Sufficient optimality conditions for a class of epidemic problems with control on the boundary

Alicja Miniak-GOrecka1, Andrzej Nowakowski

  • 1Faculty of Math and Computer Sciences, University of Lodz, Banacha 22, 90-238 Lodz, Poland.

Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
139
Steps in Outbreak Investigation01:18

Steps in Outbreak Investigation

In the ever-evolving field of public health, statistical analysis serves as a cornerstone for understanding and managing disease outbreaks. By leveraging various statistical tools, health professionals can predict potential outbreaks, analyze ongoing situations, and devise effective responses to mitigate impact. For that to happen, there are a few possible stages of the analysis:
660
Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
29.3K
Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
315
Infection01:20

Infection

When a pathogen enters the body and reproduces, it can cause an infection, damage body cells, and cause illness symptoms that eventually lead to disease. Therefore, its prevention requires breaking the chain of infection.
The chain begins with pathogens: bacteria, viruses, fungi, prions, or parasites such as protozoa helminths. These can be present on the skin as transient or resident flora, or they can be acquired from the environment. Identifying and treating the type of infection and...
13.8K
Transmission-based Precautions II: Airborne and Protective Environment01:25

Transmission-based Precautions II: Airborne and Protective Environment

Transmission-based precautions are for patients infected or suspected to be infected (or colonized) with organisms posing a significant risk to others. The transmission precautions include airborne and protective environment precautions.
Airborne precautions:
Use airborne precautions when treating patients known or suspected to have diseases that spread through the air—for example, tuberculosis or measles. These organisms are present in smaller droplets expelled by an infected person and...
2.1K