A Comparative Analysis between a SIRD Compartmental Model and the Richards Growth Model

We propose a compartmental SIRD model with time-dependent parameters that can be used to give epidemiological interpretations to the phenomenological parameters of the Richards growth model. We illustrate the use of the map between these two models by fitting the fatality curves of the COVID-19 epidemic data in Italy, Germany, Sweden, Netherlands, Cuba, and Japan, up to July 30, 2020.

Cross-Validation for the Uncertain Chapman-Richards Growth Model with Imprecise Observations

Regression analysis estimates the relationships among variables which has been widely used in growth curves, and cross-validation as a model selection method assesses the generalization ability of regression models. Classical methods assume that the observation values of variables are precise numbers while in many cases data are imprecisely collected. So this paper explores the Chapman-Richards growth model which is one of the widely used growth models with imprecise observations under the framework of uncertainty theory. The least squares estimates of unknown parameters in this model are given. Moreover, cross-validation with imprecise observations is proposed. Furthermore, estimates of the expected value and variance of the uncertain error using residuals are given. In addition, ways to predict the value of response variable with new observed values of predictor variables are discussed. Finally, a numerical example illustrates our approach.

A comparative analysis between a SIRD compartmental model and the Richards growth model

We propose a compartmental SIRD model with time-dependent parameters that can be used to give epidemiological interpretations to the phenomenological parameters of the Richards growth model. We illustrate the use of the map between these two models by fitting the fatality curves of the COVID-19 epidemic data in Italy, Germany, Sweden, Netherlands, Cuba, and Japan.

Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies

The main objective of the present article is twofold: first, to model the fatality curves of the COVID-19 disease, as represented by the cumulative number of deaths as a function of time; and second, to use the corresponding mathematical model to study the effectiveness of possible intervention strategies. We applied the Richards growth model (RGM) to the COVID-19 fatality curves from several countries, where we used the data from the Johns Hopkins University database up to May 8, 2020. Countries selected for analysis with the RGM were China, France, Germany, Iran, Italy, South Korea, and Spain. The RGM was shown to describe very well the fatality curves of China, which is in a late stage of the COVID-19 outbreak, as well as of the other above countries, which supposedly are in the middle or towards the end of the outbreak at the time of this writing. We also analysed the case of Brazil, which is in an initial sub-exponential growth regime, and so we used the generalised growth model which is more appropriate for such cases. An analytic formula for the efficiency of intervention strategies within the context of the RGM is derived. Our findings show that there is only a narrow window of opportunity, after the onset of the epidemic, during which effective countermeasures can be taken. We applied our intervention model to the COVID-19 fatality curve of Italy of the outbreak to illustrate the effect of several possible interventions.

Richards Growth Model Driven by Multiplicative and Additive Colored Noises: Steady-State Analysis

We consider a Richards growth model (modified logistic model) driven by correlated multiplicative and additive colored noises, and investigate the effects of noises on the eventual distribution of population size with the help of steady-state analysis. An approximative Fokker–Planck equation is first derived for the stochastic model. By performing detailed theoretical analysis and numerical simulation for the steady-state solution of the Fokker–Planck equation, i.e., stationary probability distribution (SPD) of the stochastic model, we find that the correlated noises have complex effects on the statistical property of the stochastic model. Specifically, the phenomenological bifurcation may be caused by the noises. The position of extrema of the SPD depends on the model parameter and the characters of noises in different ways.

COVID-19 Pandemic in Pakistan: Stages and Recommendations

We present a real-time forecast of COVID-19 in Pakistan that is important for decision-making to control the spread of the pandemic in the country. The study helps to develop an accurate plan to eradicate the COVID-19 by taking calculated steps at the appropriate time, that are crucial in the absence of a tested medicine. We use four phenomenological mathematical models, namely Discrete Exponential Growth model, the Discrete Generalized Growth model, the Discrete Generalized Logistic Growth, and Discrete Generalize Richards Growth model. Our analysis explains the important characteristics quantitatively. The study leads to understand COVID-19 pandemic in Pakistan in three evolutionary stages, and provides understanding to control its spread in the short time domain and in the long term domain. For the reason the study is helpful in devising the measures to handle the emerging threat of similar outbreaks in other countries.

Using different epidemiological models to modeling the epidemic dynamics in Brazil

In this paper we provide forecasts of the cumulative number of confirmed reported cases in Brazil, specifically in Pernambuco and Ceara, by using the generalized logistic growth model, the Richards growth model and Susceptible, Un-quanrantined infected, Quarantined infected, Confirmed infected (SUQC) phenomenological model. We rely on the Nash-Sutcliffe efficiency (NSE), root-mean-square error (RMSE) and mean absolute relative error (MARE) to quantify the quality of the models fits during the calibrationAll of these analyzes have been valid until the present date, April 14, 2020. The different models provide insights of our scenario predictions.

Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies

ABSTRACTThe main objective of the present paper is twofold: first, to model the fatality curves of the COVID-19 disease, as represented by the cumulative number of deaths as a function of time; and second, to use the corresponding mathematical model to study the effectiveness of possible intervention strategies. We applied the Richards growth model (RGM) to the COVID-19 fatality curves from several countries, where we used the data from the Johns Hopkins University database up to April 1, 2020. Countries selected for analysis were China, Italy, Spain, Iran, and Brazil. The RGM was shown to describe very well the fatality curves of China, which is in a late stage of the COVID-19 outbreak, as well as of Italy, Spain, and Iran, which supposedly are in the middle of the outbreak at the time of this writing. As for Brazil, which is still in the so-called exponential growth regime, we used the generalized growth model which is more appropriate for such cases. An analytic formula for the efficiency of intervention strategies within the context of the RGM is derived. Our findings show that there is only a narrow window of opportunity, after the onset of the epidemic, during which effective countermeasures can be taken. We applied our intervention model to the COVID-19 fatality curve of Italy to illustrate the effect of several possible interventions.