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

Transmission model

The model presented in this paper is based on the metapopulation model described in
Silal et al. 9]. The malaria transmission model has a metapopulation structure where the population
of interest is divided into discrete patches under the assumption that individuals
in these patches exhibit homogenous behaviour. Rather than modelling transmission
in these patches in isolation, a metapopulation structure allows for transmission
in a particular patch to be influenced by transmission in other patches. In this study,
the area of interest is divided into six geographical patches: five patches for the
five municipalities in Ehlanzeni District [Thaba Chewu (TC), Mbombela (MB), Umjindi
(UJ), Nkomazi (NK) and Bushbuckridge (BB)] and one patch for Maputo province (MP).
Each patch is further divided into three sub-patches representing (1) the local population
currently in the patch, (2) the local population having returned from travel to a
foreign place (Maputo, if the patch is South African and vice versa) and (3) the population
from the foreign place currently in the patch (Figure 2b). A malaria transmission model is developed for each sub-patch where the sub-patch
population is divided into six compartments representing the population susceptible
to malaria (S), the population at the infectious stage that receives treatment (I),
the untreated symptomatic population at the infectious stage (C), the untreated asymptomatic
population at the infectious stage (A), the untreated asymptomatic, sub-patent ( 100 parasites/µL) infectious population (M) and the population susceptible to malaria,
but with prior asymptomatic infection (P) (Figure 2a). The liver and blood stages of the infection are incorporated as a delay in the
flow between the susceptible and infectious stage compartments. Flows between compartments
are governed by parameters described in Table 1. While the seasonal nature of transmission is incorporated in the model using forcing
functions, the mosquito population is not modelled directly as it is assumed that
the mosquito dynamics operate on a faster time-scale than the human dynamics and hence
the mosquito population may be considered to be at equilibrium with respect to changes
in the human population 42]. Transmission is modelled in weekly time steps.

Table 1. Values, descriptions and sources of the parameters driving the base metapopulation
model of transmission ()

Figure 2. Hybrid Metapopulation DE-IBM Model flow. a Compartment transmission model for each patch i (1–6) with sub-patch j (1–3) at time step t with compartments S susceptible, I infectious and treated (tr), C infectious, symptomatic and untreated (u), A infectious, asymptomatic and untreated, M Infectious, sub-patent and untreated and P susceptible with prior asymptomatic infection. b) Metapopulation structure highlighting human movement between each local patch and foreign patch 6. Other parameters are described in Table 1 and Additional file 1.

Human movements between patches are modelled in two ways. Local travel may occur between
the five Mpumalanga patches (from all five compartments in all three sub-patches).
Foreign travel may occur between the Maputo patch and the five Mpumalanga patches
(from all five compartments) as illustrated in Figure 2b. These movements are inversely weighted by distance so that movements between patches
that are closer together are more likely than movements between patches that are further
apart. A full description of the metapopulation transmission model is presented in
Additional file 1.

FSAT model

Figure 2b shows that only movement of the local Mpumalanga population returning from Maputo
(patch 6, sub-patch 3 to patches 1–5, sub-patch 2) and the foreign population travelling
to Mpumalanga from Maputo (patch 6, sub-patch 1 to patches 1–5, sub-patch 3) are subject
to the FSAT campaign as the purpose of the campaign is to prevent infections from
entering Mpumalanga. The FSAT model has an individual-based model structure so that
individual characteristics of the participants may be taken into account. Figure 3 depicts the algorithm applied to individuals in the FSAT model. The flow of local
and foreign populations from Maputo into Mpumalanga at each time step (week) is captured
and geographical destination patch, the sub-patch and disease status (susceptible,
infectious, sub-patent etc) are stored for each individual in that flow. The first
step is to simulate a parasite count for each individual dependent on their disease
status. The log-normal distribution was selected with distribution parameters in Table 2 as it captures the skewness of parasite count distribution. To test the impact of
take-up proportion, the campaign is modelled as being optional. Should an individual
not wish to be part of the campaign, their disease status is maintained and the simulation
is stopped. Depending on the diagnostic tool used, the processing times and hence
the number of tests able to be performed per week will differ. Should capacity be
available and an individual agrees to participate in the campaign, the individual
is screened. A positive screen occurs if the individual’s simulated parasite load
is greater than the detection threshold of the diagnostic tool in use. A positive
screen will result in the individual being treated. As the treatment is likely to
be a multiple-dose regimen, there is a chance that the individual may not adhere to
the full course and may run the risk of failing treatment. In the event of successful
treatment, the individual’s disease status is updated (e.g. Infectious to “Infectious
having received FSAT” where the individual is cured from malaria at a rate of recovery
dependent on the parasite clearance time of the drug) and the simulation stops. The
model parameters governing this IBM algorithm are displayed in Table 2.

Table 2. Values, descriptions and sources of the parameters driving the FSAT Individual Based
Model

Figure 3. FSAT IBM algorithm.

Hybrid metapopulation DE-IBM model

The metapopulation DE model and the IBM model are linked such that the IBM model is
nested in the DE model. At each time step, the DE model generates flows of a population
that leave one compartment and enter another compartment (in the various sub-patches
and patches). The IBM model takes the flow value at each time step once it has been
negated from a compartment, discretises it into individuals in a population, executes
the IBM algorithm, re-groups the individuals back into a population flow, and adds
the flow to its destination compartment. In this application, only the flows of local
and foreign people entering the five Mpumalanga patches from Maputo are interrupted
to perform FSAT using the IBM model. Further details on this hybrid modelling approach
are available in the Additional file 1.

Data fitting

The metapopulation transmission model is fitted to weekly case notification data from
Mpumalanga and Maputo Province from 2002 to 2008, and then validated with data from
2009 to 2012. Ethical approval for use of this secondary data was obtained from the
Mpumalanga Department of Health and the University of Cape Town Human Research Ethics
Committee. The Mpumalanga case data displays a characteristic triple peaked pattern
in the malaria season with peaks occurring in September/October, December/January
and April/May while the Maputo Province malaria season exhibited peaks in December
and April only 10]. The seasonal forcing functions, used to determine seasonal variation in transmission,
for the six patches are derived from the data using seasonal decomposition of time
series by LOESS (STL) methods for extracting time series components 43]. ACT drug therapy and the impact of IRS implemented between 2002 and 2008 are also
included in the model. In order to reach a steady state the model is run deterministically
from 1990 before being fitted to data from 2002. The model output (predicted weekly
treated cases) is fitted to the data from 2002 to 2008 using the maximum likelihood
approach by assuming an underlying Poisson distribution with rate as the number of treated cases per week. Several parameters as detailed in Table 1 are estimated through the data fitting process using the population-based global
search algorithm of particle swarm optimisation 44], 45]. The model with the estimated parameter values is then validated with a further 3
years of data (2009–2012). A full description of the data fitting method is presented
in Additional file 1. All model development, fitting and subsequent analysis was performed in R v3.02
46]. The particle swarm optimisation routine was performed using the R package hydroPSO
v0.3-3 47], 48].

Simulated FSAT

An FSAT campaign is tested on a stochastic version of the fitted model; the same intervention
is applied to multiple model runs such that its impact on local infections can be
described with a mean effect and a 95% confidence interval. Stochastic uncertainty
and parameter sensitivity has been accounted for as follows. The model is run stochastically
by treating each flow between compartments at each time point t as a random realisation of a Poisson process with rate , the deterministic flow value at that time, and by simulating the parameter values
uniformly from their 95% confidence intervals. The predicted impact of an FSAT campaign
at the Mpumalanga–Maputo border is presented with respect to coverage levels, thresholds
of detection, take-up proportions, target levels and typical diagnostic tools. To
facilitate accurate comparison of coverage levels, targets, thresholds and diagnostic
tools, the take-up proportion of FSAT is fixed at 100%. Take-up proportion itself
is explored at low, intermediate and high levels. The FSAT campaign is assumed to
run for 8 h a day, seven days a week with a maximum of three tests being conducted
simultaneously. This number of simultaneous tests is also considered at different
levels in the simulation. As malaria elimination is defined by the World Health Organisation
as zero incidence of locally contracted cases, the impact of the simulated FSAT campaign
is measured as the decrease in local infections as result of the campaign 7]. This impact is a function of the change in onward transmission resulting from fewer
imported infections entering Mpumalanga (due to FSAT). All results are compared to
the base case of no FSAT, depicted in black in all figures. Each scenario was run
450 times so that results presented are the mean local infections per week with a
95% confidence interval shaded around the mean. In many cases, the shading is not
visible due to either narrow confidence intervals or a low resolution y-axis.

Diagnostic tools

Diagnosing malaria at a border point ideally requires a diagnostic tool that is both
sensitive, specific and has a short processing time. Several tools have been considered
for this simulation (Table 3). The Rapid Diagnostic Test (RDT) currently in use at South African public health
facilities has a theoretical detection threshold of 200 parasites/µL and a maximum
processing time of 20 min. Microscopy in experienced hands may exhibit a sensitivity
of 50 parasites/µL but is more likely to have a sensitivity in the region of 100 parasites/µL.
Real-time quantitative polymerase chain reaction (qPCR) and loop-mediated isothermal
DNA amplification (LAMP) are very sensitive tools with qPCR needing sophisticated
equipment for a processing time of 3 h. LAMP on the other hand is a less complex technique
with a 1 h processing time 49]. These diagnostic tools are also compared to a highly sensitive hypothetical RDT
with a standard process time of 20 min and a detection threshold of 5 parasites/µL.

Table 3. Descriptions of diagnostic tools used in FSAT model