16.4 Disease & Immunity
The biggest failing of Ross’s model, perhaps, was that it did not make any attempt to grapple with acquired immunity to malaria. It had always been clear that immunity to malaria was important because the prevalence of infection declined throughout adolescence and was consistently lower in adults, and because disease and severe disease were common in young children. The data accumulated through years of studying malaria, done as part of malaria therapy, provided supporting evidence for immunity. There was a difference in outcomes from being exposed to the same parasite (homologous challenge) compared with a different parasite (a heterologous challenge). Immunity had something to do with the number of different parasites that a person had seen.
The first model to grapple with immunity was the Garki Model [74]. The main idea in the Garki Model was that it would be possible to understand malaria dynamics by expanding the number of compartments: the population was sub-divided into two non-immmune or semi-immune. Infection dynamics were tracked separately within each immune category: the infections would clear faster from semi-immune individuals, they were are not infectious, and they are less likely to test positive if they were infectious. Some features of the Garki model seem odd in retrospect: there were two infected states for non-immunes (\(y_1\) and \(y_2\)), but only one for semi-immunes; there was no way to lose immunity; and the assumption that semi-immunes are not infectious.
The Garki Model has had a poweful influence on malaria modeling. Several models since then have expanded on various themes. Several compartment models have been developed that replicate infection dynamics across immune stages: we call this stage-structured immunity.
In the Garki Model, we can simulate the immuno-epidemiology of cohorts as they age. Eventually, the cohort would settle to an equilibrium. At that point, everyone is semi-immune, a sizable fraction remains non-immune after a century. By the time the cohort reaches the steady state, everyone in the cohort has died. If we focus on the dynamics in the first two decades of life, prevalence rises as people become infected, and then it falls as people become semi-immune. The changing epidemiology as cohorts age is an important feature of malaria. In models like this, the concept of a steady state teaches us something, but the models draw attention to the sharp changes in malaria that occur throught the first 20 years of life. We can adapt the idea of steady state to suit our needs – under constant exposure, cohorts trace out stable orbits as they age. These stable orbits are a basis for understanding malaria dynamics vs. age.
One application of these stable orbits is to understand the the relationship between age and infection prevalence as a function of exposure. Curiously, the Garki Model captures the basic shape of age-PfPR curves, but it does not get the details right. When we start to look at the factors affecting the PfPR by age in populations, we must acknowledge the need to add other features: drug taking and chemoprotection; differences in exposure that arise for a number of reasons; anemia, perhaps; seasonality. Not everything is about immuno-epidemiology.