The classic epidemiological model concept of the basic reproductive number R_{0} nominally represents the secondary infections resulting from a single primary infection in an immunologically naïve population. Macdonald developed the original formulation for malaria [1, 2], and others have extended the theory over time [3]. This concept has become ubiquitous in epidemiological modelling, and while it can be helpful, it can also cause confusion and even misguided planning if used incorrectly. The basic theory is that if R_{0} is reduced to a controlled reproductive number R_{c}, the number of secondary infections resulting from a single primary infection under control measures, below 1, then the disease will disappear eventually. Each infection is replaced by less than one infection, and prevalence exponentially decays to zero. While this simplified equilibrium view is true, planning eradication efforts requires investigation of the dynamics and timelines as described by Macdonald and others [4, 5], not just the equilibrium conditions.

This R_{0} tends to be implemented in simple compartmental models or ordinary differential equations, characterized by an exponential distribution for infection durations. A reduction of R_{0} to R_{c} <1 corresponds to exponential decay of the infected population. The fastest possible decay of the infected population without active clearance of infections is attained when R_{c} = 0 and has the inverse of the average duration of infection as its decay constant. For short duration infections, such as flu, the infectious reservoir decays rapidly. Malaria, on the other hand, has average infection durations of up to six months [6–8]. As such, exponential decay of the infectious reservoir can take years under the best case, and over ten years if R_{c} = 0.9. Figure 1 shows the decay of the malaria infectious reservoir for four values of R_{c}, with infection duration averaging 180 days. A controlled reproductive number of 0.9, 0.7, 0.5, or even 0 exhibits slow declines in the total number of infected individuals. In contrast, a disease with R_{c} = 0.9 but an infectious duration of just 3.5 days rapidly depletes its infectious reservoir.

When human infections are not actively cleared and elimination is driven by attaining R_{c} <1 solely through transmission reductions, this slow decay has serious programme implications that limit the chances of elimination. For many diseases the durations of interventions that reduce transmission, such as vaccines, are much longer than the durations of infection. As such, transmission reductions that reduce R_{0} below 1 can succeed in driving local eliminations of the pathogen while the interventions are still efficacious without replacement. For malaria however, the average infection duration of six months is only a factor of six away from three-year lifetimes of insecticide-treated bed nets (ITNs). Indoor residual spraying (IRS) campaigns need to be repeated every two to six months depending on the active ingredient [9] in areas with year-round transmission and need to be repeated yearly in highly seasonal settings. These frequencies are considerably faster than the timelines to elimination based on transmission reductions alone. The current lead vaccine candidate, RTS,S [10], has a duration of efficacy that is not longer than ITNs. As seen in Figure 1, the infectious reservoir may still be quite robust by the time these interventions need to be replaced, or else the reproductive number will rise back above 1 without having achieved elimination.

The result of this matching of decay constants and intervention durability drives elimination programmes down one of two routes. The first is that elimination campaigns need to reduce transmission for many years to maintain R_{c} <1, with repeated distributions. The second possible route is to actively clear the infectious reservoir with drug-based campaigns in order to reduce the duration of infections and to achieve rapid drops in prevalence. Reducing the duration of infections in fact also drives further decreases in R_{c}[3].This makes malaria more like diseases of shorter infectious duration and more susceptible to transient transmission-driven reductions of R_{c} <1.