A MATHEMATICAL MODEL OF IMMUNE RESPONSE IN CUTANEOUS LEISHMANIASIS

2007 ◽  
Vol 15 (03) ◽  
pp. 313-354 ◽  
Author(s):  
MARCOS C. DE ALMEIDA ◽  
HELMAR N. MOREIRA
Keyword(s):  
Immune Response ◽  
Growth Models ◽  
Alternative Hypothesis ◽  
Growth Curves ◽  
Parasite Growth ◽  
Logistic Growth ◽  
Natural Immunity ◽  
Existence And Stability ◽  
Clinical Correlations ◽  
Logistic Growth Model

The TH1/TH2 paradigm has been largely used in the interpretation of several diseases, particularly in leishmaniasis. As far as we know there is no mathematical description of this model related to leishmaniasis. We have extended and modified a previous published set of equations1in order to adapt it to leishmanial disease particularities. The main modifications were: (1) the analysis of logistic and exponential parasite growth curves, (2) the assumption of the TH2 arm of the immune response having a positive action on parasite growth. The set of three simultaneous differential equations describing the TH1 arm, TH2 arm and parasite growth were analyzed for conditions of existence and stability of the solutions.Stable solutions valid for the logistic and exponential parasite growth models, with its possible clinical correlations, were obtained in the following situations: (1) parasite and TH2 extinction [TH1 cure], (2) parasite extinction and TH1/TH2 co-existence [TH1/TH2 cure], (3) TH1 and parasite co-existence, TH2 extinction [stable TH1 infection], and (4) TH1, TH2 and parasite co-existence [stable TH1/TH2 infection]. TH2 and parasite co-existence associated to TH1 extinction [stable TH2 infection] was obtained only with the logistic growth model. The model also provides an alternative hypothesis for TH1 bias in resistant mice and emphazises the importance of natural immunity for the existence of chronic states.

scholarly journals The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

2018 ◽  
Author(s):  
Emanuel A. Fronhofer ◽  
Lynn Govaert ◽  
Mary I. O’Connor ◽  
Sebastian J. Schreiber ◽  
Florian Altermatt
Keyword(s):  
Population Growth ◽  
Growth Models ◽  
Population Level ◽  
Logistic Growth ◽  
Population Densities ◽  
Density Regulation ◽  
Logistic Growth Model ◽  
Regulation Functions ◽  
Consumer Resource ◽  
Population Growth Models

AbstractThe logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

scholarly journals Prediksi Akhir Pandemi COVID-19 di Indonesia dengan Simulasi Berbasis Model Pertumbuhan Parametrik

2020 ◽  
Vol 9 (2) ◽  
pp. 63-68
Author(s):  
Fransiscus Rian Pratikto
Keyword(s):  
Least Squares Method ◽  
Growth Models ◽  
Growth Curves ◽  
Nonlinear Least Squares ◽  
Gompertz Model ◽  
Population Data ◽  
Logistic Growth ◽  
Social Restriction ◽  
Nonlinear Least Squares Method

This research aims to predict the end of the COVID-19 pandemic in Indonesia based on parametric growth models. The models are chosen by considering their fitness with the data of Taiwan which is believed to have passed over the peak of the pandemic and have gone through all phases in the growth curves. The models are parameterized using the nonlinear least squares method. The deviation and confidence interval of each parameter is estimated using the k-fold cross-validation and the bootstrap techniques. Using the total cases per million population data from March 2 to June 18, 2020, it was found that two growth models fit the data, i.e. logistic and modified Gompertz, where the latter performs better. Using the information about the deviation of each model parameter, a simulation model is developed to predict the time at which the total cases curve starts to flatten, which is an indication of the end of the pandemic. It was found with 95% confidence level that based on the modified Gompertz model the pandemic will end somewhere between March 9 – September 7, 2021 with total cases per million of 206 - 555. Meanwhile, based on the logistic growth model, the end of the pandemic is between August 28 – September 23, 2020 with total cases per million of 180 - 375. This model can be extended by making comparative scenario with Taiwan based on measures that represent the quality of the pandemic mitigation such as test ratio and the intensity of social restriction.

Non-Linear fitting of Sigmoidal Growth Curves to predict a maximum limit to the total number of COVID-19 cases in the United States. (Preprint)

2020 ◽  
Author(s):  
Carlos Dutra Sr
Keyword(s):  
United States ◽  
Growth Models ◽  
Growth Curves ◽  
The United States ◽  
World Health ◽  
Logistic Growth ◽  
Linear Fitting ◽  
Nonlinear Fitting ◽  
Non Linear ◽  
Maximum Limit

UNSTRUCTURED In the present work is used non-linear fitting of the "Gompert" and "Logistic" growth models to the number of total COVID-19 cases from the United States as a country and individually by states. The methodology allowed us to estimate that the maximum limit for the total number of cases of COVID-19 patients such as those registered with the World Health Organization will be approximately one million and one hundred thousand cases to the United States. Up to 04/19/20 the models indicate that United States reached 70% of this maximum number of "total cases" and the United States will reach 95% of this limit by 05/14/2020. The application of the nonlinear fitting of growth curves to the individual data of each American state showed that only 25% of them did not reach, on 04/19/20, the percentage of 59% of the maximum limit of "total cases" and that 17 of the 50 states still will not have reached 95% of that limit on 05/14/20.

Effect of Fe2+ and Fe 3+ on the Growth of Microcystis aeruginosa, Scenedesmus quadricauda and Cyclotella sp.

2011 ◽  
Vol 183-185 ◽  
pp. 510-515
Author(s):  
Qin Wang ◽  
Zong Xue Xu ◽  
Xia Jiang ◽  
Ji Xi Gao
Keyword(s):  
Microcystis Aeruginosa ◽  
Culture Medium ◽  
Growth Curves ◽  
Scenedesmus Quadricauda ◽  
Logistic Growth ◽  
High Concentration ◽  
Nutrient Sources ◽  
Monod Equation ◽  
Maximum Biomass ◽  
Logistic Growth Model

Ferrum is one of the important nutrient sources for algae in lakes. The changes of concentration in water body have great effect on the formation of dominant algae. Microcystis aeruginosa, Scenedesmus quadricauda and Cyclotella were examined in M11 culture medium which included different Fe2+ and Fe3+ concentration. Growth curves of these three algae were fitted by logistic growth-model, respectively. The maximum biomass K, inflection t and growth rate µ of those algae were investigated. The effects of Fe2+ and Fe3+ on the growth of algae were investigated by using the Monod equation. The semi-saturation constants were calculated. The results showed that the maximum biomass of these three algae did not increase with the increasing of Fe2+ and Fe3+ concentration. Low concentration of Fe2+ (200-500 mg/L) and high concentration of Fe3+ (2000-5000 mg/L) were more suitable to the growth of three algae. The sequence of the maximum biomass was: Scenedesmus quadricauda>Microcystis aeruginosa>Cyclotella.

scholarly journals Short-term real-time prediction of total number of reported COVID-19 cases and deaths in South Africa: a data driven approach

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Tarylee Reddy ◽  
Ziv Shkedy ◽  
Charl Janse van Rensburg ◽  
Henry Mwambi ◽  
Pravesh Debba ◽  
...  
Keyword(s):  
South Africa ◽  
Growth Models ◽  
National Level ◽  
Growth Curves ◽  
Gompertz Model ◽  
Logistic Growth ◽  
Short Term ◽  
Provincial Level ◽  
Maximum Period ◽  
Data Driven Approach

Abstract Background The rising burden of the ongoing COVID-19 epidemic in South Africa has motivated the application of modeling strategies to predict the COVID-19 cases and deaths. Reliable and accurate short and long-term forecasts of COVID-19 cases and deaths, both at the national and provincial level, are a key aspect of the strategy to handle the COVID-19 epidemic in the country. Methods In this paper we apply the previously validated approach of phenomenological models, fitting several non-linear growth curves (Richards, 3 and 4 parameter logistic, Weibull and Gompertz), to produce short term forecasts of COVID-19 cases and deaths at the national level as well as the provincial level. Using publicly available daily reported cumulative case and death data up until 22 June 2020, we report 5, 10, 15, 20, 25 and 30-day ahead forecasts of cumulative cases and deaths. All predictions are compared to the actual observed values in the forecasting period. Results We observed that all models for cases provided accurate and similar short-term forecasts for a period of 5 days ahead at the national level, and that the three and four parameter logistic growth models provided more accurate forecasts than that obtained from the Richards model 10 days ahead. However, beyond 10 days all models underestimated the cumulative cases. Our forecasts across the models predict an additional 23,551–26,702 cases in 5 days and an additional 47,449–57,358 cases in 10 days. While the three parameter logistic growth model provided the most accurate forecasts of cumulative deaths within the 10 day period, the Gompertz model was able to better capture the changes in cumulative deaths beyond this period. Our forecasts across the models predict an additional 145–437 COVID-19 deaths in 5 days and an additional 243–947 deaths in 10 days. Conclusions By comparing both the predictions of deaths and cases to the observed data in the forecasting period, we found that this modeling approach provides reliable and accurate forecasts for a maximum period of 10 days ahead.

The poststagnation stage for mature tourism areas

2016 ◽  
Vol 23 (2) ◽  
pp. 387-402 ◽  
Author(s):  
Isabel P. Albaladejo ◽  
María Pilar Martínez-García
Keyword(s):  
Life Cycle ◽  
Growth Model ◽  
Logistic Model ◽  
Temporal Evolution ◽  
Growth Models ◽  
Life Cycles ◽  
Logistic Growth ◽  
Tourism Sector ◽  
Passenger Flows ◽  
Logistic Growth Model

The tourism area life cycle (TALC) model of Butler explains the temporal evolution of a tourism resort. Lundtorp and Wanhill find that the logistic growth model represents the first phases of the TALC model. However, since the logistic model assumes a fixed tourism market ceiling, it fails to explain the poststagnation stage, where rejuvenation, decline, or any other intermediate possibility may arise. Taking into account the data of passenger flows to Bornholm from 1912 to 2001 collected by Lundtorp and Wanhill, the authors find that the superposition of several logistic growth models fits better with these data. Then they propose a multilogistic growth model, where investment or innovation in the tourism sector boosts the addition of new logistic curves which superpose the old ones. The continuous birth and superposition of these new life cycles is not free; it requires the purposive effort of entrepreneurs and governments seeking new markets and the improvement of infrastructures.

scholarly journals Logistic growth models of China pinks, cultivated on seven substrates, as a function of degree days

2016 ◽  
Vol 46 (11) ◽  
pp. 1924-1931
Author(s):  
Marília Milani ◽  
Sidinei José Lopes ◽  
Rogério Antônio Bellé ◽  
Fernanda Alice Antonello Londero Backes
Keyword(s):  
Growth Model ◽  
Rice Husk ◽  
Rice Husk Ash ◽  
Growth Models ◽  
Growth Period ◽  
Leaf Number ◽  
Logistic Growth ◽  
Maximum Height ◽  
Degree Days ◽  
Logistic Growth Model

ABSTRACT: The objective of this study was to characterize the height (H) and leaf number (LN) of China pinks, grown in seven substrates, as a function of degree days, using the logistic growth model. H and LN were measured from 56 plants per substrate, for 392 plants in total. Plants that were grown on substrates formed of 50% soil with 50% rice husk ash (50% S + 50% RH) and 80% rice husk ash with 20% worm castings (80% RH + 20% W) had the longest vegetative growth period (74d), corresponding to 1317.9ºCd. The logistic growth model, adjusted for H, showed differences in the estimation of maximum expected height (α) between the substrates, with values between 10.47cm for 50% S + 50% RH and 35.75cm for Mecplant(r). When α was estimated as LN, variation was also observed between the different substrates, from approximately 30 leaves on plants growing on 50% S + 50% RH to 34 leaves on the plants growing on the substrate formed of 80% RH + 20% W. Growth of China pinks can be characterized using H or LN in the logistic growth model as a function of degree days, being the provided plants adequately fertilized. The best substrates in terms of maximum height and leaf number were 80% soil + 20% worm castings and Mecplant(r). However, users must recalibrate the model with the estimated parameters before applying it to different growing conditions.

A Logistic Growth Model for Software Reliability Estimation Considering Uncertain Factors

2021 ◽  
pp. 2150032
Author(s):  
Md. Asraful Haque ◽  
Nesar Ahmad
Keyword(s):  
Growth Model ◽  
Software Reliability ◽  
Growth Models ◽  
Reliability Estimation ◽  
Logistic Growth ◽  
Systematic Analysis ◽  
Software Reliability Growth ◽  
Logistic Growth Model ◽  
Operational Phase ◽  
Special Parameter

Software reliability growth models (SRGMs) are widely used to estimate software reliability by analyzing failure dataset throughout the testing process. A large number of SRGMs have been proposed on a regular basis by researchers since the 1970s. They are represented with a set of assumptions and a set of parameters. One major problem in SRGMs is that the uncertainties surrounding the assumptions and parameters are generally not taken into account by most of them. Therefore, sometimes, the predicted reliability on testing phase significantly varies in actual operational phase. This paper presents a logistic growth model that incorporates a special parameter to consider the effects of all possible uncertainties. A systematic analysis is carried out to identify the major uncertain factors and their impacts on the fault detection rate. The applicability of the model is shown by validating it on two different real datasets that are commonly used in various studies. The comparisons with nine established models in terms of mean square error (MSE), variance, predictive-ratio risk (PRR), [Formula: see text]and AIC have been presented.

scholarly journals Gompertz and Logistic models for morphological traits of sudangrass cultivars during sowing seasons

2019 ◽  
Vol 40 (6Supl3) ◽  
pp. 3399
Author(s):  
Rafael Vieira Pezzini ◽  
Alberto Cargnelutti Filho ◽  
Cláudia Marques de Bem ◽  
Jéssica Maronez de Souza ◽  
Gabriela Görgen Chaves ◽  
...  
Keyword(s):  
Solar Radiation ◽  
Plant Height ◽  
Growth Models ◽  
Logistic Models ◽  
Growth Curves ◽  
Stem Length ◽  
Logistic Growth ◽  
Thermal Sum ◽  
Independent Variable ◽  
Uniformity Trials

The use of mathematical models in the study plant growth allows the identification of phases important to the cultivars and comparison between cultivars of the same species. The objectives of this work were to fit the Gompertz and Logistic growth models for the traits of plant height and stem length as a function of the accumulated thermal sum and accumulated solar radiation, to compare the fittings and the behavior of the sudangrass cultivars and indicate the model that best describes the growth of the cultivars during four sowing seasons. Were conducted eight uniformity trials with sudangrass. At 15 days after emergence, were began the collect and evaluation of five plants from each trial. Were measured plant height and stem length. The models were fitted using the values obtained for the traits of the five plants in each evaluation as a function of the accumulated thermal sum and accumulated solar radiation. Were estimated the parameters, determined their interval of confidence, critical points in the growth curves and quality indicators of the fit. The intrinsic nonlinearities and the parameter effect were also quantified. The accumulated thermal sum and accumulated solar radiation are adequate for the use as an independent variable in the model fitted. Both models were adequate to describe the growth of the traits plant height and stem length of cultivars BRS Estribo and CG Farrapo. However, the Logistic model is more accurate.

scholarly journals Non-Linear Fitting of Sigmoidal Growth Curves to predict a maximum limit to the total number of COVID-19 cases in the United States

2020 ◽  
Author(s):  
Carlos Maximiliano Dutra
Keyword(s):  
United States ◽  
Growth Models ◽  
Growth Curves ◽  
The United States ◽  
World Health ◽  
Logistic Growth ◽  
Linear Fitting ◽  
Nonlinear Fitting ◽  
Non Linear ◽  
Maximum Limit

AbstractIn the present work is used non-linear fitting of the “Gompert” and “Logistic” growth models to the number of total COVID-19 cases from the United States as a country and individually by states. The methodology allowed us to estimate that the maximum limit for the total number of cases of COVID-19 patients such as those registered with the World Health Organization will be approximately one million and one hundred thousand cases to the United States. Up to 04/19/20 the models indicate that United States reached 70% of this maximum number of “total cases” and the United States will reach 95% of this limit by 05/14/2020. The application of the nonlinear fitting of growth curves to the individual data of each American state showed that only 25% of them did not reach, on 04/19/20, the percentage of 59% of the maximum limit of “total cases” and that 17 of the 50 states still will not have reached 95% of that limit on 05/14/20.

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