The two parameters in the epidemiological model that we are looking at is:

• R₀ which is the basic reproduction numbers in other words the average number of secondary cases, i.e. the number of infections that are caused by an infection person, within a normal unprotected population.
• C which is the coverage rate, in other words the proportion of people that are immune or vaccinated against the disease.

The basic idea is that if R₀ is less than 1, then the disease/infection will burn out and if R₀ is greater than 1 then it will spread.  So when trying to play the containment game, we would look at R₀(1-C) (note that this only makes sense if R₀ is greater than 1 in the first place since if it was less than 1 then it will burn out by itself, so here we will assume that), and we need to have this less than 1 for an disease/infection to be contained.  The equal then boils down to:

C > 1 - 1/R₀

The equation then says that as R₀ increases that C must also increase, here are some R₀ for various diseases and what the calculated C, coverage rates, would have to be to insure burnouts,

Note that you can see that at the top of the list is measles, with a relatively high R₀ rate of 12-18, meaning that an infected person would on average infect 12 to 18 people. 

Which suggests the highly contagious nature of measles and one of the concerns of people at the Center for Disease Control about people who are opting out of measles vaccinations for whatever reason.  It is important to note that the CDC in general, if I can quote Star Trek, "The needs of the many, out weigh the needs for the few," i.e. they must protect the population over the individual, so these rates above, dictate at what level of immunization for the various diseases must be so that the disease will not flare up in the population.  It is important to note that if you immunize a child, and assume that immunization is perfect, i.e. a child that is immunized can't get the disease, then this will determine the rate at which the disease will burn through the untreated population. 

For measles there is a 90% chance of catching the disease if you are not immunized from a person who has measles.  In 1998, an article came out in Lancet, since withdrawn by 10 out of the 12 authors, suggested a casual relationship between autism symptoms and the MMR vaccination, note that this was not a causal link, meaning that the researcher noted that symptoms started soon after receiving the MMR (measles, mumps and rubella) vaccination.  It is also worth noting that the researcher has come under heavy fire for being funded by trial lawyers. 

As the news spread about a possible link, parents stoped vaccinating their children.  In the UK (where the author was from and which had more press about the results) the vaccination rate went from 92% (slightly below the 95% we showed above) in 1996 to 83% very below,where in 1998 there were 56 cases of measles in the UK to 449 in the first 5 months on 2006 (on tract for approximately 1,078 cases for the year), leading researchers to state a 13 times increase in the incidence rate of measles.  In 2000, 1,500 case of measles with 3 deaths were reported in Ireland amid decreased immunization rates.  In the UK in 2008 measles had been declared as endemic, meaning that it had been sustained within the population.

In the US, the measles vaccination rate was 99.23% in 1995, it dropped to 97.9% in 2000, before returning to previous levels by 2002. Yet outbreaks in the US have happened as populations have become more mobile and as there are "clusters" of people who do not vaccinate their children.  In the US there have been 131 cases in the US from 2006 to 2008, of those it is known that 63 children had parents who refused vaccination, others who suffered were children under the age of 1 which have not received the vaccination.  Feb 12th, in the United States, the courts ruled that there is no scientific evidence linking MMR vaccination to autism, denying parents of autisic children who had the MMR vaccination the ability to access funds set aside for children that are medically harmed because of vaccinations.

The World Health Organization (WHO) declared that measles is the number one killer of children that can be prevented by vaccination.

Comments

B

i

u

Quote

Code

List

List item

URL

Your Name *
Email (For verification & Replies) *
Enter the black characters *   
(*) Required

Submit Comment