Understanding the Basic Reproductive Number By Raymond Inkabi
I hate maths. Sigh! My girlfriend loves it. And now, there seem to be mathematics everywhere I go and in everything I see. This relatively omnipresence governs nature. From the timing of when humans are to be born to the estimates of when a seed planted is likely to germinate and bear fruit. However, mathematics the father of all sciences has spread its all knowing smile toward viral behaviour – disease modelling, and the predictability of an infection. And like all known scientific methods of inquiry, this too is tied to what is known as the basic reproductive number, Ro. Some kind of formula or so for predicting when, where, the duration and who is likely to be infected by either an outbreak of seasonal deaths, Ebola fever or some bubonic plague, in any particular place or clime. Ro tells you, for each person infected, how many others are likely to be infected later. In some easily predicted pattern, most viruses would be subject to mathematical calculations.
The higher Ro is, the more difficult a viral infection will be to manage. Which is somehow similar to the way a pH test is done which measures how acidic or basic a substance is. We know the pH scale ranges from 0 to 14. A pH of 7 is neutral. A pH less than 7 is acidic. And a pH greater than 7 is basic. But the Ro is one of the many things scientists don’t know about the virus that will cause the next pandemic of deaths, because that virus has not yet emerged. This factor can be a problem, because it makes it hard to plan to minimise the impact in the event if an outbreak. Currently we have an Ebola outbreak in 3 West African countries: Guinea, Liberia and Sierra-Leone.
One remedy however, is to produce an effective system in which various types of virus can have some visual representations of reality, modelled and studied under controlled conditions. We need to know how often people mix with each other, because these viruses are most deadly in densely populated places. We need to also sample places where people mix (worship centers, schools, workplaces and homes), and how often and how far they travel. Such extensive modelling approach allows us the rare opportunity to look at viruses with different levels of spread and infectivity, and also at considering different strategies and options for tackling an outbreak: antiviral drugs, vaccines and travel restrictions, ban and advisories on mobility such as closing schools like Liberia to tackle outbreak and stop people travelling to perceived red zones. Sierria-Leone’s team was refused entry to Seychelles for the fear of cross border human-to-human transmission.
Another important thing we must note, is that the use of antiviral drugs to crackdown on outbreaks as they occur only works if the Ro is low and if close contacts of those affected are identified quickly and isolated — something that is futuristic – something that needs committed advanced planning by government and the scientific community. However, during any such mass treatment, the virus would most likely develop a resistance to vaccine, and the effect of this event is unknown.
And as the Ro moves from 1.6 to 1.9, a systematic scientific model employed by the research team led by Dr. Timothy Germann, of the Los Alamos National Laboratory in New Mexico, and published in the Proceedings of The National Academy of Sciences (NAS) of the USA, as far back as 2006 predicts that an outbreak of a virus will progress from the easily controlled with moderate effort to the point it will need several action to be applied targetedly. If Ro exceeds 1.9, the government must be ready to initiate a sequence of behavioural and lifestyle adjustments to the people, such as school closures and travel restrictions, and setting up of emergency screening centers and facilities at all high level traffic points.
An unusual twist of Dr. Germann’s conclusion, however, is how useful even a weakly effective vaccine could be in the event of an outburst of killer viruses. When Ro is less than 1.9 vaccines, if widely distributed, could genuinely slow the progress of a pandemic and limit the number of sick people to less than one tenth of the population. This means that useful vaccines should and must be produced in anticipation of a plague, simply by modelling which virus strain might eventually emerge. As long as the calculations are right, the resulting vaccine would create enough protection to break the path of transmission. To me, Dr Germann’s paper suggests a simulacrum of futuristic planning, which we must all participate in.
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