Idea paper: An envelope model of ecological disturbance

Disturbance is common in natural ecosystems, but increasingly defines them. While there are many descriptions for the dynamics of an ecosystem's response to disturbance, there are few descriptions for the dynamics of the disturbance itself. I describe a novel application of a model based on the production of amplitude envelopes in acoustics and electronic music synthesis, with varying parameters Attack, Decay, Sustain, and Release (ADSR). I show that varying the parameters of the ADSR model is sufficient to produce and vary the qualitative disturbance regimes described by previous authors, and is capable of producing dynamics not previously considered. I tested the utility of the ADSR model by applying it to a logistic growth model. I found that manipulating the attack and release parameters of the ADSR model changes the population dynamics estimated by these models. This implies that responses to disturbance are determined not only by the resilience and resistance of the ecological system, but also the dynamics of the disturbance itself. My hope is that the ADSR model will prove useful to researchers in either describing disturbances in long-term ecological data, or in producing disturbances for simulations or experiments.

Analysis and Prediction for Confirmed COVID-19 Cases in Czech Republic with Uncertain Logistic Growth Model

This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

Estimation of the critical points of an epidemic by means of a logistic growth model

Epidemiological models have become a very important tool in understanding an epidemic’s development, mainly because they help researchers find more efficient strategies in their fight against its spread. Several models have been proposed up to now: some use fractional calculus to solve differential equations while others use applications from other areas such as predatorprey models. The SIR and SEIR models, among others, mainly focus on the variable response and on epidemiological parameters such as the basic reproduction number (R0) and infection rate per unit of time, nevertheless they do not focus on the variable ‘time’. We propose the use of the variable time, as the main variable, by using a reparametrization in the logistic model since it will lead to the understanding of the epidemic as it goes along the time. Moreover, this model is important because it allows the estimation of the points of acceleration and deceleration, the point of maximum growth and the asymptotic point of the epidemic. This is only possible by getting an stable epidemic curve with an ‘S’ shape. In this work we use the variable ‘accumulated cases’ of COVID-19 of China and Italy and point out the main socioeconomic facts that occurred in each period of the estimated critical points from the logistic growth model.

Fitting the Portuguese population from 1850 to 2010 to a logistic growth model

This work explores how the Portuguese population fits a logistic growth model. The present study is divided into two main sections. The first one consists on the qualitative and quantitative study of the logistic equation. Qualitatively, I will look at various aspects of the differential equation, such as the equilibria and their stability and possible inflections of solutions. Quantitatively, I will use the separation of variables to find explicit solutions. Given the lack of accuracy in the linear fitting to the proportional growth rate against the population, in second chapter, I attempted a polynomial trendline fitting to the growth rate against the population. This led the focus to creating an adapted form of the logistic curve that fits the Portuguese population from 1850 to 2010. With a certain degree of accuracy, the adapted form of the logistic growth model fits the Portuguese population in the period mentioned.

Modeling and Simulation: A Study on Predicting the Outbreak of COVID-19 in Saudi Arabia

The novel coronavirus disease (COVID-19) has resulted in an ongoing pandemic affecting the health system and economy of more than 200 countries worldwide. Mathematical models are used to predict the biological and epidemiological tendencies of an epidemic and to develop methods for controlling it. In this work, we use a mathematical model perspective to study the role of behavior change in slowing the spread of COVID-19 in Saudi Arabia. The real-time updated data from March 2, 2020, to January 8, 2021, were collected from the Saudi Ministry of Health, aiming to provide dynamic behaviors of the epidemic in Saudi Arabia. During this period, 363,692 people were infected, resulting in 6293 deaths, with a mortality rate of 1.73%. There was a weak positive relationship between the spread of infection and mortality R 2 = 0.459 . We used the susceptible-exposed-infection-recovered (SEIR) model, a logistic growth model, with a special focus on the exposed, infected, and recovered individuals to simulate the final phase of the outbreak. The results indicate that social distancing, hygienic conditions, and travel limitations are crucial measures to prevent further spread of the epidemic.

Characterizing two outbreak waves of COVID-19 in Spain using phenomenological epidemic modelling

Since the first case reported of SARS-CoV-2 the end of December 2019 in China, the number of cases quickly climbed following an exponential growth trend, demonstrating that a global pandemic is possible. As of December 3, 2020, the total number of cases reported are around 65,527,000 contagions worldwide, and 1,524,000 deaths affecting 218 countries and territories. In this scenario, Spain is one of the countries that has suffered in a hard way, the ongoing epidemic caused by the novel coronavirus SARS-CoV-2, namely COVID-19 disease. In this paper, we present the utilization of phenomenological epidemic models to characterize the two first outbreak waves of COVID-19 in Spain. The study is driven using a two-step phenomenological epidemic approach. First, we use a simple generalized growth model to fit the main parameters at the early epidemic phase; later, we apply our previous finding over a logistic growth model to that characterize both waves completely. The results show that even in the absence of accurate data series, it is possible to characterize the curves of case incidence, and construct a short-term forecast of 60 days in the near time horizon, in relation to the expected total duration of the pandemic.