Model for the Vaccination against the Poliomyelitis

The poliomyelitis is an acute infection produced by the polio virus that affects the human central nervous system. It is transmitted by fecal-oral and respiratory contact.There are two types of vaccine, OPV （live attenuated virus） and IPV （inactivated polio virus）. Currently, there is a plan of vaccination until the age of 5 with OPV. The children vaccinated expel a virus （derived from the vaccine） to the environment, and some of the people that have oral contact with them, get vaccinated by the herd behavior. Nevertheless, taking into account the lately observed facts about the reversion to virulence of the oral polio vaccine during its circulation in the environment, a change in the current vaccination schedule is being contemplated, where the oral polio vaccine can be replaced by the inactivated vaccine. Nowadays, In Colombia the inactivated oral polio vaccine is recommended for children presenting immune deficiency who are vaccinated with IPV. These children do not expel poliovirus to the environment. This work presents a mathematical model that describes the dynamics of the infection in a population where the two types of vaccination are carried out. The population is divided into two groups of age and Michaelis-Menten interactions. Different strategies of vaccination are simulated and analyzed.