The mathematical definition says that a quantity that increases with a rate proportional to its current size will grow exponentially. This means that as the quantity increases so does that rate at which it grows.
The more infected people we have in the early stages of a disease outbreak, the more people they will infect and the more the cases will rise. Other situations in which exponential growth plays a critical role range from pyramid schemes to nuclear weapons. In a pyramid scheme, each new investor invites two more recruits who in turn invite two more. When the pyramid tumbles, most investors lose their money. In a nuclear fission bomb, a single uranium atom splits in two, jettisoning fast-moving neutrons and large quantities of energy in the form of electromagnetic radiation.
The neutrons then collide with more atomic nuclei, splitting more atoms and releasing yet more energy in a nuclear chain reaction that increases exponentially. At about in the morning of August 6 , the atomic bomb known as the Little Boy detonated releasing energy equivalent to 30 million sticks of dynamite in an instant, devastating the Japanese city of Hiroshima.
The surrender of Imperial Japan was announced nine days later. This is the awesome power of exponential growth. Although the concept of exponential growth is not new in the public consciousness, a lot of misconceptions surround the idea. Initially, growth is exponential because there are few individuals and ample resources available. Then, as resources begin to become limited, the growth rate decreases.
Finally, growth levels off at the carrying capacity of the environment, with little change in population size over time. Exponential and logistical population growth : When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve. In logistic growth, population expansion decreases as resources become scarce, leveling off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.
The logistic model assumes that every individual within a population will have equal access to resources and, thus, an equal chance for survival. For plants, the amount of water, sunlight, nutrients, and the space to grow are the important resources, whereas in animals, important resources include food, water, shelter, nesting space, and mates.
In the real world, the variation of phenotypes among individuals within a population means that some individuals will be better adapted to their environment than others. Intraspecific competition for resources may not affect populations that are well below their carrying capacity as resources are plentiful and all individuals can obtain what they need.
However, as population size increases, this competition intensifies. Yeast, a microscopic fungus used to make bread and alcoholic beverages, exhibits the classical S-shaped curve when grown in a test tube a. Its growth levels off as the population depletes the nutrients that are necessary for its growth. In the real world, however, there are variations to this idealized curve. Examples in wild populations include sheep and harbor seals b. In both examples, the population size exceeds the carrying capacity for short periods of time and then falls below the carrying capacity afterwards.
This fluctuation in population size continues to occur as the population oscillates around its carrying capacity. Still, even with this oscillation, the logistic model is confirmed. Logistic population growth : a Yeast grown in ideal conditions in a test tube show a classical S-shaped logistic growth curve, whereas b a natural population of seals shows real-world fluctuation.
Population regulation is a density-dependent process, meaning that population growth rates are regulated by the density of a population. In population ecology, density-dependent processes occur when population growth rates are regulated by the density of a population. Most density-dependent factors, which are biological in nature biotic , include predation, inter- and intraspecific competition, accumulation of waste, and diseases such as those caused by parasites.
Usually, the denser a population is, the greater its mortality rate. In addition, low prey density increases the mortality of its predator because it has more difficulty locating its food source. An example of density-dependent regulation is shown with results from a study focusing on the giant intestinal roundworm Ascaris lumbricoides , a parasite of humans and other mammals.
The data shows that denser populations of the parasite exhibit lower fecundity: they contained fewer eggs. One possible explanation for this phenomenon was that females would be smaller in more dense populations due to limited resources so they would have fewer eggs. This hypothesis was tested and disproved in a study which showed that female weight had no influence.
The actual cause of the density-dependence of fecundity in this organism is still unclear and awaiting further investigation. Effect of population density on fecundity : In this population of roundworms, fecundity number of eggs decreases with population density. Many factors, typically physical or chemical in nature abiotic , influence the mortality of a population regardless of its density.
They include weather, natural disasters, and pollution. An individual deer may be killed in a forest fire regardless of how many deer happen to be in that area. Its chances of survival are the same whether the population density is high or low.
In real-life situations, population regulation is very complicated and density-dependent and independent factors can interact. Examining the data of different countries around the world casts a heavy question mark on the above statement.
Nonetheless, the data shows similar time constants amongst all these countries in regard to the initial rapid growth and the decline of the disease. For example, our calculations show that the pattern of the daily new infections as a percentage of accumulated number of infections weekly averaged , is common to every country around the globe.
I want to extend my gratitude to Professor Zvi Ziegler of the Technion, who sent me his calculations and analysis regarding the weekly averaged infection rate in Israel and in twenty other countries. Certainly, a full complete lockdown reduces the spread of the virus. However, as the above data shows, there is an apparent similar decline in the rate of infection even in countries that did not enforce a full shutdown.
Further research must be performed in order to understand the underlying reason behind this observation. Severe lockdown has some negative implications. This will eventually lead to an increase in poverty and to human life loss due other diseases.
Given that the evidence reveals that the Corona disease declines even without a complete lockdown, it is recommendable to reverse the current policy and remove the lockdown.
At the same time, it is advisable to continue with low-cost measures, such as wearing masks, expanding testing for defined populations and prohibiting mass gatherings.
A relief on these restrictions in these defined areas is contingent upon a decrease to the rate of growth to less than 5 percent. It is critical to remove the bottleneck that is preventing the expansion of testing to 20, — 30, per day and to focus on acquiring medical swabs, test kits, and reagents including from local production.
The decline in growth of the Coronavirus in general, and critical-condition patients in particular, decreases the likelihood that Israel will undergo the system-wide overload that the health systems of Italy, Spain and New York experienced. Facing high rates of infection, the latter systems were unable to handle the sudden influx in patients. With that being said, Israel may face a shortage in ventilators. While this has not happened yet, it is crucial to focus on closing the gap.
In Streetwise Hebrew for the Times of Israel Community, each month we learn several colloquial Hebrew phrases around a common theme.
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