Kemwoue, Florent FeudjioDeli, VandiEdima, Helene CaroleMendimi, Joseph Marie...
18页
查看更多>>摘要：In the present work, we perform a study investigating a generic model of tumor growth with a delay distribution in the proliferation of tumor-stimulating effectors using combinations of analytical and numerical methods. We examine two borderline cases of the distribution: the first limit case is the Dirac distribution, leading to a model with constant delay and the second limit case is the exponential distribution leading to a model with an additional equation. The main objective is to assess the effect of delays in the response of the immune system on the dynamic stability of interaction between tumor, immune and host cells. Analytical and numerical investigations reveal that in the absence of delay, the stationary states of the two models can be stable or unstable for all the parameters used. In the case of constant delay, the analysis focuses on the stability switch with increasing delay. We show using the generalized Sturm criterion that the space of the parameters of concern is divided into four regions determined by a sequence of discrimination and the Routh-Hurwitz conditions: the system can undergo no stability switch and remain unstable regardless of the delay or undergo exactly a stability switch causing the coexisting equilibrium to pass from stable to unstable when the parameters are chosen in a welldefined region. This shows that the delay plays the role of destabilizer and not of stabilizer. We also show in this case that the destabilization of the system by the delay induces a chaotic behavior in the a priori non chaotic system in the absence of delay. In the case of exponential distribution, we show that the delay induces certain phenomena such as the Hopf bifurcation, the doubling of periods, the intermittence by saddle-node bifurcation and chaos. We show the importance of characterizing the delay-induced chaos and dynamic states of the system by examining the maximum tumor size for each dynamic state. In both cases of study, it is observed that small delays guarantee stability at the stable equilibrium level, but delays greater than a critical value can produce periodic solutions by Hopf bifurcation and larger delays can even lead to chaotic attractors. The implications of these results are discussed. We examined the other scenarios by showing the influence of the probability density parameters on the behavior of the solutions as well as the dynamics of the model. It is shown that, the region of stability for distributed delays is relatively larger than that of the presence of any discrete delay.(c) 2022 Elsevier Ltd. All rights reserved.
Mendoza, Daniel E.Ochoa-Sanchez, AnaSamaniego, Esteban P.
15页
查看更多>>摘要：Epidemics are complex dynamical processes that are difficult tomodel. As revealed by the SARS-CoV-2 pandemic, the social behavior and policy decisions contribute to the rapidly changing behavior of the virus' spread during outbreaks and recessions. In practice, reliable forecasting estimations are needed, especially during early contagion stageswhen knowledge and data are insipient. When stochastic models are used to address the problem, it is necessary to consider new modeling strategies. Such strategies should aim to predict the different contagious phases and fast changes between recessions and outbreaks. At the same time, it is desirable to take advantage of existing modeling frameworks, knowledge and tools. In that line, we take Autoregressivemodels with exogenous variables (ARX) and Vector autoregressive (VAR) techniques as a basis. We then consider analogies with epidemic's differential equations to define the structure of the models. To predict recessions and outbreaks, the possibility of updating the model's parameters and stochastic structures is considered, providing non-stationarity properties and flexibility for accommodating the incoming data to the models. The Generalized-Random-Walk (GRW) and the State-Dependent-Parameter (SDP) techniques shape the parameters' variability. The stochastic structures are identified following the Akaike (AIC) criterion. The models use the daily rates of infected, death, and healed individuals, which are the most common and accurate data retrieved in the early stages. Additionally, different experiments aimto explore the individual and complementary role of these variables. The results show that although both the ARX-based and VAR-based techniques have good statistical accuracy for seven-day ahead predictions, some ARX models can anticipate outbreaks and recessions. Weargue that short-time predictions for complex problems could be attained through stochastic models that mimic the fundamentals of dynamic equations, updating their parameters and structures according to incoming data. (C) 2022 Elsevier Ltd.
查看更多>>摘要：Among many other factors that affect the preventive interventions to any infectious disease, not reporting timely in a hospital is also one of the catastrophic behavior of human beings in any society. Similarly, masses who do not report make it difficult for healthcare researchers to measure the actual data and develop prevention strategies, accordingly. Therefore, there is a critical need to structure a potential epidemic model with the unreported class of individuals. This novel idea is deliberated in this paper to study the profiles of the epidemic model of virulent diseases due to the individuals that report timely and those who don't report in hospitals for any reason. Mathematically, a system of seven equations is taken into consideration, which describes the susceptible individuals, exposed, people who do not report to the hospital and those who report to the hospital, and individuals who are quarantined, infected, and recovered. So, with the consideration of new compartments, the conventional SIR epidemic model expands to SEURRPQIR. The innovative design is made more realistic by utilizing proportional fractional-order differential equations with time delay. A special simplified expansion of this derivative reduces its computational cost and produces the results with fractional index, which helps to predict each fractional change. In addition, an optimal control methodology is also carried out to analyze the effectiveness of the awareness campaign in shifting the unreported individuals to the reported class, with optimal cost function for the unreported cases. Discussions are supported through the very recent deadly pandemic as an example to conclude the practical advantage of the model. The sensitivity analysis of basic reproduction numbers based on effective awareness campaigns is also the part of this study, which infers public awareness campaigns may be devised to motivate and guide such individuals to approach any healthcare center or a hospital. (c) 2021 Elsevier Ltd. All rights reserved.
查看更多>>摘要：The lack of medical treatments and vaccines upon the arrival of the SARS-CoV-2 virus has made non pharmaceutical interventions the best allies in safeguarding human lives in the face of the COVID-19 pandemic. Here we propose a self-organized epidemic model with multi-scale control policies that are relaxed or strengthened depending on the extent of the epidemic outbreak. We show that optimizing the balance between the effects of epidemic control and the associated socio-economic cost is strongly linked to the stringency of control measures. We also show that non-pharmaceutical interventions acting at different spatial scales, from creating social bubbles at the household level to constraining mobility between different cities, are strongly interrelated. We find that policy functionality changes for better or worse depending on network connectivity, meaning that some populations may allow for less restrictive measures than others if both have the same resources to respond to the evolving epidemic.(c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
查看更多>>摘要：How to identify influencers is very significance in mastering the nature of node, controlling spreading process in complex networks. In this research field, each method has its own advantages and limitations. For example, local metrics are relatively simple, global metrics can give better results, but the computational complexity is also relatively high. A semi-local approach on basis of node dimension is proposed to identify influencers. The node dimension can detect regions with different dimensional structures by scaling the local dimension on the scale. The saturation effect is discovered in the process of identifying influencers by the node dimension. When the maximum dimension radius is close to the mean shortest path length of networks, the method has better performance. Through the saturation effect, our approach can be a tradeoff between local and global metrics. In addition, we show the correlation between different measures and node dimension with different maximum dimension radii. We employ Susceptible -Infected -Recovered (SIR) model to verify the effectiveness of our designed approach. Simulation results indicate the superiority of our algorithm.(c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：Coupled Map Lattice (CML) models are particularly suitable to study spatially extended behaviours, such as wave-like patterns, spatio-temporal chaos, and synchronisation. Complete synchronisation in CMLs emerges when all maps have their state variables with equal magnitude, forming a spatially-uniform pattern that evolves in time. Here, we derive critical values for the parameters - coupling strength, maximum Lyapunov exponent, and link density - that control the synchronisation-manifolds linear stability of diffusively-coupled, identical, chaotic maps in generic regular graphs (i.e., graphs with uniform node degrees) and class-specific cyclic graphs (i.e., periodic lattices with cyclical node permutation symmetries). Our derivations are based on the Laplacian matrix eigenvalues, where we give closed-form expressions for the smallest non-zero eigenvalue and largest eigenvalue of regular graphs and show that these graphs can be classified into two sets according to a topological condition (derived from the stability analysis). We also make derivations for two classes of cyclic graph: k-cycles (i.e., regular lattices of even degree k, which can be embedded in Tk tori) and k-Mobius ladders, which we introduce here to generalise the Mobius ladder of degree k = 3. Our results highlight differences in the synchronisation manifold's stability of these graphs - even for identical node degrees - in the finite size and infinite size limit. (c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：This paper provides a complete study on properties of symmetric gH-derivative. More precisely, a necessary and sufficient condition for the symmetric gH-differentiability of interval-valued functions is presented. Further, we clarify the relationship between the symmetric gH-differentiability and gH-differentiability. Moreover, quasimean value theorem, chain rule and some operations of symmetric gH-differentiable interval-valued functions are established. As applications, we develop the Mond-Weir duality theory for a class of symmetric gHdifferentiable interval-valued optimization problems. Weak, strong and strict converse duality theorems are formulated and proved. Also, several examples are presented in order to support the corresponding theoretical results. (C) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：The purpose of this study is to present and examine a novel non-integer model of the circumscribed selfexcited spherical strange attractor, which has not been worked yet. To design the fractional-order model, we use the Caputo-Fabrizio derivative. In order to ensure the existence of the solution Picard-Lindel and fixed-point theories are provided. Moreover, the stability of the considered fractional-order model is shown using the Picard iteration and fixed point theory approach. To get the approximate solutions of the proposed fractional model an efficient numerical scheme called the fractional Euler method(FEM) is used. To see the performance of the used method, the behavior of the numerical solutions of the model is examined under various initial conditions(ICs) and fractional orders. Considerable chaotic behaviors of the solutions are obtained which prove the accuracy and reliability of FEM. (c) 2022 Elsevier Ltd. All rights reserved.
查看更多>>摘要：The pricing of European-style vulnerable option when the price process of the underlying asset follows nonaffine stochastic volatility and double exponential jump is investigated. An approximate expression for the joint characteristic function of the log-price of underlying asset and the log-value of counterparty asset is derived. An analytical approximate price of European-style vulnerable option is also obtained by means of Fourier-cosine method. Numerical experiments are given to confirm the accuracy and efficiency of the proposed result for pricing the European-style vulnerable option compared with Monte Carlo simulation. Finally, sensitivity analysis is presented to further explain the theoretical results. (c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
查看更多>>摘要：The generalized Lienard polynomial differential systems are the differential systems of the form x'= y, y'= - f(x)y - g(x), where f and g are polynomials. We characterize all the generalized Lienard polynomial differential systems having an invariant algebraic curve. We show that the first four higher coefficients of the polynomial in the variable y, defining the invariant algebraic curve, determine completely the generalized Lienard polynomial differential system. This fact does not hold for arbitrary polynomial differential systems. 2010 mathematics subject classification: Primary 34A05. Secondary 34C05, 37C10. (C) 2022 The Authors. Published by Elsevier Ltd.
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