### Article

## Dry season malaria risk prediction in holoendemic area: the potential of small scale mathematical modeling

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Published: | September 8, 2005 |
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### Outline

### Text

#### Introduction and objectives

About 3000 children die every day in Africa from malaria [Ref. 1]. The mortality is largely limited to children under the age of five [Ref. 2]. Malaria transmission has a strong seasonal pattern driven by weather conditions, which influence the mosquito vector population dynamics [Ref. 3]. Further understanding of the transmission dynamics of malaria and weighing of potential interventions can facilitate the decision making process for malaria control. A key tool for this understanding is the use of models. The objective of this study is to enhance our understanding of the transmission dynamics of malaria in the dry season in a holoendemic region, Nouna district, Burkina Faso in West Africa using process-based modeling.

#### Material and methods

The study took place in four different sites in Nouna health district, located in the dry savannah area of Northwest Burkina Faso. The four sites, distanced 19-44 km from each other, were chosen to represent different ecological and human settings.

A cohort of 867 children, aged 6 to 60 months was followed up from December 2003 to May 2004. Participants were visited every week in their households. Axillary temperature was measured and blood sample taken for febrile (>=37.5°C) children for *Plasmodium falciparum (Pf)* detection. A child with any *Pf* detected was classified as infected.

In addition, in each sites in four different houses randomly selected, mosquito population abundance was monitored monthly by standard CDC Light Trap (LT) [Ref. 4] and Human Landing Trap (HLT) [Ref. 5]. HLT was performed every two months for calibration and evaluation of the LTC.

A mathematical model was developed on the basis that mosquitoes are transmitting the parasite from an infectious human to a susceptible human (S). The human infection (I) takes **
v
** days to develop gametocytes and hence become infectious (G). A proportion of all infectious human,

**clear the infection every day. Each mosquito bites**

*q***humans a day without preference. After biting an infectious human,**

*b***fraction**

*a***of mosquitoes will become infected within**

*γ***days for the rest of their lifespan. A fraction**

*c***of all mosquitoes die each day. This model was used to predict monthly incidence case of**

*m**Pf*infection and compare to the observed. The goodness of fit statistic is the sum of the monthly square difference between observed and model incidence . The best fit of the model parameters was achieved by determining successively the best value for each parameter.

#### Results

**
Pf
**

**Infection patterns:**The overall incidence was 313 cases among 867 participants during a six-month period involving 255 participants. The incidence of Pf infection consistently decreased from December to January in all sites followed by a second peak ending with a decrease towards the end of the dry season.

**Entomological patterns: **In all the four sites Culex is the most prominent genus throughout the observation period. In total, the Anopheles-Culex ratio is 1/6. The semi-urban site has the most number of Culex compared to the rural sites all together (622 vs 174). Gambiae was the most prominent among the Anopheles species (65%), funestus (33.3%) and nili (1.6%). The number of mosquitoes drops from December to January and rises again in February.

**Mathematical modeling:** The best fit of the model to the clinical data is shown in figure 1 [Fig. 1] where monthly prediction of cases is plotted (curve) with the observed (black square). There is a close match between the model prediction and observed cases for all months except March and May. The variance between the observed and the predicted monthly incidence was 835.

#### Discussion

*Anopheles* is more frequent in the rural sites while *Culex* is more frequent in the urban site. The site with the highest prevalence of *Anopheles spp.* may be explained by the proximity of a perennial river. The drop in numbers observed in January is probably a result of the cool dry weather. The minimum temperature in December and January, was below 16°C, which is the threshold for *An. gambiae s.l.* larval development [Ref. 6]. The extremely hot temperatures from March onwards seem to have reduced the viability of the mosquito [Ref. 7].

**Infection patterns: **While there was strong variation in the vector prevalence between sites, there was no significant difference between *Pf* incidence in the four sites. This could be a result of better protection by the inhabitants of mosquito prevalent sites from nuisance bites. The incidence in all sites dropped significantly but did not clear before the onset of the rainy season in July.

**Mathematical modeling: **The good fit of the mathematical model output to the observed *P. falciparum* infection incidence suggests that the model is indeed a good representation of the transmission dynamics. The discrepancies in May and March may be random variation due to the small number of cases. For both months, though the observed case counts are not significantly different from the previous month (Chi test; p= 0.09 and p=0.12 respectively). The model in this case is driven not by weather conditions but by actual observed vector prevalence. As a result, it can follow malaria incidence even in a dry season. To allow this model to be used as a predictive tool, the vector population itself must be simulated. The model is not very sensitive to the length of the sporogonic cycle. Similarly, time from human infection to gametocyte development is not a key element in determining the incidence level. The incidence of malaria is highly dependent on two key parameters, which are the daily mortality rate of the vector and the parasite clearance rate in human which can both be influenced by public health interventions.

#### Acknowledgments

Thank you to the Nouna Health Research Team and to the families of the participants. This project was funded by DFG and UBS Optimus Foundation.

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