Tag Archives: Basic Reproduction Rate

Reproduction Rate

The way Ebola spreads is simple: from one person to another. There’s an African animal reservoir — probably fruit bats — from which the virus finds its way into a human being once or twice a year. But from then on the virus is transmitted only through bodily fluids, not via an animal vector such as mosquitoes or fleas. Ebola spreads by a simple chain reaction: each person it infects may infect one or more additional people, and so on. The key is how many susceptible people, on average, each infected person passes the virus on to. This is called the “Effective Reproduction Rate,” or “Re”. (Almost everyone* is initially susceptible to Ebola, but Re will drop proportionately if a substantial portion of the relevant population becomes immune, either by surviving or by receiving some future vaccine. The rate at which the virus would be transmitted in a completely susceptible population, with no immunity, is called the “Basic Reproduction Rate,” or “Ro”.)

  • If, on average, each infected person passes the virus on to just one other susceptible person (Re is one) the epidemic will continue at a steady rate, neither growing nor dying out. This is called an “endemic” disease. The total number of cases grows, but the rate at which new cases occur stays the same.
  • If Re is less than one the epidemic will die out, slowly or rapidly depending on where the number falls between one and zero.
  • If Re is more than one the epidemic will mushroom until some factor pushes that number back down below one. The rate of growth will depend on how big this number is, but the epidemic will relentlessly accelerate so long as Re is greater than one. This is “exponential” or “explosive” growth.

The only way to stop an epidemic is to push Re down below one. Of course it’s also best to get as close to zero as possible as rapidly as possible, but so long as Re is less than one the disease will eventually die out.

Forty Years of Rural Outbreaks

Ebola outbreaks have so far always started in rural areas, with the likely suspect usually being some sort of bush meat, typically bats or monkeys.

Home caregivers are very likely to be infected, so at the outset an Re of at least one is almost assured. Other family members and visitors are also at risk. This mode of transmission can be greatly reduced by caring for patients, as soon as they become infectious, in a facility that follows rigorous infection-control procedures. This approach has worked for Médecins Sans Frontières (“MSF”) in all prior outbreaks. (Lugubriously, this form of transmission may also be reduced when patients aren’t cared for by anyone, either because they are the last member of a family or because they are put out of the house when they fall ill.)

Healthcare providers are especially vulnerable, particularly in the early stage of the outbreak. The initial symptoms of Ebola are similar to those of many other less-infectious diseases, so the first wave of sufferers typically walk in to clinics or hospitals and are examined and cared for like other patients. Not only are doctors and nurses likely to become infected, but before the outbreak is recognized they may pass infection on to other patients. This is tragic, and definitely helped the current outbreak get a foothold, but it may ultimately not be an important element of Re. For one thing, MSF has shown that rigorous procedures and high-quality anti-infection suits can essentially eliminate this risk. As of a recent report, no MSF employees had become infected in the West African outbreak, though many other healthcare providers have been. For another, hospitals and clinics may be closed when they have become contaminated, and patients may stop going there for any illnesses once the risk of Ebola infection becomes known. The collapse of the health care system has many adverse effects, but the silver lining is the fact that people who don’t go to a hospital at all can’t either transmit or acquire Ebola there.

African funeral practices have played a big role in amplifying Re.

  • The body of someone who dies is traditionally hand-washed by members of the family. This almost guarantees that the washers will be infected.
  • Mourners at a traditional funeral may touch and even kiss the body. This can infect many people, who bring the virus with them when they return home. The entire outbreak in Sierra Leone, for example, has been traced to fourteen women who attended a single traditional healer’s funeral in Guinea. [NYT]
  • Finally, those who bury the body are at high risk unless infection-control procedures are used.

It is obviously essential to stop these funeral practices, since one victim can infect a huge number of other people this way. Again, MSF has been able to do this in the villages affected by previous Ebola outbreaks by working with local chiefs and explaining the situation to the villagers.

The impact of funeral practices on Re is affected by the mortality rate. In prior outbreaks up to 90% of those infected died, so almost all had the potential to infect many others through their funerals. In West Africa only about half seem to be dying, so the impact of funerals is somewhat reduced. This effect is swamped, however, by the large number of potential infections from one traditional funeral. Even though the reduced mortality rate makes funerals somewhat less important it is still essential to bring traditional funeral practices to a stop if Re is to be reduced below one.

In more than a dozen rural outbreaks over nearly forty years Re has been decisively driven below one, and the outbreak stopped, by rigorous infection control, contact-tracing and quarantine. The support of local communities was obtained by personal contact and education.

New Complications in West Africa

The West African outbreak, however, presents a very different picture. The health care systems in the affected countries had been damaged by years of civil war as well as profound poverty. This is the first time Ebola has appeared in any of these countries, so they were slow to recognize it and unfamiliar with the steps needed to contain it. Whatever the reasons, the virus was able to spread for several months before being recognized, and the consequences have been tragic.

Several new elements have complicated the relatively simple pattern of previous outbreaks:

  1. Ignorance, superstition and rumor have frustrated efforts to apply the established protocol, both in certain rural villages and in poor urban neighborhoods, notably the West Point district of Monrovia. Health care personnel have had to withdraw completely from a dozen “red villages” in Guinea where residents fear that MSF and Red Cross are causing Ebola rather than seeking to control it.[NYT] People have been hiding Ebola victims instead of letting them go into isolation wards.
  2. The uncontrolled spread of Ebola into several big cities raises the risk of additional modes of transmission, such as physical contact in taxis, buses and crowds, and contamination of shared surfaces.
  3. The number of patients has overwhelmed available isolation facilities.
  4. In several cases people who had been exposed to Ebola, or were already ill, have nevertheless chosen to travel, thus putting many others at risk. [Ebola Strategy 2014-08-31]  Some people have also lied about potential exposure to gain admission to hospitals, thus risking infection to doctors, nurses, staff and other patients.

The consequence has been that Re appears to be at least one in Guinea and Sierra Leone, and more like 1.5 in Liberia. An excellent article in Science projects a tripling to around 10,000 cases by September 24, and hundreds of thousands in subsequent months, with no end in sight so long as Re stays so high. [Science 2014-08-31].

The only way to stop the outbreak is to identify and implement a suite of feasible measures that together push and hold the Effective Reproduction Rate (Re) below one. It is of course also important as a humanitarian concern to provide the best possible care for those who fall ill, but care has no effect on the rate at which the virus spreads except to the extent that it implies reduction of potentially infective contacts.

The outbreak has naturally segmented itself to some degree, into rural and urban areas, and by country. A couple of attempts at quarantine barriers, called cordons sanitaire, have attempted to segment it further, with mixed success. (I plan to discuss this in a future post.) To the extent that segmentation works it may be possible to stop the outbreak using different suites of infection-reduction measures in different segments. In particular, relatively well-organized countries such as Nigeria and Senegal may well be able to bring their own smaller outbreaks under control using the standard protocol of contact tracing, monitoring and quarantine, even if the epidemic continues to grow uncontrollably in, say, Liberia.

Wild Cards

The current situation is bad enough without worrying about how it could get worse, but there are a few uncertainties that it’s useful to keep in mind.

Ebola is mutating rapidly,[Washington Post 2014-08-28] and it’s possible that the virus could change in ways that increase its infectiousness, especially through the air. That would be very problematic, to put it mildly.

An animal transmission vector might emerge, particularly in places where bodies are not promptly disposed of.

Sexual transmission might become significant in a promiscuous segment of the population, such as a subset of gay men. Not only could an infected person pass the virus on to multiple sexual partners, but this could also happen after recovery, since Ebola is found in the semen of recovered patients for up to seven weeks. [Who Fact Sheet]

Secondary effects of the outbreak could disrupt infection-reduction measures or even destabilize affected regions. The most immediate risk is a breakdown in food supplies, but one could also imagine breakdowns in other public services. Public disorder has broken out in several places, and this could continue or worsen. In the middle term the weak economies of the affected countries will be further damaged by disruption of internal and foreign trade. Also, the breakdown of the health care systems in these countries may facilitate epidemics of other diseases.

At the bottom of Pandora’s Box there is hope:

A safe and effective vaccine could bring the outbreaks to a fairly quick end. Indeed, this may be the only real hope of doing so.

Possible Preexisting Immunity A subsequent New York Times article raises the possibility that some portion of East Africans are already immune to Ebola. [NYT 9/5/14] The article cites a 2010 study in Gabon, which had had four Ebola outbreaks from 1994 to 2002. The study found Ebola antibodies in 15% of the population, ranging from 34% in some remote villages to 3% on the coast. The investigator speculated that many of the antibodies resulted from low-level exposures that weren’t sufficient to cause illness. This is interesting because it might afford a large pool of people who are already immune, who might be able to take on hazardous jobs with less personal risk, and who might be able to donate curative antibodies. There are several cautions, however:

  1. Immunity is to a particular strain.
  2. It’s not clear what level of antibodies is protective in humans.
  3. While an injection of antibodies might help an infected person fight off the disease it would not function like a vaccine to generate long-term immunity.
  4. Levels of exposure in Gabon, which had a long history of Ebola outbreaks, might be higher than in the countries currently affected.
  5. The epidemic is currently most worrisome in coastal cities, where antibodies would probably be lowest.
  6. Whatever preexisting immunity existed in remote villages wasn’t sufficient to keep Ebola from getting a foothold there.
  7. Sophisticated techniques are needed to test for antibodies.

More Information:
[Measuring Disease Dynamics in Populations: Characterizing the Likelihood of Control, Johns Hopkins]

[Exponential Growth and the Legend of Paal Paysam]