Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration). Example scenarios are ageing populations, population growth, or population decline.
Published in Chapter:
The Stability of an Epidemic Model With Piecewise Constant Argument by Lyapunov-Razumikhin Method
Nur Cengiz (Süleyman Demirel University, Turkey) and Duygu Aruğaslan-Çinçin (Süleyman Demirel University, Turkey)
Copyright: © 2020|Pages: 24
DOI: 10.4018/978-1-7998-0134-4.ch011
Abstract
The authors propose a nonlinear epidemic model by developing it with generalized piecewise constant argument (GPCA) introduced by Akhmet. The authors investigate invariance region for the considered model. For the taken model into consideration, they obtain a useful inequality concerning relation between the values of the solutions at the deviation argument and at any time for the epidemic model. The authors reach sufficient conditions for the existence and uniqueness of the solutions. Then, based on Lyapunov-Razumikhin method developed by Akhmet and Aruğaslan for the differential equations with generalized piecewise constant argument (EPCAG), sufficient conditions for the stability of the trivial equilibrium and the positive equilibrium are investigated. Thus, the theoretical results concerning the uniform stability of the equilibriums are given.
FAQs
Population dynamics is the study of the continuously changing abundance of plants and animals in space and time.
What is population dynamics in simple terms? ›
Population dynamics refers to how populations of a species change over time. The study of a species' population dynamics usually seeks to answer questions such as: What explains average abundance of a population?
How do you explain the dynamics of the world population? ›
Patterns of Population Growth. Populations are dynamic. They are continuously gaining individuals through births and losing individuals through deaths. Populations may also gain or lose a significant number of individuals through migration when people either enter or leave a population.
What does dynamic mean in population? ›
Dynamic population: In a dynamic population, membership is defined by current status, so membership is not necessarily permanent. A person is a member of the population as long as they meet the definition of the population, and they cease to be a members of the population when they no longer meet the definition.
What is the population dynamics of a country? ›
Population dynamics explores changes in population through fertility, migration, and mortality. Fertility relates to the ability to have babies, migration involves people moving in and out of regions, and mortality refers to death.
What is an example of population dynamics? ›
Population dynamics is the field of life sciences that investigates population size and age as driving systems, because the biological and environmental mechanisms that drive them (for example birth rates and death rates, and by immigration and emigration).
What are the 4 components of population dynamics? ›
After all, population change is determined ultimately by only four factors: birth, death, immigration, and emigration. This apparent simplicity is deceptive. It is easy to underestimate the complexity of biotic and abiotic interactions in the natural world that can influence these four population parameters.
What are the issues of population dynamics? ›
Population dynamics are strongly inter-linked with development issues such as sexual and reproductive health (including maternal health, family planning and HIV), the needs of young people, gender equality and poverty reduction.
What are the three population dynamics? ›
The three fundamental processes determining population growth and distribution are fertility, mortality, and migration. All three processes are likely to affect and be affected by global change.
What is the population dynamics paragraph? ›
Human population dynamics is a field that identifies the factors related to changes in population such as fertility, mortality, life expectancy and migration. Predicting population changes is important because these demographic trends effect economic, social and environmental systems.
Population dynamics has important effects on the nature and rate of evolution. While in infinite populations, the fixation and accumulation of mutations is governed by the rates of mutation and selection only, in finite populations stochastic effects also play a role.
How do population dynamics affect the environment? ›
In addition to direct loss of coral reef, consequences include coastal erosion and a local increase in sea level. This example provides a clear and direct link between population growth and coastal degradation. Population growth can lead to many other coastal and marine environmental disturbances.
What is population dynamics quizlet? ›
population dynamics. the study of changes in population characteristics. "the change in a population over time" population size. (Nt ) the number of individuals of a specific species that occupies a given area or volume at a given time.
What is the definition of population distribution? ›
Population distribution means the pattern of where people live. World population distribution is uneven. Places which are sparsely populated contain few people. Places which are densely populated contain many people. Sparsely populated places tend to be difficult places to live.
