Predicting the course of Covid-19 and other epidemic and endemic disease

The Gompertz Function is an accurate model for epidemics from Cholera in 1853 to Spanish Flu in 1918 and Ebola in 2014. It also describes the acute phase of annual outbreaks of endemic influenza and in all of these instances it has significant predictive power. For Covid-19, we show that the Gompertz Function provides accurate forecasts not just for cases and deaths but, independently, for hospitalisations, intensive care admissions and other medical requirements. In particular Gompertz Function projections of healthcare requirements have been reliable enough to allow planning for: hospital admissions,intensive care admissions,ventilator usage, peak loads and duration. Analysis of data from the Spanish Flu pandemic and the endemic influenza cycle reveals alternating periods of Gompertz Function growth and linear growth in cumulative cases or deaths. Linear growth means the Reproduction Number is equal to 1 which in turn indicates endemicity. The same pattern has been observed with Covid-19. All the initial outbreaks ended in linear growth. Each new outbreak has been preceded by a period of linear growth and has ended with a transition from Gompertz Function growth to linear growth. This suggests that each of these outbreak cycles ended with a transition to endemicity for the current dominant strain and that the normal seasonal respiratory virus periods will continue to see new outbreaks. It remains to be seen if widespread vaccination will disrupt this cyclicality. Because both Gompertz Function Growth and linear growth are accurately predictable, the forecasting problem is reduced to identifying the transition between these modes and to improving the performance in the early Gompertz Function growth phase where its predictive power is lowest. The dynamics of the Gompertz Function are determined by the Gumbel probability distribution. This is an exceptional distribution with respect to the geometry determined by the affine group on the line which is the key to the Gumbel distribution's role as an Extreme Value Theory attractor. We show that this, together with the empirically observed asymmetry in epidemic data, makes the Gompertz Function growth essentially inevitable in epidemic models which agree with observations.

Genetic Effect and Growth Curve Parameter Estimation under Heat Stress in Slow-Growing Thai Native Chickens

Heat stress is becoming a major problem because it limits growth in poultry production, especially in tropical areas. The development of genetic lines of Thai native chickens (TNC) which can tolerate the tropical climate with the least compromise on growth performance is therefore necessary. This research aims to analyze the appropriate growth curve function and to estimate the effect of heat stress on the genetic absolute growth rate (AGR) in TNC and Thai synthetic chickens (TSC). The data comprised 35,355 records for body weight from hatching to slaughtering weight of 7241 TNC and 10,220 records of 2022 TSC. The best-fitting growth curve was investigated from three nonlinear regression models (von Bertalanffy, Gompertz, and logistic) and used to analyze the individual AGR. In addition, a repeatability test-day model on the temperature-humidity index (THI) function was used to estimate the genetic parameters for heat stress. The Gompertz function produced the lowest mean squared error (MSE) and Akaike information criterion (AIC) and highest the pseudo-coefficient of determination (Pseudo-R2) in both chicken breeds. The growth rates in TSC were higher than TNC; the growth rates of males were greater than females, but the age at inflection point in females was lower than in males in both chicken breeds. The THI threshold started at 76. The heritability of the AGR was 0.23 and 0.18 in TNC and TSC, respectively. The additive variance and permanent environmental variance of the heat stress effect increased sharply after the THI of 76. The growth rate decreased more severely in TSC than TNC. In conclusion, the Gompertz function can be applied with the THI to evaluate genetic performance for heat tolerance and increase growth performance in slow-growing chicken.

Modeling the Growth of Four Commercial Broiler Genotypes Reared in the Tropics

Genetic improvement in commercial broilers worldwide is heavily focused on selection for higher final body weight at a given age. Although commercial broilers are mostly sold by their final body weight, it is important to pay attention to how this weight is attained and at what cost. The cost of feeding broilers, which constitutes about 70% of the total cost of broiler production, varies considerably at different stages of the bird. It is, therefore, important to pay attention to the growth curve of broilers and the parameters of the growth curve to maximise profitability of commercial broiler production. The objective of this study was to model the variations of the growth curves of 4 commercial broiler genotypes reared in Ghana using the Gompertz and polynomial growth functions. Data on body weights at 1, 7, 14, 21, 28, 35 and 42 days for 4 unsexed commercial broiler genotypes were used to model both the Gompertz and polynomial growth functions. The 4 genotypes ranked differently for Gompertz predicted early (1 - 28 days), late growth (28 – 42 days) and body weight at 42 days. Gompertz function predicted growth better for broiler chicken than the polynomial as the parameters of the Gompertz function are biologically meaningful and heritable. Selection of broiler genotypes for production based on their growth curve (slower early growth and faster late growth) could minimize cost of production and thereby increase the profitability of commercial broiler production in the tropics.

Fuzzy rank-based fusion of CNN models using Gompertz function for screening COVID-19 CT-scans

COVID-19 has crippled the world’s healthcare systems, setting back the economy and taking the lives of several people. Although potential vaccines are being tested and supplied around the world, it will take a long time to reach every human being, more so with new variants of the virus emerging, enforcing a lockdown-like situation on parts of the world. Thus, there is a dire need for early and accurate detection of COVID-19 to prevent the spread of the disease, even more. The current gold-standard RT-PCR test is only 71% sensitive and is a laborious test to perform, leading to the incapability of conducting the population-wide screening. To this end, in this paper, we propose an automated COVID-19 detection system that uses CT-scan images of the lungs for classifying the same into COVID and Non-COVID cases. The proposed method applies an ensemble strategy that generates fuzzy ranks of the base classification models using the Gompertz function and fuses the decision scores of the base models adaptively to make the final predictions on the test cases. Three transfer learning-based convolutional neural network models are used, namely VGG-11, Wide ResNet-50-2, and Inception v3, to generate the decision scores to be fused by the proposed ensemble model. The framework has been evaluated on two publicly available chest CT scan datasets achieving state-of-the-art performance, justifying the reliability of the model. The relevant source codes related to the present work is available in: GitHub.

Modelling of a relative income tax bracket-based progression with the effect of a slower tax burden growth

This study aims to model the distribution of the tax burden in schedular progressive taxation and to describe the key characteristics of such models, in particular their differences from the models based on continuously increasing smooth functions of the relationship between the tax burden and the taxpayer's income. Our hypothesis is that the use of the Gompertz function to model the main indicators of tax burden distribution of the schedular progressive income tax will help us approximate and formalize the distribution of the tax burden in a relative income tax bracket-based progression. Our research relies on the hypothetico-deductive model, more specifically, on mathematical hypothesis testing. The methodological framework comprises models of progressive taxation and mathematical methods, including data approximation based on the use of the Gompertz function, analysis of the antiderivative and convexity of functions and their properties. The resulting model can be used to describe the dynamic characteristics of the relationship between the tax burden and certain parameters of schedular taxation. This model can help identify the level of income beyond which the progression of the tax burden becomes formal and does not generate commensurately high revenue growth. The existence of such income level results in what can be considered the key drawback of the relative progression in question – the impossibility to provide a significant difference (step) of the tax burden progression in the whole interval of the taxpayer's income. What makes this research practically significant is that the proposed methodology allows us to take into account the actual tax burden in modelling the parameters of the relative progression.

Predictive modeling to estimate the demand for intensive care hospital beds nationwide in the context of the COVID-19 pandemic

Introduction SARS CoV-2 pandemic is pressing hard on the responsiveness of health systems worldwide, notably concerning the massive surge in demand for intensive care hospital beds. Aim This study proposes a methodology to estimate the saturation moment of hospital intensive care beds (critical care beds) and determine the number of units required to compensate for this saturation. Methods A total of 22,016 patients with diagnostic confirmation for COVID-19 caused by SARS-CoV-2 were analyzed between March 4 and May 5, 2020, nationwide. Based on information from the Chilean Ministry of Health and ministerial announcements in the media, the overall availability of critical care beds was estimated at 1,900 to 2,000. The Gompertz function was used to estimate the expected number of COVID-19 patients and to assess their exposure to the available supply of intensive care beds in various possible scenarios, taking into account the supply of total critical care beds, the average occupational index, and the demand for COVID-19 patients who would require an intensive care bed. Results A 100% occupancy of critical care beds could be reached between May 11 and May 27. This condition could be extended for around 48 days, depending on how the expected over-demand is managed. Conclusion A simple, easily interpretable, and applicable to all levels (nationwide, regionwide, municipalities, and hospitals) model is offered as a contribution to managing the expected demand for the coming weeks and helping reduce the adverse effects of the COVID-19 pandemic.

Universality in COVID-19 spread in view of the Gompertz function

We demonstrate that universal scaling behavior is observed in the current coronavirus (SARS-CoV-2) spread, the COVID-19 pandemic, in various countries. We analyze the numbers of infected people who tested positive (cases) in 11 selected countries (Japan, USA, Russia, Brazil, China, Italy, Indonesia, Spain, South Korea, UK, and Sweden). By using a double exponential function called the Gompertz function, $f_\mathrm{G}(x)=\exp(-e^{-x})$, the number of cases is well described as $N(t)=N_0 f_\mathrm{G}(\gamma(t-t_0))$, where $N_0$, $\gamma$, and $t_0$ are the final number of cases, the damping rate of the infection probability, and the peak time of the daily number of new cases, $dN(t)/dt$, respectively. The scaled data of cases in most of the analyzed countries are found to collapse onto a common scaling function $f_\mathrm{G}(x)$ with $x=\gamma(t-t_0)$ being the scaling variable in the range of $f_\mathrm{G}(x)\pm 0.05$. The recently proposed indicator, the so-called $K$ value, the increasing rate of cases in one week, is also found to show universal behavior. The mechanism for the Gompertz function to appear is discussed from the time dependence of the produced pion numbers in nucleus–nucleus collisions, which is also found to be described by the Gompertz function.

Mathematical evaluation of responses to surgical stimuli under general anesthesia

Surgical invasion activates nociception, while anesthesia suppresses it. Under general anesthesia, stimulation, which is the balance between nociception and anti-nociception, induces responses, including activation of the autonomic nervous system. To evaluate the associations between stimulation (S) and the resultant responses (R), we examined R values, which were calculated using mathematical models of Stevens’ power law, Gompertz function and logistic function. The previously developed Nociceptive Response (NR) formula was applied as a modified logistic model. S values were calculated using a linear function in the NR formula. In a retrospective study, we developed an exponential model of Stevens’ power law and a sigmoidal model of Gompertz function using differential equations, by adjusting R values to correspond to NR values, in consecutive patients undergoing surgery under general anesthesia (n = 4,395). In a subsequent prospective study, we validated the superiority of R values of Gompertz function and the NR formula in an exponential model in adult patients undergoing tympanoplasty (n = 141) and laparoscopic cholecystectomy (n = 86). In conclusion, both modified logistic function and Gompertz function are likely appropriate mathematical models for representing responses to stimulation resulting from the balance between nociception/anti-nociception during surgical procedures under general anesthesia.