Time Delayed Logistic Equations

1979 ◽  
pp. 35-46
Author(s):  
James C. Frauenthal
Keyword(s):  
Logistic Equations

scholarly journals Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

2021 ◽  
Vol 11 (9) ◽  
pp. 4159
Author(s):  
Lode K. J. Vandamme ◽  
Paulo R. F. Rocha
Keyword(s):  
Mental Health ◽  
Exponential Growth ◽  
Characteristic Time ◽  
Age Groups ◽  
Recovery Phase ◽  
Limited Growth ◽  
Logistic Equations ◽  
Quantitative Understanding ◽  
Returning Travellers ◽  
Verhulst Model

Pandemic curves, such as COVID-19, often show multiple and unpredictable contamination peaks, often called second, third and fourth waves, which are separated by wide plateaus. Here, by considering the statistical inhomogeneity of age groups, we show a quantitative understanding of the different behaviour rules to flatten a pandemic COVID-19 curve and concomitant multi-peak recurrence. The simulations are based on the Verhulst model with analytical generalized logistic equations for the limited growth. From the log–lin plot, we observe an early exponential growth proportional to . The first peak is often τgrow @ 5 d. The exponential growth is followed by a recovery phase with an exponential decay proportional to . For the characteristic time holds: . Even with isolation, outbreaks due to returning travellers can result in a recurrence of multi-peaks visible on log–lin scales. The exponential growth for the first wave is faster than for the succeeding waves, with characteristic times, τ of about 10 d. Our analysis ascertains that isolation is an efficient method in preventing contamination and enables an improved strategy for scientists, governments and the general public to timely balance between medical burdens, mental health, socio-economic and educational interests.

A peaked logistic-based selection curve

2014 ◽  
Vol 71 (3) ◽  
pp. 351-355 ◽  
Author(s):  
James A. Smith ◽  
Matthew D. Taylor
Keyword(s):  
Large Range ◽  
Logistic Distribution ◽  
Fishing Gear ◽  
Normal Curve ◽  
Logistic Curve ◽  
Size Classes ◽  
Logistic Equations ◽  
Selection For

Length-based selection curves define the relative catchability of fish to specific types of fishing gear, with catchability often highest at intermediate fish lengths. Distributions such as the normal, lognormal, or gamma are often used to define “peaked” selection curves, but these have limited capabilities to describe strongly asymmetric selection relationships, such as those sometimes observed for hooks or gillnets. Another, more flexible, peaked selection curve is proposed, which is derived by combining multiple logistic distributions. While the logistic distribution is frequently used to describe monotonic selection curves, incorporating multiple logistic equations (that describe either the increasing or decreasing catchability) can define a large range of asymmetric peaked selection curves. This “peak-logistic” curve also allows nonzero asymptotic selection for the largest size classes, which may be the selection occurring in some hook-and-line fisheries. We demonstrate examples of selection in hook, haul net, and mixed hook fisheries, for which the peak-logistic curve is more appropriate than comparative lognormal and binormal selection curves. We also promote an alternative to the peak-logistic: the two-sided normal curve.

Positive Solutions for the Generalized Nonlinear Logistic Equations

2016 ◽  
Vol 59 (01) ◽  
pp. 73-86 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Type Result ◽  
Logistic Equations ◽  
Nonhomogeneous Differential Operator

AbstractWe consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiòusive type. Using variationalmethods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

scholarly journals Weed Interference Affects Dry Bean Yield and Growth

2012 ◽  
Vol 4 (3) ◽  
pp. 70-75 ◽  
Author(s):  
Hossein GHAMARI ◽  
Goudarz AHMADVAND
Keyword(s):  
Chenopodium Album ◽  
Growing Season ◽  
Amaranthus Retroflexus ◽  
Growth And Yield ◽  
Weed Competition ◽  
Weed Species ◽  
Dry Bean ◽  
Logistic Equations ◽  
Weed Interference ◽  
Minimum Number

Dry bean is one of the most important pulse crops in Iran. Field study was conducted in 2011 to evaluate effects of weed competition from a natural flora on growth and yield of dry bean (Phaseolus vulgaris L.). The treatments consisted of weed infestation and weed removal periods (10, 20, 30, 40 and 50 days) after crop emergence. Control plots kept weed-infested and weed-free throughout growing season. To assess the weed competition effect on crop characteristics, Richards, Gompertz and logistic equations were fitted to the data. The most abundant weed species were Chenopodium album and Amaranthus retroflexus. Increase in duration of weed interference decreased the stem height of dry bean. At the end of the growing season, dry bean was 20 cm taller in season-long weed-free treatment compared to the season-long weed-infested treatment. As the number of days of weed interference increased, a declining trend of LAI and number of pods was observed. The minimum number of pods was obtained in season-long weed-infested treatment (5.01 pods/plant). Weed interference during the whole growing season, caused a 60% reduction in yield. Considering 5% and 10% acceptable yield lost, the critical period of weed competition was determined from 20 to 68 and 23 to 55 days after planting (DAE), respectively.

Dwarfism does not modify mean area per leaf and light interception in indeterminate autumn-sown white lupin

1996 ◽  
Vol 127 (3) ◽  
pp. 337-345 ◽  
Author(s):  
N. Harzic ◽  
C. Huyghe
Keyword(s):  
Lupinus Albus ◽  
Leaf Size ◽  
Branch Length ◽  
Light Interception ◽  
White Lupin ◽  
Low Light ◽  
First Order ◽  
Logistic Equations ◽  
Wide Range ◽  
Number Of Leaves

SUMMARYThe effect of dwarfism on leaf number and size was investigated on six pairs of tall and dwarf nearisogenic lines of indeterminate autumn-sown white lupins (Lupinus albus L.). Dwarfism reduced mainstem height by 41% and first-order branch length by 22%. It also slightly decreased the number of leaves on the mainstem and first-order branches without affecting the time of flowering. Leaf size was not reduced. Logistic equations were used to analyse differences in the patterns of light interception by leaf canopies relative to thermal time from sowing during the growth of seven dwarf lines and three tall cultivars sown on different dates. The genotypes studied had long periods of low light interception during their early growth. No differences were found between most of the equation parameters for dwarf and tall genotypes. Only the proportion of light intercepted at flowering differed and this was explained by differences in flowering time. The dwarf character did not limit the ability of the crop canopies to intercept light. It is concluded that the character can be introduced into a wide range of genetic backgrounds without deleterious effects.

The Uniqueness of Rape: Reporting Assaultive Violence to the Police

1985 ◽  
Vol 31 (2) ◽  
pp. 169-190 ◽  
Author(s):  
Alan J. Lizotte
Keyword(s):  
Logistic Equations ◽  
The Difference

Is rape unique in terms of the factors that determine whether or not women will report it to the police? Or, is rape similar to other forms of assaultive violence? This research answers these questions by employing the National Crime Survey to develop models for the reporting of rape and assaults on women and men to the police. Logistic equations predicting reports to the police are developed for each type of offense. The analysis shows that unique factors determine the reporting of a rape. Additionally, the difference between reporting rape and reporting assault cannot be totally accounted for by the sex of the victim or offender. This suggests that separate explanations of rape and assault victimization are necessary. The findings in this analysis could be used to develop a policy that would increase victims' reporting of rape and assault to the police.

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