Exponential Ebola

Exponential expansion of an infectious disease occurs when the rate of growth is proportional to the number of people currently infected. The mathematical formula for exponential growth is:  

[x_t = x_0(1+r)^t]

In the case of Ebola, xt represents the total number of people infected, xₒ represents the number of index cases at the starting point, r represents the rate of disease transmission (believed to be about 2 for Ebola, i.e.: each Ebola victim transmits the disease on average to 2 other people), and t (as an exponent) represents the time interval used for measurement (months). The formula reduces to xt = 3ᵗ for a transmission rate of two with a single index case. Since 70% of Ebola patients die, and since the survivors no longer transmit the disease, the formula for Ebola cases further reduces to xt = 2ᵗ.

With a transmission rate of 2 and a one-month transmission time, there would be 2 active Ebola cases at the end of the first month, assuming the index case either died or survived with immunity. In two months there would be 4 cases, in three months 8 cases, in four months 16 cases, in six months 64 cases, in nine months 512 cases, in one year 4,096 cases, and in two years 16,777,216 cases. If cases emerge after three weeks instead of four weeks, the numbers are much worse. If healthcare workers die off early in the Ebola epidemic, as one would expect with no vaccination and inadequate protection, then the transmission rate would increase from 2 to who knows how high, also leading to much higher case numbers.

As we speak the Ebola epidemic in West Africa is expanding exponentially, doubling each month, apparently with most cases unreported. What if our healthcare system, as good as it is, was unable to alter a transmission rate (r) of 2 for Ebola? All that would be necessary for this to happen is for each Ebola victim in turn to infect one family member, and one friend, stranger or healthcare worker. CDC recommended precautions for your local hospital are currently inadequate to prevent nosocomial (hospital) Ebola transmission, and the CDC's failure to quarantine all Ebola contacts in the community (the proper way to monitor them) could easily lead to transmission of the dreaded disease in our neighborhoods. If the CDC can't properly monitor Ebola transmission among our doctors and nurses at Texas Health Presbyterian Hospital, then why would we expect them to properly monitor Ebola transmission in the community?

"The pool of people being monitored for potential exposure to the disease appeared to more than double, from 48 to perhaps more than 100, none of whom had reported any symptoms of Ebola. All of those now being evaluated for the first time were workers at Presbyterian who cared for Mr. Duncan after he was admitted. Though the precise number of workers remains unknown, questions were also being raised about why they had not been monitored previously."

The CDC inevitably will be unaware of new index Ebola cases from endemic areas, asymptomatic individuals escaping detection from thermometers at the airport, and likewise unaware of some ensuing secondary contacts in the community, thus each new Ebola index case may transmit the disease to a family member, neighbor or stranger, and the CDC, along with the rest of us, would be in the dark. We would be unaware until index cases present themselves to a clinic or hospital having first transmitted Ebola to secondary contacts prior to arrival at the clinic or hospital – transmission occurring before symptoms were admitted to or were clinically evident in the index cases. Some of the secondary contacts would be strangers to the index case – shaking hands with salespersons at a counter, a waitress, coughing or sneezing near someone in public transportation, etc., secondary contacts unknown to the index case and thus untraceable by the CDC. The ensuing secondary cases repeat the same pattern, transmitting Ebola to known and anonymous tertiary individuals, both initially unaware of the terrible truth, and so on…. Remember, in order to achieve exponential growth, each new case only has to transmit Ebola to two others.

"Moreover, said some public health specialists, there is no proof that a person infected -- but who lacks symptoms -- could not spread the virus to others. 'It's really unclear,' said Michael Osterholm, a public health scientist at the University of Minnesota who recently served on the U.S. government's National Science Advisory Board for Biosecurity. 'None of us know.'"

Under current CDC "leadership" exponential expansion of Ebola in the United States could occur. Unless things change drastically and quickly, and with thanks to our President, FDA, and CDC Director, we could have thousands dead within one year of an index case (Xₒ), and millions dead in two years, and even worse if we end up with multiple index cases via unblocked inbound air travel (and sea travel) from West Africa -- or from future geographic areas of epidemic -- like South or Central America. Where is the ZMapp and other effective therapy which would not only cure cases but also reduce the nosocomial transmission rate? Where is the vaccine? Without widely available effective therapy and widespread Ebola vaccination we the American people are reduced to sitting ducks. What has happened to the all-American virtues of intelligence and common sense -- have we become that blind to a clear and present danger?

We now have enough information which should lead us to distrust our government regarding the Ebola epidemic -- we should question their dogma against airborne transmission of Ebola -- they are not an infallible priesthood. Having failed in their primary duty to protect the American people, we find ourselves in harms’ way.

(paragraph six updated by author)