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Table 1 Model parameters and notation

From: Theory of reactive interventions in the elimination and control of malaria

Symbol Parameter Assumed value or limits Source
\(I_{t}\) Number of infectious individuals at time t \(0 \le I_{t} \le 10000\)  
\(N\) Total human population \(N = 10,000\) Approximate population of Zambian health centre catchment
\(\beta\) Transmission parameter, i.e. the potential number of new infections per infected individual at the next time step \(\beta > 0\)  
\(\gamma\) Proportion of infectious population that remains infectious at next time step (which includes the removal of infections through passive detection) \(0 < \gamma < 1\)  
\(\varphi_{t}\) Number of infections detected (and treated) at time t \(\varphi_{t} > 0\)  
\(\varepsilon_{t}\) Escape probability: the proportion of infections that escape treatment at time t \(0 < \varepsilon_{t} < 1\)  
\(p\) Proportion of population that is (patently) infected \(0 < p < 1\)  
\(\upiota\) Number of index cases investigated per unit time \(\upiota > 0\)  
\(\upnu\) Number of neighbours of passively-detected index cases investigated \(0 < \nu < N\) Fixed property of programme
\(\uptau\) Targeting ratio: ratio of the size of a random sample that would be need to be tested and treated, to the number actually treated, in order to achieve the same number of effective treatments. This is a measure of clustering of malaria infections \(\uptau \ge 1\) Estimated from cross-sectional survey data