VaccinationVaccination is the administration of a vaccine to help the immune system develop immunity from a disease. Vaccines contain a microorganism or virus in a weakened, live or killed state, or proteins or toxins from the organism. In stimulating the body's adaptive immunity, they help prevent sickness from an infectious disease. When a sufficiently large percentage of a population has been vaccinated, herd immunity results. Herd immunity protects those who may be immunocompromised and cannot get a vaccine because even a weakened version would harm them.
Vaccination policyA vaccination policy is a health policy adopted in order to prevent the spread of infectious disease. These policies are generally put into place by State or local governments, but may also be set by private facilities, such as workplaces or schools. Many policies have been developed and implemented since vaccines were first made widely available. The main purpose of implementing a vaccination policy is complete eradication of a disease, as was done with smallpox. This, however, can be a difficult feat to accomplish or even confirm.
COVID-19Coronavirus disease 2019 (COVID-19) is a contagious disease caused by the virus SARS-CoV-2. The first known case was identified in Wuhan, China, in December 2019. The disease quickly spread worldwide, resulting in the COVID-19 pandemic. The symptoms of COVID‐19 are variable but often include fever, cough, headache, fatigue, breathing difficulties, loss of smell, and loss of taste. Symptoms may begin one to fourteen days after exposure to the virus. At least a third of people who are infected do not develop noticeable symptoms.
COVID-19 pandemicThe COVID-19 pandemic, also known as the coronavirus pandemic, is a global pandemic of coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The novel virus was first identified in an outbreak in the Chinese city of Wuhan in December 2019. Attempts to contain it there failed, allowing the virus to spread to other areas of Asia and later worldwide in 2020. The World Health Organization (WHO) declared the outbreak a public health emergency of international concern (PHEIC) on 30 January 2020.
COVID-19 vaccineA COVID19 vaccine is a vaccine intended to provide acquired immunity against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes coronavirus disease 2019 (COVID19). Prior to the COVID19 pandemic, an established body of knowledge existed about the structure and function of coronaviruses causing diseases like severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS). This knowledge accelerated the development of various vaccine platforms during early 2020.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.
Optimal controlOptimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
SARS-CoV-2Severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) is a strain of coronavirus that causes COVID-19, the respiratory illness responsible for the COVID-19 pandemic. The virus previously had the provisional name 2019 novel coronavirus (2019-nCoV), and has also been called human coronavirus 2019 (HCoV-19 or hCoV-19). First identified in the city of Wuhan, Hubei, China, the World Health Organization designated the outbreak a public health emergency of international concern from January 30, 2020, to May 5, 2023.
COVID-19 testingCOVID-19 testing involves analyzing samples to assess the current or past presence of SARS-CoV-2. The two main types of tests detect either the presence of the virus or antibodies produced in response to infection. Molecular tests for viral presence through its molecular components are used to diagnose individual cases and to allow public health authorities to trace and contain outbreaks. Antibody tests (serology immunoassays) instead show whether someone once had the disease.
Perceptual control theoryPerceptual control theory (PCT) is a model of behavior based on the properties of negative feedback control loops. A control loop maintains a sensed variable at or near a reference value by means of the effects of its outputs upon that variable, as mediated by physical properties of the environment. In engineering control theory, reference values are set by a user outside the system. An example is a thermostat. In a living organism, reference values for controlled perceptual variables are endogenously maintained.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Influenza vaccineInfluenza vaccines, also known as flu shots, are vaccines that protect against infection by influenza viruses. New versions of the vaccines are developed twice a year, as the influenza virus rapidly changes. While their effectiveness varies from year to year, most provide modest to high protection against influenza. The United States Centers for Disease Control and Prevention (CDC) estimates that vaccination against influenza reduces sickness, medical visits, hospitalizations, and deaths.
Smallpox vaccineThe smallpox vaccine is the first vaccine to have been developed against a contagious disease. In 1796, British physician Edward Jenner demonstrated that an infection with the relatively mild cowpox virus conferred immunity against the deadly smallpox virus. Cowpox served as a natural vaccine until the modern smallpox vaccine emerged in the 20th century. From 1958 to 1977, the World Health Organization (WHO) conducted a global vaccination campaign that eradicated smallpox, making it the only human disease to be eradicated.
Vaccine hesitancyVaccine hesitancy is a delay in acceptance, or refusal, of vaccines despite the availability of vaccine services and supporting evidence. The term covers refusals to vaccinate, delaying vaccines, accepting vaccines but remaining uncertain about their use, or using certain vaccines but not others. The scientific consensus that vaccines are generally safe and effective is overwhelming. Vaccine hesitancy often results in disease outbreaks and deaths from vaccine-preventable diseases.
Polio vaccinePolio vaccines are vaccines used to prevent poliomyelitis (polio). Two types are used: an inactivated poliovirus given by injection (IPV) and a weakened poliovirus given by mouth (OPV). The World Health Organization (WHO) recommends all children be fully vaccinated against polio. The two vaccines have eliminated polio from most of the world, and reduced the number of cases reported each year from an estimated 350,000 in 1988 to 33 in 2018. The inactivated polio vaccines are very safe.
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
H-infinity methods in control theoryH∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. H∞ techniques have the advantage over classical control techniques in that H∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of H∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled.
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.
Bellman equationA Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes.
