Table 3 Descriptions of state variables, parameters, and derived parameters used in the model
State variable or parameter | Description and units |
|---|---|
State variables | |
Pk | Number of imported infections in patch k. Humans. |
Tk | Number of introduced infections in patch k. Humans. |
Dk | Number of indigenous infections in patch k. Humans. |
Parameters | |
Nk | Total number of people in patch k (assumed to be constant). Humans. |
βk | The effective malaria transmission rate from humans to other humans in patch k. Day−1. |
θij | The proportion of time the average resident of patch j spends in patch i. ∑iθij = 1 ∀ j. Dimensionless. |
μ | Natural infection clearance rate. Day−1. |
\({\tau }_{k}^{(h)}\) | Ratio of malaria prevalence in the index household tested in RCD as compared to the general population in patch k. |
\({\tau }_{k}^{(n)}\) | Ratio of malaria prevalence in neighbouring households tested in RCD as compared to the general population in patch k. |
\({\nu }_{k}^{(h)}\) | Number of people tested in the index household during follow-up per index case in patch k. Dimensionless. |
\({\nu }_{k}^{(n)}\) | Number of people tested in neighbouring households during follow-up per index case in patch k. Dimensionless. |
ρ | Rapid diagnostic test sensitivity. Dimensionless. |
η | The proportion of cases arriving at the health facility that are followed up. Dimensionless. |
ξk | The daily rate at which an infected individual seeks treatment in patch k. Day−1. |
Derived parameters | |
Sk | Number of susceptible humans in patch k, i.e. Sk = Nk − Pk − Tk − Dk. Humans. |
Ik | Proportion of humans who are infectious in patch k, i.e. (Pk + Tk + Dk)/Nk. Dimensionless. |
φk | Treatment rate due to RCD programme in patch k. Day−1. |
ιk | Total number of cases arriving at a health facility in patch k. Humans per day. |
