The Anderson-May Framework
Roy Anderson and Robert May revolutionized parasitology in the late 1970s by applying mathematical ecology to host-parasite systems. Their framework distinguishes macroparasites (helminths, ectoparasites) from microparasites (viruses, bacteria) based on a crucial difference: macroparasite pathology depends on burden — the number of parasites per host — not merely on infection status. This requires tracking the full distribution of parasites across the host population.
The Negative Binomial Distribution
A universal finding in parasitology is that macroparasites are overdispersed among hosts. The negative binomial distribution, characterized by mean burden and aggregation parameter k, describes this pattern. When k is small (k < 1), most hosts have few parasites while a minority carry extremely heavy burdens. This 20/80 pattern (20% of hosts harbor 80% of parasites) has profound implications for control — treating the most heavily infected individuals removes a disproportionate share of the parasite population.
R0 and Transmission Dynamics
The basic reproduction number R0 represents the average number of successful offspring per adult parasite in a fully susceptible host population. When R0 > 1, the parasite can establish and persist; below 1, it goes extinct. The model reveals how R0 depends on transmission rate, host recovery, parasite-induced mortality, and the aggregation pattern — each offering a potential point of intervention.
Control Strategy Implications
Adjust the parameters to explore different control strategies. Reducing beta (transmission) through vector control or sanitation lowers R0. Increasing gamma (recovery) through mass drug administration accelerates parasite clearance. The aggregation parameter k determines whether uniform mass treatment or targeted treatment of high-burden individuals is more efficient — a question central to current WHO helminth control policy.