Logistic Growth Model in Human Birth Rate

Logistic Growth Model in Human Birth Rate


The study discusses how the logistic equation, which is a mathematical model of population growth, can be used to forecast the human birth rate concerning available resources. Most of the world’s resources are nonrenewable. While this is a widely accepted fact, the 21st century presents unique challenges in terms of balancing demand for resources such as water, fish, and land with sustainability requirements. Seo (18) states that the effects of climate change have only made the situation worse, especially as rainfall patterns are becoming increasingly unpredictable, water sources are becoming depleted, forest cover is declining, the acreage of arable land is shrinking, and fish populations are dwindling. While all this is happening, the global community continues to grow, raising serious questions about the planet’s ability to support itself.

Is there a way that the correlation between human birth rate and resource utilization can be analyzed, predicted, and modeled to enable better population planning? At what point can available resources become incapable of supporting the human birth rate? By using the logistic growth model, the relationship between the human birth rate and resource availability can be modeled using the following differential equation: dP/dt=kP(1-P/N)-λ. In this formula, the population is represented by P(t), the birth rate is denoted by k, N symbolizes rate of resource consumption, and the carrying capacity is signified by λ. An examination of the answers to this equation for different resource consumption levels confirms that a critical resource consumption level, also referred to as a bifurcation value, is a reality.

The model reveals that if the resource consumption level surpasses this bifurcation value by the smallest degree, then the birth rate will dramatically reduce (Schiesser 49). The logic behind the equation is that when a region, country, society, or community is approaching the bifurcated value, the slightest increase in resource utilization can have devastating effects on birth rate (Schiesser 68).

A community that grazes its cattle on a public piece of land, for instance, may not take any action to moderate the intensity of grazing that the cattle are allowed to engage in. After some time, pastures on the land will become extinct and unable to sustain the population of the community, leading to low birth rates. Overutilization of resources leading to the collapse or extinction of whole societies or communities also referred to as overharvesting, is not a new phenomenon. Indeed, there are historical accounts that prove it should be treated as a matter of urgency. According to Seo (29), a good example is the deterioration of the community on Easter Island, home to the Rapa Nui people. Credible documents show that a key ingredient in society’s disintegration was the total depletion of forest cover on the island, made possible by human deforestation.

Today, many would wonder how naive the Rapa Nui were to decimate all trees in their habitat. How did no one realize that the forest cover was rapidly disappearing? Why did no one intervene to arrest the situation? These questions are easy to pose now, but back then the Rapa Nui were oblivious to the level of destruction they were causing to themselves and their environment. Seo (57) adds that ironically, while it is easy for current generations to feel arrogantly smarter than the Rapa Nui, it is likely that future generations will ask the same questions regarding actions that are presently causing the extinction of species and overconsumption of food sources.



Growth models

Estimating the world population and the carrying capacity limit can help the world to plan on how to use its natural resources sparingly to sustain the world for a longer period, without total destruction. Several models have been put forward to predict the population growth rate. However, some of these models have limitation. One such model is exponential growth rate model.  Malthus proposed exponential growth model in 1798, and hence often referred to as the Malthusian Growth Model. The logistic growth model was proposed by Verhulst in 1845. Both models emanated from the observations of biological reproduction process (Balakrishnan 14).  But in relation to human population, the constant rate of growth ca

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