Background
Other recent studies in Zambia and Benin have also shown that withdrawal or relaxation of vector control efforts can lead, over short time periods, to resurgences in malaria prevalence, clinical incidence and transmission [5, 6]. The Cohen et al. review makes it clear that reductions in funding and weakening of control programmes, especially the withdrawal of vector control, are strongly associated with resurgence. However, it only examined events where resurgence did occur, and did not include cases where vector control interventions were withdrawn with no resurgence. A full picture of the risk of reductions in vector control effort or withdrawal must also consider the potential for resurgence not to occur after reductions in or withdrawal of vector control.Reasons for funding reductions or cessation were not clear for all events, but in several, donors appear to have reallocated funding specifically because successful reductions in malaria burden had occurred. [Emphasis ours]
Methods
Outline
Baseline African scenario parameterization
Baseline Western Pacific scenario parameterization
Experiment set-up
-
Transmission level: Levels of baseline (pre-intervention) EIR of {0.1, 0.5, 1, 2, 5} infectious bites per adult per year are simulated to represent a range of historical transmission intensities, with an upper limit of 5 infectious bites per adult per year because it is unlikely that an area with a higher historical transmission rate would consider withdrawing vector control unless it could permanently reduce receptivity.
-
Coverage of vector control interventions: Coverage of LLINs is varied with values of {0, 0.2, 0.5, 0.8} of the proportion of the population sleeping under an LLIN on a given night during the VC period to simulate a wide range of vector control coverage.
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Importation rate: Importation rates of {0.1, 1, 10} infections per 1000 people per year are chosen to simulate a reasonable range of potential importation. Imported infections are simulated as new infections (not caused by the local mosquito population) in randomly chosen individuals with a probability drawn from a Poisson distribution, implicitly assuming that the imported cases have a similar level of acquired immunity to the local population.
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Case management coverage: Values of 20, 50, 80% are assumed for the percentage of all uncomplicated malaria cases are treated effectively to simulate a wide range of case management coverage.
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Active case detection: Mass screen and treat (MSAT) interventions every 3 months using rapid diagnostic tests (RDTs) and artemether–lumefantrine is simulated at coverage levels of {0, 2.5, 10, 20%} of the population to model increased active surveillance. Although it is unlikely that any programme would sustain quarterly MSAT campaigns of 20% of its population for 20 years, this is included as an approximation of targeted active surveillance.
-
Model variants: Fourteen model variants, as described in more detail below, from a previous publication [16] are simulated to explore the implications of various model assumptions such as varying rates of decay of acquired immunity in humans and correlations of heterogeneities in humans.
-
Stochasticity: Ten random seeds per model parameterization are simulated to include the effects of stochasticity.
Model variants
-
R0001: Base OpenMalaria model.
-
R0063: Mass action of the force of infection.
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R0065: Mass action of the force of infection.
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R0068: Mass action of the force of infection.
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R0111: Fixed decay in effective cumulative exposure (half-life 1000 years).
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R0115: Fixed decay in effective cumulative exposure (half-life 10 years).
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R0121: Fixed decay in immune proxies (half-life 1000 years).
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R0125: Fixed decay in immune proxies (half-life 10 years).
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R0131: Estimation of decay in effective cumulative exposure (half-life 1187 years).
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R0132: Estimation of decay in immune proxies (half-life 14 years).
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R0133: Estimation of decay in effective cumulative exposure (half-life 250 years) and immune proxies (half-life 19 years).
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R0670: Heterogeneity in susceptibility to comorbidity.
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R0674: Uncorrelated heterogeneities in access to treatment and susceptibility to comorbidity.
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R0678: Heterogeneity in access to treatment.
Precision and bias
Results
Descriptive results of OpenMalaria simulation outputs
Var. | Lev. |
\(\mathbf {Elim}_0\)
| %0
|
\(\mathbf {Elim}_1\)
| %1
|
\(\mathbf {Elim}_{\text{all}}\)
| %all
|
---|---|---|---|---|---|---|---|
Elim. | 0 | 31,232 | 100.0 | 0 | 0.0 | 31,232 | 31.0 |
1 | 0 | 0.0 | 69,544 | 100.0 | 69,544 | 69.0 | |
p < 0.0001 | All | 31,232 | 100.0 | 69,544 | 100.0 | 100,776 | 100.0 |
Resur. | 0 | 1530 | 4.9 | 44,263 | 63.6 | 45,793 | 45.4 |
1 | 29,702 | 95.1 | 25281 | 36.4 | 54,983 | 54.6 | |
p < 0.0001 | All | 31,232 | 100.0 | 69,544 | 100.0 | 100,776 | 100.0 |
Var. | Lev. |
\(\mathbf {ITN}_0\)
| %0
|
\(\mathbf {ITN}_{0.2}\)
| %0.2
|
\(\mathbf {ITN}_{0.5}\)
| %0.5
|
\(\mathbf {ITN}_{0.8}\)
| %0.8
| ITNall
| %all
|
---|---|---|---|---|---|---|---|---|---|---|---|
Elim.
| 0 | 23,729 | 94.2 | 7397 | 29.4 | 106 | 0.4 | 0 | 0.0 | 31,232 | 31.0 |
1 | 1467 | 5.8 | 17,797 | 70.6 | 25,084 | 99.6 | 25,196 | 100.0 | 69,544 | 69.0 | |
p < 0.0001 | All | 25,196 | 100.0 | 25,194 | 100.0 | 25,190 | 100.0 | 25,196 | 100.0 | 100,776 | 100.0 |
Resur.
| 0 | 1741 | 6.9 | 11770 | 46.7 | 15,382 | 61.1 | 16,900 | 67.1 | 45,793 | 45.4 |
1 | 23,455 | 93.1 | 13,424 | 53.3 | 9808 | 38.9 | 8296 | 32.9 | 54,983 | 54.6 | |
p < 0.0001 | All | 25,196 | 100.0 | 25,194 | 100.0 | 25,190 | 100.0 | 25,196 | 100.0 | 100,776 | 100.0 |
Var. | Lev. |
\(\mathbf {CM_{\mathrm {0.2}}}\)
|
\(\mathbf {\%_{\mathrm {0.2}}}\)
|
\(\mathbf {CM_{\mathrm {0.5}}}\)
|
\(\mathbf {\%_{\mathrm {0.5}}}\)
|
\(\mathbf {CM_{\mathrm {0.8}}}\)
|
\(\mathbf {\%_{\mathrm {0.8}}}\)
|
\(\mathbf {CM_{\mathrm {all}}}\)
|
\(\mathbf {\%_{\mathrm {all}}}\)
|
---|---|---|---|---|---|---|---|---|---|
Elim.
| 0 | 11,439 | 34.0 | 10,269 | 30.6 | 9524 | 28.4 | 31,232 | 31.0 |
1 | 22,161 | 66.0 | 23,326 | 69.4 | 24,057 | 71.6 | 69,544 | 69.0 | |
p < 0.0001 | All | 33,600 | 100.0 | 33,595 | 100.0 | 33,581 | 100.0 | 100,776 | 100.0 |
Resur.
| 0 | 11,646 | 34.7 | 15,770 | 46.9 | 18,377 | 54.7 | 45,793 | 45.4 |
1 | 21,954 | 65.3 | 17,825 | 53.1 | 15,204 | 45.3 | 54,983 | 54.6 | |
p < 0.0001 | All | 33,600 | 100.0 | 33,595 | 100.0 | 33,581 | 100.0 | 100,776 | 100.0 |
Regression results
Var. | Lev. |
\(\mathbf {EIR_{\mathrm {0.1}}}\)
|
\(\mathbf {\%_{\mathrm {0.1}}}\)
|
\(\mathbf {EIR_{\mathrm {0.5}}}\)
|
\(\mathbf {\%_{\mathrm {0.5}}}\)
|
\(\mathbf {EIR_{\mathrm {1}}}\)
|
\(\mathbf {\%_{\mathrm {1}}}\)
|
\(\mathbf {EIR_{\mathrm {2}}}\)
|
\(\mathbf {\%_{\mathrm {2}}}\)
|
\(\mathbf {EIR_{\mathrm {5}}}\)
|
\(\mathbf {\%_{\mathrm {5}}}\)
|
\(\mathbf {EIR_{\mathrm {all}}}\)
|
\(\mathbf {\%_{\mathrm {all}}}\)
|
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Elim. | 0 | 3785 | 18.8 | 4886 | 24.2 | 5249 | 26.0 | 7205 | 35.7 | 10107 | 50.1 | 31,232 | 31.0 |
1 | 16,352 | 81.2 | 15,274 | 75.8 | 14910 | 74.0 | 12,955 | 64.3 | 10,053 | 49.9 | 69,544 | 69.0 | |
p < 0.0001 | All | 20,137 | 100.0 | 20,160 | 100.0 | 20159 | 100.0 | 20,160 | 100.0 | 20,160 | 100.0 | 100,776 | 100.0 |
Resur. | 0 | 15,652 | 77.7 | 12,268 | 60.9 | 9390 | 46.6 | 6393 | 31.7 | 2090 | 10.4 | 45,793 | 45.4 |
1 | 4485 | 22.3 | 7892 | 39.1 | 10769 | 53.4 | 13,767 | 68.3 | 18,070 | 89.6 | 54,983 | 54.6 | |
p < 0.0001 | All | 20,137 | 100.0 | 20,160 | 100.0 | 20,159 | 100.0 | 20,160 | 100.0 | 20,160 | 100.0 | 100,776 | 100.0 |
Var. | Lev. |
\(\mathbf {IIR_{\mathrm {0.1}}}\)
|
\(\mathbf {\%_{\mathrm {0.1}}}\)
|
\(\mathbf {IIR_{\mathrm {1}}}\)
|
\(\mathbf {\%_{\mathrm {1}}}\)
|
\(\mathbf {IIR_{\mathrm {10}}}\)
|
\(\mathbf {\%_{\mathrm {10}}}\)
|
\(\mathbf {IIR_{\mathrm {all}}}\)
|
\(\mathbf {\%_{\mathrm {all}}}\)
|
---|---|---|---|---|---|---|---|---|---|
Elim. | 0 | 10,455 | 31.1 | 10,512 | 31.3 | 10,265 | 30.6 | 31,232 | 31.0 |
1 | 23,134 | 68.9 | 23,083 | 68.7 | 23,327 | 69.4 | 69,544 | 69.0 | |
p = 0.10 | All | 33,589 | 100.0 | 33,595 | 100.0 | 33,592 | 100.0 | 100,776 | 100.0 |
Resur. | 0 | 21,085 | 62.8 | 14,281 | 42.5 | 10,427 | 31.0 | 45,793 | 45.4 |
1 | 12,504 | 37.2 | 19,314 | 57.5 | 23,165 | 69.0 | 54,983 | 54.6 | |
p < 0.0001 | All | 33,589 | 100.0 | 33,595 | 100.0 | 33,592 | 100.0 | 100,776 | 100.0 |
Var. | Lev. |
\(\mathbf {AS_{\mathrm {0}}}\)
|
\(\mathbf {\%_{\mathrm {0}}}\)
|
\(\mathbf {AS_{\mathrm {0.025}}}\)
|
\(\mathbf {\%_{\mathrm {0.025}}}\)
|
\(\mathbf {AS_{\mathrm {0.1}}}\)
|
\(\mathbf {\%_{\mathrm {0.1}}}\)
|
\(\mathbf {AS_{\mathrm {0.2}}}\)
|
\(\mathbf {\%_{\mathrm {0.2}}}\)
|
\(\mathbf {AS_{\mathrm {all}}}\)
|
\(\mathbf {\%_{\mathrm {all}}}\)
|
---|---|---|---|---|---|---|---|---|---|---|---|
Elim.
| 0 | 7804 | 31.0 | 7812 | 31.0 | 7830 | 31.1 | 7786 | 30.9 | 31,232 | 31.0 |
1 | 17,389 | 69.0 | 17,382 | 69.0 | 17,367 | 68.9 | 17,406 | 69.1 | 69,544 | 69.0 | |
p = 0.98 | All | 25,193 | 100.0 | 25,194 | 100.0 | 25,197 | 100.0 | 25,192 | 100.0 | 100,776 | 100.0 |
Resur. | 0 | 10,499 | 41.7 | 10,793 | 42.8 | 11,672 | 46.3 | 12,829 | 50.9 | 45,793 | 45.4 |
1 | 14,694 | 58.3 | 14,401 | 57.2 | 13,525 | 53.7 | 12,363 | 49.1 | 54,983 | 54.6 | |
p < 0.0001 | All | 25,193 | 100.0 | 25,194 | 100.0 | 25,197 | 100.0 | 25,192 | 100.0 | 100,776 | 100.0 |
Dependent variable: | ||
---|---|---|
Resurgence | 95% C.I. | |
Mean API during VC (per 1000) | 1.077*** | (1.072, 1.082) |
Case Management Cov. | 0.021*** | (0.019, 0.023) |
EIR | 3.304*** | (3.239, 3.371) |
(10x) Active Surv. Cov. | 0.590*** | (0.574, 0.606) |
0.2 ITN | 0.152*** | (0.136, 0.170) |
0.5 ITN | 0.066*** | (0.058, 0.075) |
0.8 ITN | 0.040*** | (0.035, 0.045) |
IIR 1 | 10.409*** | (9.784, 11.079) |
IIR 10 | 16.165*** | (14.998, 17.427) |
R0063 | 0.839*** | (0.751, 0.938) |
R0065 | 0.442*** | (0.394, 0.496) |
R0068 | 0.798*** | (0.715, 0.892) |
R0111 | 0.873** | (0.782, 0.975) |
R0115 | 0.619*** | (0.554, 0.692) |
R0121 | 1.041 | (0.933, 1.162) |
R0125 | 1.356*** | (1.217, 1.512) |
R0131 | 1.344*** | (1.205, 1.499) |
R0132 | 1.860*** | (1.669, 2.074) |
R0133 | 1.241*** | (1.113, 1.384) |
R0670 | 1.068 | (0.957, 1.192) |
R0674 | 2.520*** | (2.261, 2.810) |
R0678 | 3.170*** | (2.844, 3.535) |
Constant | 1.296*** | (1.128, 1.488) |
Observations | 100,776 | |
Log Likelihood | − 27,995.100 | |
Akaike Inf. Crit. | 56,036.200 |
Discussion
Dependent variable | ||
---|---|---|
Time to resurgence | 95% C.I. | |
Mean API during VC (per 1000) | 1.038*** | (1.036, 1.040) |
Case Management Cov. | 0.484*** | (0.468, 0.500) |
EIR | 1.271*** | (1.265, 1.278) |
(10x) Active Surv. Cov. | 0.901*** | (0.893, 0.910) |
ITN coverage | 0.281*** | (0.271, 0.291) |
IIR | 1.092*** | (1.089, 1.095) |
R0063 | 0.757*** | (0.727, 0.788) |
R0065 | 0.773*** | (0.743, 0.804) |
R0068 | 0.914*** | (0.878, 0.951) |
R0111 | 0.975 | (0.936, 1.014) |
R0115 | 0.958** | (0.921, 0.997) |
R0121 | 1.022 | (0.982, 1.063) |
R0125 | 1.078*** | (1.036, 1.121) |
R0131 | 1.050** | (1.009, 1.092) |
R0132 | 1.085*** | (1.043, 1.129) |
R0133 | 1.029 | (0.989, 1.070) |
R0670 | 1.032 | (0.992, 1.073) |
R0674 | 1.109*** | (1.066, 1.154) |
R0678 | 1.186*** | (1.140, 1.234) |
Observations | 70,908 | |
R2
| 0.302 | |
Max. possible R2
| 1.000 | |
Log likelihood | − 694,204.000 | |
Wald test | 26,609.350*** (df = 19) | |
LR Test | 25,491.790*** (df = 19) | |
Score (Logrank) test | 28,846.640*** (df = 19) |
Dependent variable | ||
---|---|---|
Severity | ||
Case Management Coverage | − 22.556*** | (− 24.298, − 20.813) |
EIR | 25.260*** | (25.017, 25.502) |
(10x) Active Surv. Cov. | − 22.729*** | (− 23.277, − 22.180) |
0.2 ITN | 114.306*** | (113.099, 115.513) |
0.5 ITN | 92.247*** | (91.040, 93.454) |
0.8 ITN | 82.173*** | (80.966, 83.380) |
IIR 1 | 13.928*** | (12.883, 14.973) |
IIR 10 | 42.540*** | (41.495, 43.586) |
R0063 | − 6.713*** | (− 8.973, − 4.454) |
R0065 | − 9.736*** | (− 11.994, − 7.477) |
R0068 | − 13.044*** | (− 15.303, − 10.786) |
R0111 | − 0.193 | (−2.451, 2.066) |
R0115 | − 3.134*** | (− 5.392, − 0.876) |
R0121 | 1.154 | (− 1.104, 3.412) |
R0125 | 7.293*** | (5.035, 9.552) |
R0131 | 3.567*** | (1.309, 5.825) |
R0132 | 9.814*** | (7.556, 12.072) |
R0133 | 4.119*** | (1.861, 6.377) |
R0670 | 2.113* | (− 0.145, 4.371) |
R0674 | 18.419*** | (16.161, 20.677) |
R0678 | 19.057*** | (16.799, 21.315) |
Constant | − 84.218*** | (− 86.361, − 82.076) |
Observations | 100,776 | |
R2
| 0.490 | |
Adjusted R2
| 0.490 | |
Residual Std. Error | 69.120 (df = 100,754) | |
F Statistic | 4,603.479*** (df = 21; 100,754) |