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Table 1 Values, descriptions and sources of the parameters driving the base metapopulation model of transmission (\(i =\lbrace TC; MB; UJ; NK; BB; MP\rbrace\))

From: Predicting the impact of border control on malaria transmission: a simulated focal screen and treat campaign

Parameter Description Value Source
N Population size for the six patches \(2.5 \ \times 10^6\) [58, 59]
\(\mu\) Mortality/birth rate \(\frac{105}{10{,}000}\) [60]
\(\sigma\) Period between liver stage and onset of gametocytemia 2 weeks [6164]
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 [66, 67]
\(pf_{yr}\) 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 [33, 68]
\(i_3\) 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) [63, 70]
\(pc_2\) 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  
\(\frac{1}{\alpha }\) 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  
\(\frac{1}{z}\) 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  
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