The COVID-19 global pandemic has rapidly expanded, with the UK being one of the countries with the highest number of cases and deaths in proportion to its population. Major clinical and human ...behavioural measures have been taken by the UK government to control the spread of the pandemic and to support the health system. It remains unclear how exactly human mobility restrictions have affected the virus spread in the UK. This research uses driving, walking and transit real-time data to investigate the impact of government control measures on human mobility reduction, as well as the connection between trends in human-mobility and severe COVID-19 outcomes. Human mobility was observed to gradually decrease as the government was announcing more measures and it stabilized at a scale of around 80% after a lockdown was imposed. The study shows that human-mobility reduction had a significant impact on reducing COVID-19-related deaths, thus providing crucial evidence in support of such government measures.
•Initial measures aimed at human-mobility reduction had a direct impact on the number of COVID-19 related deaths in the UK•Social-distancing measures may need to continue to reduce the risk of a resurgence in COVID-19 transmission in the UK•UK’s human mobility gradually decreased as measures were announced and stabilized at around 80% after lockdown was imposed•A shift in transport mode from public transport to driving was observed
•A Stochastic SIRS epidemic model with logistic growth and nonlinear incidence is probed.•A critical parameter R0s for the ergodicity is presented.•A unique stationary distribution exists under ...certain criteria.•The existence of a unique stationary distribution implies stochastic weak stability.•Sufficient conditions for the extinction of the disease are obtained.
A stochastic SIRS model with logistic growth and nonlinear incidence rate is probed in this paper. We exemplify that the proposed stochastic SIRS model reveals a global and positive solution. By applying suitable Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic SIRS model are derived. Furthermore, we acquire the sufficient conditions for extinction of the infectious disease.
Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, ...in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for general discrete time domains with the continuous domain. Our definition of ν-periodicity preserves crucial translation invariant properties of integrals over ν-periodic functions and, for ν(t)=t+ω, ν-periodicity is equivalent to the classical periodicity condition with period ω. We use the classification of ν-periodic functions to discuss the existence and uniqueness of ν-periodic solutions to linear homogeneous and nonhomogeneous differential equations. If ν(t)=t+ω, our results coincide with the results known for periodic differential equations. By using our concept of ν-periodicity, we gain new insights into the classes of solutions to linear nonautonomous differential equations. We also investigate the existence, uniqueness, and global stability of ν-periodic solutions to the nonlinear logistic model and apply it to generalize the Cushing–Henson conjectures, originally formulated for the discrete Beverton–Holt model.
•Generalization of periodicity by introducing ν-periodic functions.•Exploring the relations between continuous and discrete models.•Providing theorems regarding the existence and uniqueness of ν-periodic solutions for linear differential equations.•Applications of ν-periodicity to the nonlinear logistic growth model, a popular model in population ecology.•Extension of the Cushing–Henson conjectures, originally formulated for the discrete Beverton–Holt model.
Understanding and modeling behavioral changes during epidemic outbreaks is crucial for devising effective public health interventions. In this paper, we introduce an enhanced behavioral epidemic ...model that integrates novel elements to better capture real-world phenomena. Our model incorporates logistic growth as a recruitment rate, reflecting the population’s intrinsic growth constraints. Additionally, we consider two incidence rates to account for varying transmission dynamics. To extend the model’s applicability, we introduce perturbations through second-order jump–diffusion processes, allowing for abrupt changes in population dynamics. We define a threshold parameter based on the properties of an auxiliary system, which distinguishes between the existence of a unique stationary distribution and stochastic extinction. Through numerical simulations, we validate our theoretical findings and demonstrate the impact of nonlinear noise on the model dynamical behavior.
•We introduce a behavioral epidemic model with logistic growth, dual incidence rates, and second-order jumps.•We provide insights into optimal conditions for stationarity and extinction in the system.•We Illustrate the impact of second-order jumps on the dynamical bifurcation of perturbed systems through numerical examples.
Over the past decade, global sales of electric vehicles (EVs) have experienced significant growth. However, predictions of future sales developments, which are needed for the planning of EV ...production as well as supporting policies and a sufficient energy supply, are still sparse. In this study, a long-term forecast of the EV inventory in 26 countries across five continents is provided by means of a logistic growth model. Using actual sales data from 2010 to 2018, predictions were made for these countries until 2035. Findings indicate that, overall, 30% of the worldwide passenger vehicle fleet will be EVs in 2032. However, results also display vast differences between countries, which can particularly be attributed to divergences in governmental support. EV growth predictions were additionally analyzed in terms of sustainability impacts. The analysis showed that reductions in CO2 emissions can be achieved with the predicted EV growth, given that countries invest heavily in renewable energy sources. Given the current energy mixes though, worldwide CO2 emissions will continue to rise until 2035 despite a nearly 50% share of EVs. The paper further discusses the amount of energy that will be required to meet the growing demand and highlights that the production of EV batteries will be the key bottleneck in the development of EVs. Finally, important implications for policymakers, marketers and future research are derived.
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•In 2032, 30% of all passenger cars worldwide are predicted to be EVs.•Despite an almost 50% share of EVs in 2035, CO2 emissions will continue to rise.•EV growth reduces CO2 emissions if countries adapt low emission electricity mixes.
This paper is concerned with the following chemotaxis-growth system ut=Δu−∇⋅u∇v+μ(u−uα),x∈Ω,t>0,vt=Δv−v+w,x∈Ω,t>0,wt=Δw−w+u,x∈Ω,t>0,in a smooth bounded domain Ω⊂Rn(n⩾2) with nonnegative initial data ...and null Neumann boundary condition, where μ>0,α>1. It is stated that if α>n4+12, the solution is globally bounded. Moreover, if μ>0 is sufficiently large, the solution (u,v,w) emanating from nonnegative initial data u0,v0,w0 with u0⁄≡0 is globally bounded and satisfies ‖u⋅,t−1‖L∞Ω+‖v⋅,t−1‖L∞Ω+‖w⋅,t−1‖L∞Ω→0as t→∞.
In this paper, a stochastic epidemic model with logistic growth and saturated treatment is formulated to probe the effect of white noise on population. We show that the proposed autonomous stochastic ...model possess a unique and non-negative solution. We obtain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic autonomous epidemic model with probability one. That is, if ℛ0˜<1, under some parametric conditions then the infection goes to extinction with probability one and if ℛ0˜>1, under some parametric conditions then the infection persist with probability one. By using Has’minskii’s theory of periodic solutions, we show that the stochastic non-autonomous epidemic model has at least one nontrivial positive θ-periodic solution. Finally, the theoretical results are illustrated by numerical simulations which obtains some additional interesting phenomena.
•A stochastic epidemic model with logistic growth and saturated treatment is formulated.•The sufficient conditions for the extinction and persistence are derived.•The existence of periodic solutions of the stochastic non-autonomous system is obtained.•Irregularity of stochastic variation and range of fluctuation depends on the strength of white noise.•Numerical investigations conforms the dynamics of stochastic model.
•This study applied a logistic growth model with parameters estimated by a non-linear least squares (NLS) method to daily new COVID-19 cases.•The model fitted time-series data exceedingly well for ...the whole of China, eleven selected Chinese provinces and municipalities, South Korea and Iran.•This study provided key estimates and a 95% confidence interval for parameters K, r, and P0.•This study found that the growth rates of outbreaks differed between provinces in China and between South Korea and Iran.•As of March 13, 2020, this study's model suggested that countries such as the U.S.A., France, Italy, and Spain were still in the early stages of outbreaks.
As the coronavirus disease 2019 (COVID-19) pandemic continues to proliferate globally, this paper shares the findings of modelling the outbreak in China at both provincial and national levels. This paper examines the applicability of the logistic growth model, with implications for the study of the COVID-19 pandemic and other infectious diseases.
An NLS (Non-Linear Least Squares) method was employed to estimate the parameters of a differentiated logistic growth function using new daily COVID-19 cases in multiple regions in China and in other selected countries. The estimation was based upon training data from January 20, 2020 to March 13, 2020. A restriction test was subsequently implemented to examine whether a designated parameter was identical among regions or countries, and the diagnosis of residuals was also conducted. The model's goodness of fit was checked using testing data from March 14, 2020 to April 18, 2020.
The model presented in this paper fitted time-series data exceedingly well for the whole of China, its eleven selected provinces and municipalities, and two other countries - South Korea and Iran - and provided estimates of key parameters. This study rejected the null hypothesis that the growth rates of outbreaks were the same among ten selected non-Hubei provinces in China, as well as between South Korea and Iran. The study found that the model did not provide reliable estimates for countries that were in the early stages of outbreaks. Furthermore, this study concured that the R2 values might vary and mislead when compared between different portions of the same non-linear curve. In addition, the study identified the existence of heteroskedasticity and positive serial correlation within residuals in some provinces and countries.
The findings suggest that there is potential for this model to contribute to better public health policy in combatting COVID-19. The model does so by providing a simple logistic framework for retrospectively analyzing outbreaks in regions that have already experienced a maximal proliferation in cases. Based upon statistical findings, this study also outlines certain challenges in modelling and their implications for the results.
In the present article two flocculation models, given in 5 (LG model) and 36 (S model) are compared. Both models give the time evolution dL/dt where L is the size of a particle undergoing ...flocculation, and t is the time. The LG model is based on logistic growth theory, whereas the S model is based on the theory originally derived by Smoluchowski. Both models have the advantage of easy implementation in, for instance, large-scale sediment transport numerical models. However, it is found that they do not obey the same kinetics. A series of laboratory experiments is presented where the flocculation of a mineral clay by polyelectrolyte is studied as a function of clay concentration and shear rate. From modelling these experiments, it is found that the LG model reproduces the time dependence of the floc sizes found experimentally, whereas the S model does not. It is shown that the LG model can be used to model the data over the whole range of clay concentration and shear investigated. Based on the study presented in this article, it was found that the average floc growth in time for the clay type and conditions applied in the experiments could be modelled by: dL/dt=40×10−4G0.75×exp(−2×10−4G0.75t)/1+20exp(−2×10−4G0.75t)L.
•Logistic growth theory is compared with Smoluchowski-based theory.•The models do not have the same kinetics.•Only logistic growth theory agrees with experiments.•Logistic growth theory models data for all clay concentrations.•Logistic growth theory models data for all shears investigated.
A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any ...given time depend not only on their values at that time, but also on their values at previous times. For the mathematical description of the memory effects, we use the theory of derivatives of non-integer order. Crises are considered as sharp splashes (bursts) of the price, which are mathematically described by the delta-functions. Using the equivalence of fractional differential equations and the Volterra integral equations, we obtain discrete maps with memory that are exact discrete analogs of fractional differential equations of economic processes. We derive logistic map with memory, its generalizations, and “economic” discrete maps with memory from the fractional differential equations, which describe the economic natural growth with competition, power-law memory and crises.
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