Transmission dynamics

Transmission dynamics are in a very real sense the driving force behind the overall population dynamics of pathogens, but they are often the aspect about which we have least data (compared, say, to the fecundity of parasites or the death rate of infected hosts). We can, none the less, build a picture of the principles behind transmission dynamics (Begon et al., 2002).

The rate of production of new infections in a population, as a result of transmission, depends on the per capita transmission rate (the rate of transmission per susceptible host 'target') and the number of susceptible hosts there are (which we can call S). In turn, per capita transmission rate is usually proportional, first, to the contact rate, k, between susceptible hosts and whatever it is that carries the infection. It also depends on the probability, p, that a contact that might transmit infection actually does so. Clearly, this probability depends on the infectiousness of the parasite, the susceptibility of the host, and so on. Putting these three components together we can say:

the rate of production of new infections = k • p • S. (12.1)

The details of the contact rate, k, the contact rate are different for different types of transmission.

• For parasites transmitted directly from host to host, we deal with the rate of contact between infected hosts and susceptible (uninfected) hosts.

• For hosts infected by long-lived infective agents that are isolated from hosts, it is the rate of contact between these and susceptible hosts.

• With vector-transmitted parasites we deal with the contact rate between host and vector (the 'host-biting rate'), and this goes to determine two key transmission rates: from infected hosts to susceptible vectors and from infected vectors to susceptible hosts.

But what is it that determines the per capita contact rate between susceptibles and infecteds? For long-lived infective agents, it is usually assumed that the contact rate is determined essentially by the density of these agents. For direct and vector-borne transmission, however, the contact rate needs to be broken down further into two components. The first is the contact rate between a susceptible individual and all other hosts (direct transmission) or all vectors; we can call this c. The second is then the proportion of those hosts or vectors that are infectious; we call this I/N, where I is the number of infecteds and N the total number of hosts (or vectors). Our expanded equation is now:

the rate of production of new infections = c • p • S •(I/N). (12.2)

We need to try to understand c and I/N in turn.

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