Background
Methods
Transmission model
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
| |
\(\frac{1}{\alpha }\)
| 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 |
FSAT model
Parameter | Description | Value | Source |
---|---|---|---|
fson
| Focal Screen and Treat Switch | Binary | |
cov
| FSAT coverage | 25; 50; 75; 100% | Values to be tested |
Baseline FSAT coverage | 70% | Assumed | |
fsprop[t] | Proportion Screened and Treated through Border Control | fson \(\times\) cov | |
opt
| Take-up proportion for FSAT | 25; 50; 75; 100% | Values to be tested |
adh
| Probability of adherance | 0.90 | [51] |
fail
| Probability of treatment failure | 0.01 | [51] |
rep
| Number of screens tests performed simultaneously | 3 | Assumed |
\(\mu _C\)
| Geometric mean of log-normal parasite distribution for clinical infections | 25,000 | |
\(\sigma _C\)
| Log standard deviation of log-normal parasite distribution for clinical infections | 1.3 | |
\(\mu _A\)
| Geometric mean of log-normal parasite distribution for asymptomatic infections | 1,000 | |
\(\sigma _A\)
| Log standard deviation of log-normal parasite distribution for asymptomatic infections | 1.5 | |
\(\mu _S\)
| Geometric mean of log-normal parasite distribution for sub-patent infections | 50 | [55] |
\(\sigma _S\)
| Log standard deviation of log-normal parasite distribution for sub-patent infections | 0.75 | Assumed |
Hybrid metapopulation DE-IBM model
Data fitting
Simulated FSAT
Diagnostic tools
Tool | Detection threshold (parasites/µL) | Process time (h) | Target per week (tests per/h \(\times\) 3 reps \(\times\) 8 h \(\times\) 7 days) | Source |
---|---|---|---|---|
RDT | 200 | 0.33 | 504 | [49] |
Microscopy | 100 | 2.25 | 75 | Expert opinion, [49] |
qPCR | 1 | 3 | 63 | [49] |
LAMP | 5 | 1 | 168 | |
Hypothetical RDT | 5 | 0.33 | 504 |
Results
Estimation of parameters through data-fitting
Diagnostic tools
Coverage, detection thresholds, take-up proportions and target levels
Factor | Standardised regression coefficient | 95% confidence interval |
---|---|---|
Coverage | 0.41795 | (0.38181, 0.45409) |
Take-up proportion | 0.36715 | (0.33100, 0.40329) |
Adherence | 0.00095 | (−0.03520, 0.03709) |
Detection threshold | −0.47861 | (−0.51475, −0.44247) |
Target level | 0.34027 | (0.30413, 0.37642) |