Simple Models
In This Section
To introduce the basics, we start with a very short introduction to Ross’s ideas about a priori pathometry, and a short historical discussion about the origins of the Ross-Macdonald model [1]. Next, we take some time to focus on the blood feeding and parasite transmission.
Our starting point for introducing dynamical systems models for malaria in populations is a set of three vignettes. Each one describes some basic aspects of malaria transmission and infection dynamics:
We present dynamical system describing malaria transmission and infection dynamics that is consistent with ideas and analyses that Macdonald published in the early 1950s [2–5]. we call it The Ross-Macdonald Model.
We discuss what it means to Solve Dynamical Systems.
We introduce threshold concepts and The Basic Reproductive Number.
Next, we present a closely related system, published in 1982 by Aron & May [6], that is easier to extend and apply. We like it for two reasons:
The variables are population densities, not fractions;
mosquito density is a variable (not a parameter) forced by emergence of adult mosquitoes from aquatic habitats.
We revisit the Ross-Macdonald model and discuss some of the critical concepts, including vectorial capacity, following the analysis of Smith & McKenzie [7].
In these vignettes, “The Ross-Macdonald Model” means the equations in our vignette: The Ross-Macdonald Model. In a broader sense, the Ross-Macdonald model is includes those equations and all of the basic theory that was developed around it [1].
Up Next
Up next:
We introduce malaria metrics
We discuss realism as a concern for malaria analysts.