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. 2013 Feb 18:12:65.
doi: 10.1186/1475-2875-12-65.

A regional-scale, high resolution dynamical malaria model that accounts for population density, climate and surface hydrology

Adrian M Tompkins  1 , Volker Ermert
Affiliations

A regional-scale, high resolution dynamical malaria model that accounts for population density, climate and surface hydrology

Adrian M Tompkins et al. Malar J. .

Abstract

Background: The relative roles of climate variability and population related effects in malaria transmission could be better understood if regional-scale dynamical malaria models could account for these factors.

Methods: A new dynamical community malaria model is introduced that accounts for the temperature and rainfall influences on the parasite and vector life cycles which are finely resolved in order to correctly represent the delay between the rains and the malaria season. The rainfall drives a simple but physically based representation of the surface hydrology. The model accounts for the population density in the calculation of daily biting rates.

Results: Model simulations of entomological inoculation rate and circumsporozoite protein rate compare well to data from field studies from a wide range of locations in West Africa that encompass both seasonal endemic and epidemic fringe areas. A focus on Bobo-Dioulasso shows the ability of the model to represent the differences in transmission rates between rural and peri-urban areas in addition to the seasonality of malaria. Fine spatial resolution regional integrations for Eastern Africa reproduce the malaria atlas project (MAP) spatial distribution of the parasite ratio, and integrations for West and Eastern Africa show that the model grossly reproduces the reduction in parasite ratio as a function of population density observed in a large number of field surveys, although it underestimates malaria prevalence at high densities probably due to the neglect of population migration.

Conclusions: A new dynamical community malaria model is publicly available that accounts for climate and population density to simulate malaria transmission on a regional scale. The model structure facilitates future development to incorporate migration, immunity and interventions.

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Figures

Figure 1
Figure 1
Schematic of the VECTRI model. The top row shows the larvae status divided into a series of bins representing the fractional development state. The ’X’ in each bin represents the density of larvae in a specific fractional growth stage. The middle block represents the vector state in two dimensions: the egg development within the female and the infective state. The lower row models the host infective state. The curved arrows represent the progression direction of the larvae, vector and host state, while the straight red arrows mark the parasite transmission pathways between host and vector.
Figure 2
Figure 2
Larvae Flushing. Fractional reduction in larvae survival rate (Kflush) as a function of larvae growth stage (Lf) and rain rate as implemented in VECTRI.
Figure 3
Figure 3
Vector to host transmission. Contour plot of Pv→h as a function of Pvh and EIRa. The horizontal dashed line highlights Pvh = 0.3 as specified by the default VECTRI model. The vertical line marks EIRa = 365, for which Pv→h would equal Pvh if the distribution in biting rate were not taken into account.
Figure 4
Figure 4
Surface hydrology. An subsection of a multi-year VECTRI integration for Bobo-Dioulasso showing the evolution of model water fraction for three rainy seasons.
Figure 5
Figure 5
Sensitivity of pond model to parameter settings. Simulated mean EIR for multi-year VECTRI integrations at Bobo-Dioulasso between 1973 and 2006 with each pixel giving the value for an parameter setting according to certain wmax and Kw values, with each panel representing a different infiltration rate.
Figure 6
Figure 6
Equilibrium integrations. Equilibrium integrations of (a) VECTRI and (b) LMM2010 as a function of constant input of daily mean temperature (T2m) and daily rainfall amounts.
Figure 7
Figure 7
Observations and simulations of EIR and CSPR. Box-and-whisker plots of the VECTRI and LMM2010 simulated annual Entomological Inoculation Rate (EIRa; in infectious bites per human per year) for eight West African locations. The box-and-whisker plots of the LMM2010 are illustrated in blue. VECTRI results in terms of rural and urban areas are taken green and red, respectively. Also the latitudinal, longitudinal position, and used population density (km-2) is indicated. Climate varies from a semi-arid (Podor) to a tropical climate (Douala). Field EIRa observations are furthermore included as brown squares, black dots and blue triangles in rural, urban and irrigated areas, respectively. The number of field observations is entered behind the location names in the following order: 1) rural, 2) urban, and 3) irrigated observations. The number of clustered observations on the logarithmic scale is indicated by a digit above the symbols.
Figure 8
Figure 8
EIR and CSPR interannual variability in Bobo-Dioulasso. Simulated and observed malaria transmission in the area of Bobo-Dioulasso. (a) Annual EIR rates (EIRa; in infectious bites per human per year) and (b) annual mean CSPR (CSPRa; in %). The blue lines represent LMM2010 and the red and green lines VECTRI simulations (red: human population density H = 1037 km-2; green: H = 32.2 km-2). The brown squares, blue triangles, and black dots stand for observed EIRa and CSPRa values in rural, irrigated and urban areas, respectively. See [30] for a definition of rural, irrigated and urban areas and for the sources of the field observations (their Additional file Two; the Word Meteorological Organisation (WMO) station number 65510 of Bobo-Dioulasso is assigned to the data).
Figure 9
Figure 9
Seasonal transmission in Bobo-Dioulasso. Monthly mean EIR rates (EIRm) for (a) LMM2010 (b) rural VECTRI (density 32.2 km-2) and (c) urban VECTRI (density 1037 km-2). The large letter ‘X’ highlights the month in which the model produces a maximum in EIR. The start (‘S’), peak (‘X’) and end (‘E’) months for transmission measured in various field campaigns are marked in smaller font. The rural observations (brown) are placed on the left of the square of a particular month, the irrigated observations (blue) in the middle and the urban observations (black) to the right.
Figure 10
Figure 10
Annual cycle of PR in Bobo-Dioulasso. Annual cycle of monthly mean asexual parasite ratio (PRm; in %) for a rural area near Bobo-Dioulasso from the 34 year simulation of VECTRI. The boxes mark the 25 and 75% quantiles while the whiskers give the minimum and maximum values.
Figure 11
Figure 11
Regional simulation of PR in Eastern Africa. Mean asexual parasite ratio (PR; fraction) from (a) a 10 year-long VECTRI integration for East Africa and (b) MAP PR analysis. See text for details of model integration and data source.
Figure 12
Figure 12
Joint probability function of PR. Joint probability density function of PR from MAP and VECTRI (a) with larvae growth rate fixed to 12 day cycle and (b) water temperature dependent growth rate according to [47].
Figure 13
Figure 13
Sensitivity of EIR to population density. VECTRI modelled annual EIR as a function of population density divided into Western and Eastern zones of Africa, and the field survey data adapted from Figure Two of [33] (see their Figure One for survey locations). The VECTRI integrations were rerun with a range of values for τzoo, shown by the thin bars, representing values of 35, 50 (default), 70 and 100 km-1 respectively from left to right.
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