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[EN] This paper presents a methodology to deal with the randomness associated to ecological modelling. Data variability makes it necessary to analyse the impact of random perturbations on the fitted model parameters. We conduct such analysis for the logistic growth model with a certain sigmoid functional form of the carrying capacity, which was proposed in the literature for the study of parasite growth during infection. We show how the probability distributions of the parameters are set via the maximum entropy principle. Then the random variable transformation method allows for computing the density function of the population., Spanish Ministerio de Economia y Competitividad, Grant/Award Number: PID2020-115270GB-I00; Agencia Estatal de Investigacion

Our aim in this article is to present a collocation method to solve two population models for single and interacting species. For this, logistic growth model and prey–predator model are examined. These models are solved numerically by Pell–Lucas collocation method. The method gives the approximate solutions of these models in form of truncated Pell–Lucas series. By utilizing Pell–Lucas collocation method, non-linear mathematical models are converted to a system of non-linear algebraic equations. This non-linear equation system is solved and the obtained coefficients are the coefficients of the truncated Pell–Lucas serie solution. Furthermore, the residual correction method is used to find better approximate solutions. All results are shown in tables and graphs for different $(N, M) $ values, and additionally the comparisons are made with other methods from. It is seen that the method gives effective results to the presented model problems.

Coronavirus disease 2019 (COVID-19) continues to spread worldwide since its emergence in December 2019 in Wuhan, China, and as of January 3, 2021 more than 84.4 million cases and 1.8 million deaths have been reported. To predict COVID-19 cases in Algeria, we applied two models—the logistic growth model and the polynomial regression model—using the data on COVID-19 cases reported by the Algerian Ministry of Health from February 25 to December 2, 2020. Results showed that the polynomial regression model better fitted the data of COVID-19 in Algeria compared with the logistic model. The first model estimated the number of cases on January 19, 2021 to reach 387,673. This model can help Algerian authorities in the fight against this disease.

[EN] In this paper, we deal with the logistic growth model with a time-dependent carrying capacity that was proposed in the literature for the study of the total bacterial biomass during occlusion of healthy human skin. Accounting for data and model errors, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty is quantified by approximations of the solution stochastic process via truncated series solution together with the random variable transformation method. Numerical examples illustrate the theoretical results., This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI), and Fondo Europeo de Desarrollo Regional (FEDER UE) Grant MTM2017-89664-P.

Background: The rising number of novel pathogens threatening the human population has motivated the application of mathematical modeling for forecasting the trajectory and size of epidemics. Materials and methods: We summarize the real-time forecasting results of the logistic equation during the 2015 Ebola challenge focused on predicting synthetic data derived from a detailed individual-based model of Ebola transmission dynamics and control. We also carry out a post-challenge comparison of two simple phenomenological models. In particular, we systematically compare the logistic growth model and a recently introduced generalized Richards model (GRM) that captures a range of early epidemic growth profiles ranging from sub-exponential to exponential growth. Specifically, we assess the performance of each model for estimating the reproduction number, generate short-term forecasts of the epidemic trajectory, and predict the final epidemic size. Results: During the challenge the logistic equation consistently underestimated the final epidemic size, peak timing and the number of cases at peak timing with an average mean absolute percentage error (MAPE) of 0.49, 0.36 and 0.40, respectively. Post-challenge, the GRM which has the flexibility to reproduce a range of epidemic growth profiles ranging from early sub-exponential to exponential growth dynamics outperformed the logistic growth model in ascertaining the final epidemic size as more incidence data was made available, while the logistic model underestimated the final epidemic even with an increasing amount of data of the evolving epidemic. Incidence forecasts provided by the generalized Richards model performed better across all scenarios and time points than the logistic growth model with mean RMS decreasing from 78.00 (logistic) to 60.80 (GRM). Both models provided reasonable predictions of the effective reproduction number, but the GRM slightly outperformed the logistic growth model with a MAPE of 0.08 compared to 0.10, averaged across all scenarios and time points. Conclusions: Our findings further support the consideration of transmission models that incorporate flexible early epidemic growth profiles in the forecasting toolkit. Such models are particularly useful for quickly evaluating a developing infectious disease outbreak using only case incidence time series of the early phase of an infectious disease outbreak. Keywords: Logistic growth model, Richards model, Generalized Richards model, Ebola challenge

L'etude explore la recolte optimale des ressources renouvelables comme la peche. La dynamique de la biomasse des poissons est decrite par un modele de croissance non lineaire qui maximise le revenu net total tout en tenant compte de l'utilisation effective et durable de la ressource. En outre, la dynamique de la stabilite du modele est evaluee grâce une analyse de bifurcation. Le principe maximal de Pontryagin est utilise pour deriver le systeme d'optimalite et caracteriser le controle optimal. Une methode iterative numerique employant le schema Runge-Kutta de quatrieme ordre facilite la solution du systeme d'optimalite. Les resultats de simulation obtenus sont ensuite discutes. Ils montrent que la somme de la recolte maximale admissible et du niveau de biomasse finale ne doit pas depasser le rendement maximal durable (MSY).

[EN] In this paper, we deal with the non-autonomous logistic growth model with time-dependent intrinsic growth rate and carrying capacity. Accounting for errors in recorded data, randomness is incorporated into the equation by assuming that the input parameters are random variables. The uncertainty of the model output is quantified by approximations of the first probability density function via the random variable transformation method. A numerical example illustrates the results., This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) Grant MTM2017-89664-P

In this paper, we study and investigate the spread of the coronavirus disease 2019 (COVID-19) in Iraq and Egypt by using compartmental, logistic regression, and Gaussian models. We developed a generalized SEIR model for the spread of COVID-19, taking into account mildly and symptomatically infected individuals. The logistic and Gaussian models were utilized to forecast and predict the numbers of confirmed cases in both countries. We estimated the parameters that best fit the incidence data. The results provide discouraging forecasts for Iraq from 22 February to 8 October 2020 and for Egypt from 15 February to 8 October 2020. To provide a forecast of the spread of COVID-19 in Iraq, we present various simulation scenarios for the expected peak and its timing using Gaussian and logistic regression models, where the predicted cases showed a reasonable agreement with the officially reported cases. We apply our compartmental model with a time-periodic transmission rate to predict the possible start of the second wave of the COVID-19 epidemic in Egypt and the possible control measures. Our sensitivity analyses of the basic reproduction number allow us to conclude that the most effective way to prevent COVID-19 cases is by decreasing the transmission rate. The findings of this study could therefore assist Iraqi and Egyptian officials to intervene with the appropriate safety measures to cope with the increase of COVID-19 cases.

Interpolated twitch technique (ITT) is a non-invasive method for assessing the completeness of muscle activation in clinical settings. Voluntary activation level (VA), measured by ITT and estimated by a conventional linear model, was reported to have a non-linear relationship with true voluntary contraction force at higher activation levels. The relationship needs to be further clarified for the correct use by clinicians and researchers. This study was to established a modified voluntary activation (modified VA) and define a valid range by fitting a non-linear logistic growth model. Eight healthy male adults participated in this study. Each subject performed three sets of voluntary isometric ankle plantar flexions at 20, 40, 60, 80 and 100% maximal voluntary contraction (MVC) with real-time feedback on a computer screen. A supramaximal electrical stimulation was applied on tibia nerve at rest and during contractions. The estimated VA was calculated for each contraction. The relationship between the estimated VA and the actual voluntary contraction force was fitted by a logistic growth model. The result showed that according to the upper and lower limit points of the logistic curve, the valid range was between the 95.16% and 10.55% MVC. The modified VA estimated by this logistic growth model demonstrated less error than the conventional model. This study provided a transfer function for the voluntary activation level and defined the valid range which would provide useful information in clinical applications.

Background\ud \ud Ever since the Coronavirus disease (COVID-19) outbreak emerged in China, there has been several attempts to predict the epidemic across the world with varying degrees of accuracy and reliability. This paper aims to carry out a short-term projection of new cases; forecast the maximum number of active cases for India and selected high-incidence states; and evaluate the impact of three weeks lock down period using different models.\ud Methods\ud \ud We used Logistic growth curve model for short term prediction; SIR models to forecast the maximum number of active cases and peak time; and Time Interrupted Regression model to evaluate the impact of lockdown and other interventions.\ud Results\ud \ud The predicted cumulative number of cases for India was 58,912 (95% CI: 57,960, 59,853) by May 08, 2020 and the observed number of cases was 59,695. The model predicts a cumulative number of 1,02,974 (95% CI: 1,01,987, 1,03,904) cases by May 22, 2020. As per SIR model, the maximum number of active cases is projected to be 57,449 on May 18, 2020. The time interrupted regression model indicates a decrease of about 149 daily new cases after the lock down period, which is statistically not significant.\ud Conclusion\ud \ud The Logistic growth curve model predicts accurately the short-term scenario for India and high incidence states. The prediction through SIR model may be used for planning and prepare the health systems. The study also suggests that there is no evidence to conclude that there is a positive impact of lockdown in terms of reduction in new cases.