodness of fit (R2) of 0.9979 and a tremendous speedup of 1815000X. Further, we illustrate the applicability of the neural network in an online medical app that takes the patient's age into account.
  PubDate: 2023-01-30T00:00:00Z
Early childhood learning analytics: A case study of Learning Jungle
- Authors: Rui Liang, Hongmei Zhu, Grant Lawson, Zhao Lian, Yuqi Huang, Shengyuan Chen
  Abstract: The benefits of participating in high-quality Early Childhood Education (ECE) have been recognized by people for many years; and the need for high-quality ECE has never been greater. In this case study, we focus on whether ECE can improve learning speed in five domains: social, emotional, communication, cognition, and physical development. The initial ages for each of these five domains, in months since birth, are collected and compared with that of common children as described in Nipissing District Developmental Screen (NDDS). We find that children in the ECE program learned faster with a p-value no>0.0078. In addition, students in an ECE program are labeled by their ages at enrollment as Cohort 1 (infant) and Cohort 2 (toddler), and we conduct the following statistical tests on their difference: Welch's t-test, Hoteling's T2-test, and survival analysis. We find that the average initial observation age of Cohort 1 is 4.82 months earlier than that of Cohort 2 with a p-value no>0.009. We are convinced that ECE programs could advance students' learning in all five domains.
  PubDate: 2023-01-25T00:00:00Z
Curtailing crime dynamics: A mathematical
approach|Introduction|Methods|Results and discussion
- Authors: Theophilus Kwofie, Matthias Dogbatsey, Stephen E. Moore
  Abstract: IntroductionCrime and criminal activities have huge influences on society and societal development. The social makeup of the society has a significant impact on the propagation of crime within a population. It is a well-known reality that crime spreads across society like an infectious disease, despite the fact that there are many elements that might affect this dynamic. So, understanding crime and the factors influencing its spread are essential in formulating policies to reduce the prevalence and impacts of crime.MethodsWe formulate a deterministic mathematical model using a system of nonlinear ordinary differential equations incorporating education programs as tools to assess the population-level impact on the spread of crime. The model has a global asymptotically stable crime-free equilibrium whenever a certain criminological threshold, known as the effective reproduction number RE, is less than unity.Results and discussionThe model is fitted with prison data reported from July 2021 to June 2022 by the State of Illinois in The United States. The simulations are carried out to assess the population-level impact of the widespread use of the intervention programs and the compliance rate in the State of Illinois. We hypothetically fixed the efficacy of the intervention programs at 25% while varying the compliance rate (by the general public). With no compliance, a high level of active criminal population was recorded. As the compliance rates were significantly improved, the active population level decreased. The global sensitivity analysis is performed primarily to determine the parameters with the most effect on the spread of crime in the State of Illinois. The results demonstrate that the effective community contact rate, βc, for the criminally active individuals is the main driver of crime in the State of Illinois.
  PubDate: 2023-01-24T00:00:00Z
Enhancing the predictability of ecology in a changing world: A call for an
organism-based approach
- Authors: C. J. M. Musters, Don L. DeAngelis, Jeffrey A. Harvey, Wolf M. Mooij, Peter M. van Bodegom, Geert R. de Snoo
  Abstract: Ecology is usually very good in making descriptive explanations of what is observed, but is often unable to make predictions of the response of ecosystems to change. This has implications in a human-dominated world where a suite of anthropogenic stresses are threatening the resilience and functioning of ecosystems that sustain mankind through a range of critical regulating and supporting services. In ecosystems, cause-and-effect relationships are difficult to elucidate because of complex networks of negative and positive feedbacks. Therefore, being able to effectively predict when and where ecosystems could pass into different (and potentially unstable) new states is vitally important under rapid global change. Here, we argue that such better predictions may be reached if we focus on organisms instead of species, because organisms are the principal biotic agents in ecosystems that react directly on changes in their environment. Several studies show that changes in ecosystems may be accurately described as the result of changes in organisms and their interactions. Organism-based theories are available that are simple and derived from first principles, but allow many predictions. Of these we discuss Trait-based Ecology, Agent Based Models, and Maximum Entropy Theory of Ecology and show that together they form a logical sequence of approaches that allow organism-based studies of ecological communities. Combining and extending them makes it possible to predict the spatiotemporal distribution of groups of organisms in terms of how metabolic energy is distributed over areas, time, and resources. We expect that this “Organism-based Ecology” (OE) ultimately will improve our ability to predict ecosystem dynamics.
  PubDate: 2023-01-24T00:00:00Z
Editorial: Data driven modeling in mathematical biology
- Authors: Jacques Demongeot, Pierre Magal
  PubDate: 2023-01-24T00:00:00Z
Tying decentralization and income redistribution to fight corruption:
Empirical evidence from developed and developing countries
- Authors: Antonio N. Bojanic
  Abstract: Utilizing a panel data set for OECD and non-OECD countries for the period 1980–2016, I analyze the effects on corruption of interacting different forms of decentralization—fiscal, administrative, political, and overall decentralization—with an indicator of income inequality. The findings demonstrate that fiscal, administrative, and overall decentralization by themselves are not conducive to lowering corruption, but when moderated by the Gini index, corruption levels decrease in all countries. Moreover, as income inequality decreases, the impact of these forms of decentralization in lowering corruption increases, highlighting that decentralization can be an effective tool in combating corruption particularly when income inequality improves. The findings also demonstrate that in non-OECD countries, decentralization is an important tool to fight corruption up to high levels of inequality, proving that decentralization in developing countries is essential even when issues of income distribution have not been fully solved.
  PubDate: 2023-01-16T00:00:00Z
Hybrid Fourier series and smoothing spline path non-parametrics estimation
model
- Authors: Atiek Iriany, Adji Achmad Rinaldo Fernandes
  Abstract: Pathway analysis is one way to determine whether there is a causal relationship between extrinsic and intrinsic factors. The linearity assumption is something that can change the model. The shape of the model is subject to linearity assumptions. Path analysis is parametric when the linearity assumption is true, whereas non-parametric path analysis is used when the non-linear shape is unknown and there is no knowledge of the data pattern. Non-linear path analysis is used when the non-linear shape and data pattern are unknown. This work aimed to combine the smoothing spline method and the Fourier series method to compute non-parametric path function and it is believed that they would be able to produce more flexible function estimations for data patterns since both have the benefit of being accurate or close to the real data pattern. As a result, we found that Fourier series and smoothing splines can be used in non-parametric path analysis only if the linearity assumption is violated. Non-parametric regression-based path analysis estimators were then obtained using the ordinary least squares (OLS) approach. It uses a non-parametric approach and therefore gives non-unique estimation results.
  PubDate: 2023-01-13T00:00:00Z
Lattice Boltzmann model in general curvilinear coordinates applied to
exactly solvable 2D flow problems
- Authors: Alexei Chekhlov, Ilya Staroselsky, Raoyang Zhang, Hudong Chen
  Abstract: Numerical simulation results of basic exactly solvable fluid flows using the previously proposed by H. Chen Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a fundamental one-to-one exact advection feature in producing minimal numerical diffusion, as the Cartesian lattice Boltzmann model. As we numerically show, the new model converges to exact solutions of basic fluid flows with the increase of grid resolution in the presence of both natural curvilinear geometry and/or grid non-uniform contraction, both for near equilibrium and non-equilibrium LBM parameter choices.
  PubDate: 2023-01-11T00:00:00Z
A study of the spillover effects of digital financial agglomeration on
economic resilience|Introduction|Method|Result|Discussion
- Authors: Zhiming Zhu, Yuanyuan Yang, Hongyan Li
  Abstract: IntroductionDigital finance is the combination of digital information technology and traditional finance. And digital financial agglomeration plays a pivotal role in the process of improving economic resilience in the new era.MethodThis paper introduces digital financial agglomeration, measures the economic resilience of each province and conducts spatial correlation tests by using 30 inter-provincial (except Hainan Province) panel data from 2011 to 2020, and constructs a Spatial Durbin Model to empirically analyze the relationship between digital financial agglomeration and economic resilience based on the theory of diffusion effect of digital financial agglomeration and research hypotheses.ResultThe results show that: (1) Digital financial agglomeration can have a positive effect on economic resilience by expanding the scale of consumption. (2) Digital financial agglomeration has a direct effect on the economic resilience of the region and an indirect spillover effect on the economic resilience of neighboring regions. (3) The effects of the main explanatory variables on economic resilience pass the robustness test: the positive effects of digital financial agglomeration, consumption scale and the interaction term of the two on economic resilience are significant.DiscussionThis paper focuses on the phenomenon of digital financial agglomeration, which is a unique perspective, and explores the influence mechanism of digital financial agglomeration on economic resilience from the perspective of spatial spillover effects of digital financial agglomeration, which is somewhat innovative.
  PubDate: 2023-01-11T00:00:00Z
Dynamical solutions and quadratic resonance of nonlinear perturbed
Schrödinger equation
- Authors: Sidheswar Behera
  Abstract: This work investigates the perturbed nonlinear Schrödinger equation using the modified (G′G2)-expansion method. The obtained results are generalized and classified into classes of trigonometric, hyperbolic, and rational solutions. The kinematics of soliton and kink profiles are very helpful to understand the propagation of electromagnetic waves inside nonlinear optical fibers. The proposed modified method is unique, straightforward, concise, and effective in the sense that it gives more traveling wave solutions. The findings of this study can strengthen a system's nonlinear dynamic behavior and show how practical the methodology used to attempt to replicate has been. Wolfram Mathematica 11 is used for mathematical simplification and MATLAB is used for graphical simulation.
  PubDate: 2023-01-09T00:00:00Z
A novel conservative chaos driven dynamic DNA coding for image encryption
- Authors: Vinod Patidar, Gurpreet Kaur
  Abstract: Recently, many image encryption algorithms based on hybrid DNA and chaos have been developed. Most of these algorithms utilize chaotic systems exhibiting dissipative dynamics and periodic windows/patterns in the bifurcation diagrams along with co-existing attractors in the neighborhoods of parameter space. Therefore, such algorithms generate several weak keys, thereby making them prone to various chaos- specific attacks. In this paper, we propose a novel conservative chaotic standard map-driven dynamic DNA coding (encoding, addition, subtraction and decoding) for image encryption. It is the first hybrid DNA and conservative chaos-based image encryption algorithm having effectively infinite key space. The proposed image encryption algorithm is a dynamic DNA coding algorithm i.e., for the encryption of each pixel different rules for encoding, addition/subtraction, decoding etc. are randomly selected based on the pseudorandom sequences generated with the help of the conservative chaotic standard map. We propose a novel way to generate pseudo-random sequences through the conservative chaotic standard map and also test them rigorously through the most stringent test suite of pseudo-randomness, the NIST test suite, before using them in the proposed image encryption algorithm. Our image encryption algorithm incorporates unique feed-forward and feedback mechanisms to generate and modify the dynamic one-time pixels that are further used for the encryption of each pixel of the plain image, therefore, bringing in the desired sensitivity on plaintext as well as ciphertext. All the controlling pseudorandom sequences used in the algorithm are generated for a different value of the parameter (part of the secret key) with inter-dependency through the iterates of the chaotic map (in the generation process) and therefore possess extreme key sensitivity too. The performance and security analysis has been executed extensively through histogram analysis, correlation analysis, information entropy analysis, DNA sequence-based analysis, perceptual quality analysis, key sensitivity analysis, plaintext sensitivity analysis, classical attack analysis, etc. The results are promising and prove the robustness of the algorithm against various common cryptanalytic attacks.
  PubDate: 2023-01-09T00:00:00Z
Joint modeling of rainfall and temperature in Bahir Dar, Ethiopia:
Application of copula|Objective|Methods|Results|Conclusion
- Authors: Haile Mekonnen Fenta, Demeke Lakew Workie, Dereje Tesfaye Zikie
  Abstract: ObjectiveClimate change has effects on the economy development of any country. This paper aimed to fit the best marginal and joint distribution models of rainfall with minimum and maximum temperatures.MethodsThe average values of minimum and maximum monthly temperature, and rainfall were used in this study. For the marginal model, five probability distributions and five families of copula models were employed to show the interdependence between the maximum and minimum average annual temperature with rainfall. The Kendall's tau (τ) correlation coefficient was used to find out the correlations between rainfall with minimum and maximum temperature. Both the Akaki Information Criteria (AIC) and Bayesian information criteria (BIC) were used to select the best marginal and copula.ResultsThe result revealed that there is a significant negative relationship between the maximum temperature and rainfall. The maximum average rainfall was obtained from June to August and the maximum temperature is almost consistent in all months. Based on AIC/BIC, the Weibull distribution for rainfall, the Beta for minimum, and the Gaussian for maximum temperature were identified as the best marginal distributions. The Clayton copula distribution was identified as the best copula for rainfall and minimum temperature (with parameter of θ =1. 21, tau correlation = −0.41, p < 0.001), and Frank copula was identified for rainfall and maximum temperature (with unique Frank parameter of θ = −3.94, correlation = −0.38, p < 0.001).ConclusionThe result showed that there is a significant positive relationship between the average annual minimum temperature and rainfall; whereas a negative relationship occurred between the maximum temperature and rainfall. The Clayton and Frank copula were found to be the most appropriate to the model of a bivariate distribution of mean annual rainfall with minimum/maximum temperature respectively.
  PubDate: 2023-01-09T00:00:00Z
Bifurcation analysis of a predator–prey model involving age structure,
intraspecific competition, Michaelis–Menten type harvesting, and memory
effect
- Authors: Hasan S. Panigoro, Emli Rahmi, Resmawan Resmawan
  Abstract: The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators and the nonlinear harvesting of prey following the Michaelis–Menten type term. Some biological validities are shown for the constructed model such as the existence and uniqueness as well as the non-negativity and boundedness of solutions. Three equilibrium points, namely the origin, axial, and interior points, are found including their global dynamics by employing the Lyapunov function along with the generalized Lassale invariant principle. The changes in dynamical behaviors driven by the harvesting and the memory effect are exhibited, including transcritical, saddle-node, backward, and Hopf bifurcations. The appearance of these interesting phenomena is strengthened by giving numerical simulations consisting of bifurcation diagrams, phase portraits, and their time series.
  PubDate: 2023-01-06T00:00:00Z
Dynamic analysis and optimal control of COVID-19 with comorbidity: A
modeling study of Indonesia
- Authors: Muhammad Abdurrahman Rois, Fatmawati, Cicik Alfiniyah, Chidozie W. Chukwu
  Abstract: Comorbidity is defined as the coexistence of two or more diseases in a person at the same time. The mathematical analysis of the COVID-19 model with comorbidities presented includes model validation of cumulative cases infected with COVID-19 from 1 November 2020 to 19 May 2021 in Indonesia, followed by positivity and boundedness solutions, equilibrium point, basic reproduction number (R0), and stability of the equilibrium point. A sensitivity analysis was carried out to determine how the parameters affect the spread. Disease-free equilibrium points are asymptotically stable locally and globally if R0 < 1 and endemic equilibrium points exist, locally and globally asymptotically stable if R0> 1. In addition, this disease is endemic in Indonesia, with R0 = 1.47. Furthermore, two optimal controls, namely public education and increased medical care, are included in the model to determine the best strategy to reduce the spread of the disease. Overall, the two control measures were equally effective in suppressing the spread of the disease as the number of COVID-19 infections was significantly reduced. Thus, it was concluded that more attention should be paid to patients with COVID-19 with underlying comorbid conditions because the probability of being infected with COVID-19 is higher and mortality in this population is much higher. Finally, the combined control strategy is an optimal strategy that provides an effective guarantee to protect the public from the COVID-19 infection based on numerical simulations and cost evaluations.
  PubDate: 2023-01-06T00:00:00Z
Reduction of uncertainty using adaptive modeling under stochastic criteria
of information content
- Authors: Dmitry Anatolyevich Garanin, Nikita Sergeevich Lukashevich, Sergey Vladimirovich Efimenko, Igor Georgievich Chernorutsky, Sergey Evgenievich Barykin, Ruben Kazaryan, Vasilii Buniak, Alexander Parfenov
  Abstract: Entropy is the concepts from the science of information must be used in the situation where undefined behaviors of the parameters are unknown. The behavior of the casual parameters representing the processes under investigation is a problem that the essay explores from many angles. The provided uniformity criterion, which was developed utilizing the maximum entropy of the metric, has high efficiency and straightforward implementation in manual computation, computer software and hardware, and a variety of similarity, recognition, and classification indicators. The tools required to automate the decision-making process in real-world applications, such as the automatic classification of acoustic events or the fault-detection via vibroacoustic methods, are provided by statistical decision theory to the noise and vibration engineer. Other statistical analysis issues can also be resolved using the provided uniformity criterion.
  PubDate: 2023-01-06T00:00:00Z
Numerical treatment of singularly perturbed unsteady Burger-Huxley
equation
- Authors: Imiru Takele Daba, Gemechis File Duressa
  Abstract: This article deals with the numerical treatment of a singularly perturbed unsteady Burger-Huxley equation. The equation is linearized using the Newton-Raphson-Kantorovich approximation method. The resulting linear equation is discretized using the implicit Euler method and an exponential spline method for time and space variables, respectively. Richardson's extrapolation technique is employed to increase the accuracy in the temporal direction. The stability and uniform convergence of the proposed scheme are investigated. The scheme is shown uniformly convergent with the order of convergence O(τ + ℓ2) and O(τ2 + ℓ2) before and after Richardson extrapolation, respectively. Several test examples are considered to validate the applicability and efficiency of the scheme. It is observed that the proposed scheme provides more accurate results than the methods available in the literature.
  PubDate: 2023-01-04T00:00:00Z