Table 1 Values, descriptions and sources of the parameters driving the base metapopulation model of transmission (\(i =\lbrace TC; MB; UJ; NK; BB; MP\rbrace\))
Parameter | Description | Value | Source |
|---|---|---|---|
N | Population size for the six patches | \(2.5 \ \times 10^6\) | |
\(\mu\) | Mortality/birth rate | \(\frac{105}{10{,}000}\) | [60] |
\(\sigma\) | Period between liver stage and onset of gametocytemia | 2 weeks | |
r | Artemether Lumefantrine elimination half-life | 6 days | [65] |
\(\tau\) | Time to seek treatment | 1/2 weeks | Expert opinion |
ptf | Probability of treatment failure | 0.01 | [51] |
p | Proportion of local infected population receiving treatment | 0.95 | |
\(pf_{yr}\) | Proportion of foreign infected population that receive treatment in a local patch | \(pf_1 = 0.5851 \ (0.5850, 0.5853)\) (pre April 2005) \(pf_2= 0.7000 \ (0.6998, 0.7010)\) (post April 2005) | Estimated from model fitting process |
\(i_1\) | Duration of clinical infection before becoming asymptomatic | 0.7 weeks | [33] |
\(i_2\) | Duration of asymptomatic infection before becoming sub-patent | 5.5 weeks | |
\(i_3\) | Duration of sub-patent infection | 24 weeks | [33] |
\(\rho\) | Duration of clinical immunity | 5 years | [69] |
\(pc_1\) | Probability of clinical infection from naive individuals | 0. 9997 (0.9756, 0.9999) | |
\(pc_2\) | Probability of clinical infection from partially immune individuals | 0.883 (0.877, 0.888) | Estimated from data |
\(seas_i\) | Seasonal forcing function for foreign sourced cases | Derived from data | [10] |
\(\beta _i\) | Annual number of mosquito bites per person × proportion of bites testing positive for sporozoites for patch i | \(\beta _{TC} = 4.488 \ (4.178, 4.798)\) \(\beta _{MB} = 6.034 \ (5.967, 6.101)\) \(\beta _{UJ} = 0.655 \ (0.589, 0.723)\) \(\beta _{NK} = 1.546 \ (1.521, 1.571)\) \(\beta _{BB} = 4.436 \ (4.264, 4.609)\) \(\beta _{MP} = 99.065 \ (98.920, 99.210)\) | Estimated from model fitting process |
\(\lambda _i(t)\) | Force of infection | See Additional file 1 | Â |
\(\frac{1}{\alpha }\) | Rate of assimilation of population in sub-patch 2 (locals having returned from foreign travel) back into sub-patch 1 from whence they originated | 1.5 week−1 | Expert opinion |
\(\frac{1}{k}\) | Rate of movement between five Mpumalanga municipalities | 1/ 201.436 (1/204.833, 1/198.040) week−1 | Estimated from model fitting process |
\(\frac{1}{v_{yr}}\) | Maputo residents: rate of movement between Maputo and five Mpumalanga municipalities | \(\frac{1}{v_1}= 1/7{,}616.743\) week−1 \((1/7{,}663.186, 1/7{,}570.299)\) (pre April 2005) \(\frac{1}{v_2}= 1/3{,}227.213\) week−1 \((1/3{,}187.684, 1/3{,}266.742)\) (post April 2005) | Estimated from model fitting process |
\(\frac{1}{\varpi _{i,j}}\) | Maputo residents: rate of movement between Maputo and 5 Mpumalanga municipalities based on \(\frac{1}{v_{yr}}\) and distance between patches | See Additional file 1 | Â |
\(\frac{1}{z}\) | Mpumalanga residents: rate of movement between 5 Mpumalanga municipalities and Maputo | \(\frac{1}{z}= 1/359.462\) week−1 (1/361.057, 1/357.866) | Estimated from model fitting process |
\(\frac{1}{\zeta _{i,j}}\) | Mpumalanga residents: rate of movement between 5 Mpumalanga municipalities and Maputo based on \(\frac{1}{z}\) and distance between patches | See Additional file 1 | Â |
fwgt | Foreign movement weight intensity | 10.615 (10.512, 10.719) | Estimated from model fitting process |
lwgt | Local movement weight intensity | 1.419 (1.343, 1.495) | Estimated from model fitting process |
vef | Effectiveness of vector control | 0.9785 (0.9783, 0.9787) | Estimated from model fitting process |
\(vc_i[t]\) | Vector control coverage in patch i \(\times\) efficiency | Derived from data | Â |