Compartmental models in epidemiologyCompartmental models are a very general modelling technique. They are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels – for example, S, I, or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.
DiffusionDiffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.
CholeraCholera ('kɒlərə) is an infection of the small intestine by some strains of the bacterium Vibrio cholerae. Symptoms may range from none, to mild, to severe. The classic symptom is large amounts of watery diarrhea that lasts a few days. Vomiting and muscle cramps may also occur. Diarrhea can be so severe that it leads within hours to severe dehydration and electrolyte imbalance. This may result in sunken eyes, cold skin, decreased skin elasticity, and wrinkling of the hands and feet. Dehydration can cause the skin to turn bluish.
Wildlife corridorA wildlife corridor, habitat corridor, or green corridor is an area of habitat connecting wildlife populations separated by human activities or structures (such as roads, development, or logging). This allows an exchange of individuals between populations, which may help prevent the negative effects of inbreeding and reduced genetic diversity (via genetic drift) that often occur within isolated populations. Corridors may also help facilitate the re-establishment of populations that have been reduced or eliminated due to random events (such as fires or disease).
History of choleraSeven cholera pandemics have occurred in the past 200 years, with the first pandemic originating in India in 1817. The seventh cholera pandemic is officially a current pandemic and has been ongoing since 1961, according to a World Health Organization factsheet in March 2022. Additionally, there have been many documented major local cholera outbreaks, such as a 1991–1994 outbreak in South America and, more recently, the 2016–2021 Yemen cholera outbreak.
1846–1860 cholera pandemicThe third cholera pandemic (1846–1860) was the third major outbreak of cholera originating in India in the 19th century that reached far beyond its borders, which researchers at University of California, Los Angeles (UCLA) believe may have started as early as 1837 and lasted until 1863. In the Russian Empire, more than one million people died of cholera. In 1853–1854, the epidemic in London claimed over 10,000 lives, and there were 23,000 deaths for all of Great Britain.
Facilitated diffusionFacilitated diffusion (also known as facilitated transport or passive-mediated transport) is the process of spontaneous passive transport (as opposed to active transport) of molecules or ions across a biological membrane via specific transmembrane integral proteins. Being passive, facilitated transport does not directly require chemical energy from ATP hydrolysis in the transport step itself; rather, molecules and ions move down their concentration gradient reflecting its diffusive nature.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
Basic reproduction numberIn epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted (pronounced R nought or R zero), of an infection is the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. The definition assumes that no other individuals are infected or immunized (naturally or through vaccination).
Landscape connectivityIn landscape ecology, landscape connectivity is, broadly, "the degree to which the landscape facilitates or impedes movement among resource patches". Alternatively, connectivity may be a continuous property of the landscape and independent of patches and paths. Connectivity includes both structural connectivity (the physical arrangements of disturbance and/or patches) and functional connectivity (the movement of individuals across contours of disturbance and/or among patches).
Habitat fragmentationHabitat fragmentation describes the emergence of discontinuities (fragmentation) in an organism's preferred environment (habitat), causing population fragmentation and ecosystem decay. Causes of habitat fragmentation include geological processes that slowly alter the layout of the physical environment (suspected of being one of the major causes of speciation), and human activity such as land conversion, which can alter the environment much faster and causes the extinction of many species.
Landscape ecologyLandscape ecology is the science of studying and improving relationships between ecological processes in the environment and particular ecosystems. This is done within a variety of landscape scales, development spatial patterns, and organizational levels of research and policy. Concisely, landscape ecology can be described as the science of "landscape diversity" as the synergetic result of biodiversity and geodiversity.
Separable extensionIn field theory, a branch of algebra, an algebraic field extension is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). There is also a more general definition that applies when E is not necessarily algebraic over F. An extension that is not separable is said to be inseparable.
Field extensionIn mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
Restoration ecologyRestoration ecology is the scientific study supporting the practice of ecological restoration, which is the practice of renewing and restoring degraded, damaged, or destroyed ecosystems and habitats in the environment by active human interruption and action. Ecological restoration can reverse biodiversity loss, combat climate change and support local and global economies.
Abelian extensionIn abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group can be decomposed into a series of normal extensions of an abelian group. Every finite extension of a finite field is a cyclic extension.
MetapopulationA metapopulation consists of a group of spatially separated populations of the same species which interact at some level. The term metapopulation was coined by Richard Levins in 1969 to describe a model of population dynamics of insect pests in agricultural fields, but the idea has been most broadly applied to species in naturally or artificially fragmented habitats. In Levins' own words, it consists of "a population of populations".
Reaction–diffusion systemReaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space. Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature.
Explicit memoryExplicit memory (or declarative memory) is one of the two main types of long-term human memory, the other of which is implicit memory. Explicit memory is the conscious, intentional recollection of factual information, previous experiences, and concepts. This type of memory is dependent upon three processes: acquisition, consolidation, and retrieval. Explicit memory can be divided into two categories: episodic memory, which stores specific personal experiences, and semantic memory, which stores factual information.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
