Use of growth functions to describe disease vector population dynamics—Additional assumptions are required and are important

Some important diseases are carried by vectors which can infect susceptible hosts or be infected by infectious hosts. Growth functions may be applied to the vector population. Many growth functions can be constructed from an underlying differential-equation model where birth and mortality processes are identified explicitly. However, this is possible in a variety of ways. The model could be applied to (say) a midge population where infection by a virus is possible when a susceptible midge bites an infectious host, giving rise to incubating and then infectious categories of midge. An infectious midge can then, if biting an uninfected host, infect that host, leading to pathogenic consequences. The submodel used for the vector population partially defines overall disease dynamics, which not only depend on the growth function chosen but also on any extra assumptions about birth and mortality processes which do not affect the growth function per se. The logistic equation is an example of a sigmoidal asymptotic growth function, the asymptote being attained when births and mortality occur at equal rates. Traditionally in the logistic, the interpretation is that birth rate is constant and mortality rate increases as the population increases. A rate function, constant or variable, may be added to both birth and mortality rates without changing total vector population dynamics from the logistic. However, the dynamics of propagation of infection can be substantially different with different assumptions about birth and mortality. This is highly relevant to studies of diseases such as bluetongue in ruminants (involving midges) or dengue in humans (where mosquitoes are involved).