How to Halt Disease with Limited Amounts of Vaccine

When you have a limited amount of vaccine, what’s the best way to use it to halt the spread of disease? That’s more than an academic question. A good vaccination strategy saves time, money and, of course, lives.

One line of thought is that to wipe out a disease, as many individuals as possible ought to be vaccinated. This eliminates the disease by brute force.

But today, Michael Khasin at Michigan State University in East Lansing and a couple of buddies suggest another strategy. They say that the timing of the vaccination is important too. In fact, it is possible to speed up the eradication of the disease with a series of periodic vaccination “bursts”. So when the amount of vaccine is limited, this is the best strategy.

The problem is that in large populations, disease dynamics can lead to a state in which a fraction of the population stays infected for a long time.

That’s just the result of the randomness of processes of infection, re-infection, the rate of recovery and the death rate (which epidemiologists euphemistically call the “removal rate”). This low level of “noise” keeps the residual infection ticking over.

However, bigger fluctuations can wipe out the disease entirely. That’s how vaccination works: it causes a big change in the rate of infection which leads to an exponential increase in the disease extinction rate.

What Khasin and co have done is show that the optimal vaccination protocol is a series of vaccine spikes and that this approach is model independent; ie it should work for any disease.

One problem, however, is that the effect depends strongly on the period of the vaccination pulses. Get this right and the extinction rate of the disease rises exponentially. Khasin and co say there is a kind of resonance effect when the vaccine pulse sequence is close to the characteristic period of oscillations of the disease itself.

But this works both ways. Get the period wrong and you can actually reduce the disease extinction rate. In that case, you can worsen the outbreak.

Nevertheless, this is potentially important work. Vaccines are often in short supply, perhaps because they are expensive, dangerous to store in large amounts, as in the case of anthrax, or have a limited shelf life because the infectious agent regularly mutates as it does for flu.

It may also help lead to a more equitable distribution of vaccines. When scientists developed a vaccine for swine flu last year, the initial thinking was that individuals would need two shots to be properly inoculated. Rich western countries scrambled to buy in enough of the stuff to treat their own populations.

Later, it emerged that one shot should be sufficient, leaving many countries with huge stockpiles which they are currently selling off at bargain rates to developing countries.

Perhaps more efficient vaccination strategies could allow a fairer distribution from the start.

Ref:arxiv.org/abs/1001.0170: Speeding Up Disease Extinction With a Limited Amount of Vaccine