Related papers: Dynamics of inhomogeneous populations and global d…
We show that a simple nonlinear differential equation (originally studied in the physics of disordered systems) is able to mathematically describe the global population growth over the past 12000 years. Different regimes of population…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…
The report considers the dynamics of the global population as the unique case of the Socio-Economic Soft Matter system. This category was introduced for complex systems dominated by mesoscale assemblies, emerging due to the inherent…
A simple but useful method of reciprocal values is introduced, explained and illustrated. This method simplifies the analysis of hyperbolic distributions, which are causing serious problems in the demographic and economic research. It…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…
Economic growth and the growth of human population in the past 2,000,000 years are extensively examined. Data are found to be in a clear contradiction of the currently accepted explanations of the mechanism of growth, which revolve around…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number…
We analyze mathematical models of the global human population growth and compare them to actual dynamics of the world population and of the world surplus product. We consider a possibility that the so-called world's demographic transition…
Is there an advantage to heterogeneity in a population where individuals grow and divide by fission? This is a broad question, to which there is no easy universal answer. This article aims to provide a quantitative answer in the specific…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A…
Data describing the growth of the world population in the past 12,000 years are analysed. It is shown that, if unchecked, population does not increase exponentially but hyperbolically. This analysis reveals three approximately-determined…
Data describing historical growth of income per capita [Gross Domestic Product per capita (GDP/cap)] for the world economic growth and for the growth in Western Europe, Eastern Europe, Asia, former USSR, Africa and Latin America are…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
Using current empirical data from 10,000 BCE to 2023 CE, we re-examine a hyperbolic pattern of human population growth, which was identified by von Foerster et al. in 1960 with a predicted singularity in 2026. We find that human population…
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent on dynamically changing population structures, appear in a…