Infectious Diseases Dynamics models are used to assess the spread and control of diseases within correctional facilities and repercussions on the general population. An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. Mathematical models need to integrate the increasing volume of data being generated on host-pathogen interactions. Many theoretical studies of the population dynamics, structure and evolution of infectious diseases of plants and animals, including humans, are concerned with this problem.

The rapid technological and theoretical progress has dramatically enhanced our arsenal in fighting epidemics and we are getting better on it. The global surveillance network is growing under an intensive worldwide effort. We are now able to produce effective vaccines and antiviral drugs and knowledge goes deep in details such as the molecular structure of a variety of viruses. A large and intensive research is evolving for the design of better drugs and vaccines. Yet, studies warn us that a new pandemic influenza-type is the most worrisome one is sooner or later on the way.

The rapid technological and theoretical progress has dramatically enhanced our arsenal in fighting epidemics and we are getting better on it. The global surveillance network is growing under an intensive worldwide effort. We are now able to produce effective vaccines and antiviral drugs and knowledge goes deep in details such as the molecular structure of a variety of viruses. A large and intensive research is evolving for the design of better drugs and vaccines.

The very first publication addressing the mathematical modeling of epidemics dates back in 1766. In this seminal paper, Essai d’une nouvelle analyze de la mortalité causée par la petite vérole,6 Daniel Bernoulli developed a mathematical model to analyze the mortality due to smallpox in England, which at that time was one in 14 of the total mortality. Bernoulli used his model to show that inoculation against the virus would increase the life expectancy at birth by about three years.