James’ ideas are well supported by the theoretical principles of malaria transmission. Pioneered by Ronald Ross [
11] they were formulated by George Macdonald [
12‐
14] in terms that, although subject to ongoing analysis and modification, are still broadly accepted. A central concept presented by Macdonald is that of the “
basic reproduction number for malaria”—the number of new cases resulting from each existing case of malaria—now designated R0, is given in what is widely known as a Ross/Macdonald equation [
14]. In such an equation (e.g., Box
1) R0 is, among other factors, a function of ‘M’, the number of adult female malaria vector mosquitoes in a defined locality, and of ‘a’, their daily biting rate upon humans. Reducing either or both M and a reduces R0. Because R0 is proportional to a
2 (Box
1), anything that reduces a, the daily rate at which vector mosquitoes take a human blood meal, is particularly powerful in reducing the value of R0. Improved house-type construction that is secure against mosquito entry reduces a. It is likely that there are other malaria transmission-reducing effects that result from those types of housing that resist entry by mosquitoes. These include their impact upon mosquito egg-laying rates due to the lower frequency of blood meals. Recent analysis indicates that such effects on M (Box
1) could also significantly reduce R0 [
15]. Improvements in housing are, therefore, as James proposed, likely to have contributed greatly to the reduction leading to disappearance of indigenous malaria transmission in England.
Box 1 A Ross/Macdonald equation
The following formulation is given of a Ross/Macdonald equation:
R0, as defined by Macdonald (see below) is “The number of infections distributed in a community as a direct result of a single primary non-immune case”. In the case of malaria he proposed the following relationship between R0 and its determining factors:
R0 = (M/H)a2.c.b.pv/(−lnp.r)
M is the density (e.g., numbers per sq km) of adult female vector Anopheles mosquitoes in a (defined) locality;
H is the density of humans (i.e., numbers per sq km) in this locality;
a is the proportion of female mosquitoes that feed on humans each day;
c is the proportion of blood meals on an infected human that will yield an infection in the mosquito;
b is the proportion of bites by an infectious mosquito that infect a human;
p is the daily probability of survival of a mosquito;
v is the time in days from a human blood meal until a mosquito becomes potentially infectious to a human;
r is the daily rate at which each infected human completely clears infection.
As pointed out in the text, the probability that an adult female mosquito takes a human blood meal, ‘a’, has a powerful effect upon R0 because it is squared in the equation for R0. For example reducing a by a half reduces R0 by a quarter; reducing a by 90% reduces R0 to 1% and so on. Compared to many traditional forms of rural housing in Sri Lanka, modern housing with sealed doors, windows, eaves, etc. and interiors with fewer resting places for mosquitoes, reduces the human biting rate by mosquitoes, a, many fold. In addition, reducing the frequency of mosquito blood meals proportionately reduces their egg-laying rate and hence the numbers of adult female mosquitoes ‘M’.
The Ross/Macdonald equation, presented here, derives from that given by George Macdonald in 1952 [
12] when he put forward the concept of a reproduction number for malaria. Indeed, this appears to have been the first statement of the idea of a reproduction number, R0 (which he called Z0 at the time), for any infectious disease. As he would point out [
13] “
Should this (number, i.e. R0) fall below one, successive generations of cases would be smaller than their predecessors and the disease would disappear; should it be greater than one, successive generations would increase and the disease would mount in the population.”