Compound Poisson distributionIn probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. The result can be either a continuous or a discrete distribution. Suppose that i.e., N is a random variable whose distribution is a Poisson distribution with expected value λ, and that are identically distributed random variables that are mutually independent and also independent of N.
Immunity (medical)In biology, immunity is the state of being insusceptible or resistant to a noxious agent or process, especially a pathogen or infectious disease. Immunity may occur naturally or be produced by prior exposure or immunization. The immune system has innate and adaptive components. Innate immunity is present in all metazoans, immune responses: inflammatory responses and phagocytosis. The adaptive component, on the other hand, involves more advanced lymphatic cells that can distinguish between specific "non-self" substances in the presence of "self".
Superspreading eventA superspreading event (SSEV) is an event in which an infectious disease is spread much more than usual, while an unusually contagious organism infected with a disease is known as a superspreader. In the context of a human-borne illness, a superspreader is an individual who is more likely to infect others, compared with a typical infected person. Such superspreaders are of particular concern in epidemiology.
Contact tracingIn public health, contact tracing is the process of identifying persons who may have been exposed to an infected person ("contacts") and subsequent collection of further data to assess transmission. By tracing the contacts of infected individuals, testing them for infection, and isolating or treating the infected, this public health tool aims to reduce infections in the population. In addition to infection control, contact tracing serves as a means to identify high-risk and medically vulnerable populations who might be exposed to infection and facilitate appropriate medical care.
Rejection samplingIn numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of exact simulation method. The method works for any distribution in with a density. Rejection sampling is based on the observation that to sample a random variable in one dimension, one can perform a uniformly random sampling of the two-dimensional Cartesian graph, and keep the samples in the region under the graph of its density function.
Quasi-likelihoodIn statistics, quasi-likelihood methods are used to estimate parameters in a statistical model when exact likelihood methods, for example maximum likelihood estimation, are computationally infeasible. Due to the wrong likelihood being used, quasi-likelihood estimators lose asymptotic efficiency compared to, e.g., maximum likelihood estimators. Under broadly applicable conditions, quasi-likelihood estimators are consistent and asymptotically normal. The asymptotic covariance matrix can be obtained using the so-called sandwich estimator.
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).
Poisson distributionIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Opportunistic infectionAn opportunistic infection is an infection caused by pathogens (bacteria, fungi, parasites or viruses) that take advantage of an opportunity not normally available. These opportunities can stem from a variety of sources, such as a weakened immune system (as can occur in acquired immunodeficiency syndrome or when being treated with immunosuppressive drugs, as in cancer treatment), an altered microbiome (such as a disruption in gut microbiota), or breached integumentary barriers (as in penetrating trauma).
Compound probability distributionIn probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables. If the parameter is a scale parameter, the resulting mixture is also called a scale mixture.
