InfectionAn infection is the invasion of tissues by pathogens, their multiplication, and the reaction of host tissues to the infectious agent and the toxins they produce. An infectious disease, also known as a transmissible disease or communicable disease, is an illness resulting from an infection. Infections can be caused by a wide range of pathogens, most prominently bacteria and viruses. Hosts can fight infections using their immune systems. Mammalian hosts react to infections with an innate response, often involving inflammation, followed by an adaptive response.
Negative binomial distributionIn probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted ) occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ().
OverdispersionIn statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model. A common task in applied statistics is choosing a parametric model to fit a given set of empirical observations. This necessitates an assessment of the fit of the chosen model. It is usually possible to choose the model parameters in such a way that the theoretical population mean of the model is approximately equal to the sample mean.
Emerging infectious diseaseAn emerging infectious disease (EID) is an infectious disease whose incidence has increased recently (in the past 20 years), and could increase in the near future. The minority that are capable of developing efficient transmission between humans can become major public and global concerns as potential causes of epidemics or pandemics. Their many impacts can be economic and societal, as well as clinical. EIDs have been increasing steadily since at least 1940.
Bloodstream infectionsBloodstream infections (BSIs), septicemia which include bacteremias when the infections are bacterial and fungemias when the infections are fungal, are infections present in the blood. Blood is normally a sterile environment, so the detection of microbes in the blood (most commonly accomplished by blood cultures) is always abnormal. A bloodstream infection is different from sepsis, which is the host response to bacteria.
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.
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.
Poisson regressionIn statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables.
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.
Beta-binomial distributionIn probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution.
Vertically transmitted infectionA vertically transmitted infection is an infection caused by pathogenic bacteria or viruses that use mother-to-child transmission, that is, transmission directly from the mother to an embryo, fetus, or baby during pregnancy or childbirth. It can occur when the mother has a pre-existing disease or becomes infected during pregnancy. Nutritional deficiencies may exacerbate the risks of perinatal infections. Vertical transmission is important for the mathematical modelling of infectious diseases, especially for diseases of animals with large litter sizes, as it causes a wave of new infectious individuals.
Social distancingIn public health, social distancing, also called physical distancing, is a set of non-pharmaceutical interventions or measures intended to prevent the spread of a contagious disease by maintaining a physical distance between people and reducing the number of times people come into close contact with each other. It usually involves keeping a certain distance from others (the distance specified differs from country to country and can change with time) and avoiding gathering together in large groups.
Infectious diseases (medical specialty)Infectious diseases or ID, also known as infectiology, is a medical specialty dealing with the diagnosis and treatment of infections. An infectious diseases specialist's practice consists of managing nosocomial (healthcare-acquired) infections or community-acquired infections. An ID specialist investigates the cause of a disease to determine what kind of Bacteria, viruses, parasites, or fungi the disease is caused by. Once the pathogen is known, an ID specialist can then run various tests to determine the best antimicrobial drug to kill the pathogen and treat the disease.
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).
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).
Dirichlet negative multinomial distributionIn probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands.
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.
ZoonosisA zoonosis (zoʊˈɒnəsɪs,_ˌzoʊəˈnoʊsɪs; plural zoonoses) or zoonotic disease is an infectious disease of humans caused by a pathogen (an infectious agent, such as a bacterium, virus, parasite or prion) that can jump from a non-human (usually a vertebrate) to a human and vice versa. Major modern diseases such as Ebola virus disease and salmonellosis are zoonoses. HIV was a zoonotic disease transmitted to humans in the early part of the 20th century, though it has now evolved into a separate human-only disease.
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".
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.
