A new model of unreported COVID-19 cases outperforms three known epidemic-growth models in describing data from Cuba and Spain

Estimating the unreported cases of Covid-19 in a region/country is a complicated problem. We propose a new mathematical model that, combined with a deterministic model of the total growth of cases, describes the time evolution of the unreported cases for each reported Covid-19 case. The new model considers the growth of unreported cases in plateau periods and the decrease towards the end of an epidemic wave. We combined the new model with a Gompertz-growth model, a generalized logistic model, and a susceptible-infectious-removed (SIR) model; and fitted them via Bayesian methods to data from Cuba and Spain. The combined-model fits yielded better Bayesian-Information-Criterion values than the Gompertz, logistic, and SIR models alone. This suggests the new model can achieve improved descriptions of the evolution of a Covid-19 epidemic wave.

A generalized Gompertz growth model with applications and related birth-death processes

In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.

Mathematical Analysis of Some Reaction Networks Inducing Biological Growth/Decay Functions.

In this work, we study some characteristics of sigmoidal growth/decay functions that are solutions of dynamical systems. In addition, the studied dynamical systems have a realization in terms of reaction networks that are closely related to the Gompertzian and logistic type growth models. Apart from the growing species, the studied reaction networks involve an additional species interpreted as an environmental resource. The reaction network formulation of the proposed models hints for the intrinsic mechanism of the modeled growth process and can be used for analyzing evolutionary measured data when testing various appropriate models, especially when studying growth processes in life sciences. The proposed reaction network realization of Gompertz growth model can be interpreted from the perspective of demographic and socio-economic sciences. The reaction network approach clearly explains the intimate links between the Gompertz model and the Verhulst logistic model. There are shown reversible reactions which complete the already known non-reversible ones. It is also demonstrated that the proposed approach can be applied in oscillating processes and social-science events. The paper is richly illustrated with numerical computations and computer simulations performed by algorithms using the computer algebra system Mathematica.

A generalized Gompertz growth model with applications and related birth-death processes

In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $d_2$-distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process.

Age and growth estimates of the jumbo flying squid (Dosidicus gigas) off Peru

Mantle length (ML) and age data were analyzed to describe the growth patterns of the flying jumbo squid, Dosidicus gigas, in Peruvian waters. Six non-asymptotic growth models and four asymptotic growth models were fitted. Length-at-age data for males and females were analysed separately to assess the growth pattern. Multi-model inference and Akaike's information criterion were used to identify the best fitting model. For females, the best candidate growth model was the Schnute model with L∞ = 106.96 cm ML (CI 101.23–110.27 cm ML, P < 0.05), age at growth inflection 244.71 days (CI 232.82–284.86 days, P < 0.05), and length at growth inflection 57.26 cm ML (CI 55.42–58.51 cm ML, P < 0.05). The growth pattern in males was best described by a Gompertz growth model with L∞ = 127.58 cm ML (CI 115.27–131.80 cm ML, P < 0.05), t0 = 21.8 (CI 20.06–22.41, P < 0.05), and k = 0.007 (CI 0.006–0.007, P < 0.05). These results contrast with the growth model previously reported for D. gigas in the region, where the growth pattern was identified as non-asymptotic.

Epidemics and Yield Losses due to Corynespora cassiicola on Cotton

Target spot, caused by Corynespora cassiicola, has recently emerged as a problematic foliar disease of cotton. This pathogen causes premature defoliation during boll set and maturation that can subsequently impact yield, and on certain cotton cultivars loss can be substantial. This study sought to better understand target spot epidemics and disease-incited yield losses on cotton. In order to establish a range of disease, varying numbers of fungicide applications were made to each of two cotton cultivars in each of four site-years. Target spot intensity was rated over several dates beginning in late July or early August and continuing into September. Yield of seed plus lint (seed cotton) was recorded at harvest. When analyzed across cultivars, a second or third fungicide application increased yield compared with no treatment. Lack of significant yield response with a single fungicide application may have been due to timing of that application which preceded disease onset. The cultivar PhytoGen 499 WRF had consistently greater defoliation than any of the three Deltapine cultivars grown in each site-year. However, yields of both cultivars responded similarly to the fungicide regimes. Yield loss models based on late August defoliation were only predictive at site-years where conditions favored target spot development, i.e., abundant rain and moderate temperatures. Epidemic development fit the Gompertz growth model better than it did a logistic model. Knowledge of the underlying mathematical character of the epidemiology of target spot will prove useful for development of a predictive model for the disease.