# Targeting Malaria Hotspots to Reduce Transmission Incidence in Senegal

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## Abstract

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## 1. Introduction

- Focused Mass Drug Administration (MDA), consisting of systematically treating individuals in a selected geographic area with antimalarial drugs, without screening for infection.
- Focused Mass Screen and Treat (MSAT), consisting of malaria screening, using a rapid diagnostic test and providing treatment to those with a positive test result, in a selected area.
- Seasonal Malaria Chemoprevention (SMC), consisting of intermittently administrating preventive antimalarial treatment to children during the main transmission period.
- Long-Lasting Insecticide-treated Nets (LLIN), intended to avoid mosquito bites, relying on physical and chemical barriers of manufactured nets.

## 2. Materials and Methods

#### 2.1. Study Area and Dataset

#### 2.2. Model Structure

_{kj}were estimated via the radiation model of human mobility [24] and is represented here as Equation (2):

#### 2.3. Model Calibration

#### 2.4. Hotspots Definitions and Interventions

- Low transmission period hotspots (LT hotspots) were defined as villages reporting at least one malaria case in the previous low transmission period (December to May).
- High transmission period hotspots (HT hotspots) were villages with the highest malaria incidences during the previous transmission season (June to November).
- High connectivity hotspots (HC hotspots) were villages highly connected to neighboring villages based on human mobility potential.

_{0}and I

_{I}were the cumulative incidences of malaria, respectively before and after intervention.

## 3. Results

#### 3.1. Parameters Estimates and Sensitivity Analysis

#### 3.2. Sensitivity of Hotspot Definitions

#### 3.3. Intervention Simulations

#### 3.4. Pre-Elimination/Elimination Stage

#### 3.5. Rebound Effects Due to Human Mobility

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## List of Abbreviations

LLIN | long-lasting insecticide-treated bed nets |

RDT | rapid diagnostic tests |

ACT | artemisinin-based combination therapy |

WHO | World Health Organization |

MDA | mass drug administration |

MSAT | mass screen and treat |

SMC | seasonal malaria chemoprevention |

SEIR | susceptible-exposed-infected-recovered |

GPS | global positioning system |

MCMC | Markov Chain Monte Carlo |

LT hotspots | low transmission period hotspots |

HT hotspots | high transmission period hotspots |

HC hotspots | high connectivity hotspots |

HTP | high transmission period |

LTP | low transmission period |

EIR | entomological inoculation rate |

IRS | indoor residual spraying |

## Appendix A

#### Appendix A.1. Model Description

- ${S}_{k}\left(t\right)$: proportion of humans susceptible to malaria infection.
- ${I}_{k}\left(t\right)$: proportion of blood-stage infected humans, with few gametocytes, not immune and positive to rapid diagnostic test (RDT).
- $P\left(t\right)$: proportion of humans with partial immunity (premunition). Individuals could remain in this state for many years, but could lose their immunity if pregnant or on cessation of exposure. They were assumed to be RDT positive and with few gametocytes.
- $G{a}_{k}\left(t\right)$: proportion of infected humans, gametocyte-positive, asymptomatic.
- $G{m}_{k}\left(t\right)$: proportion of infected humans, gametocyte-positive, symptomatic.
- ${R}_{k}\left(t\right)$: proportion of humans who were temporarily not susceptible to new infection, as a result of the prophylactic effect of treatment.
- $A{i}_{k}\left(t\right)$: proportion of female mosquitoes that carry sporozoites in their salivary glands.
- $A{s}_{k}\left(t\right)$: proportion of female mosquitoes that have survived the cycle and were free from malaria sporozoites.
- $m$: proportion of people in the overall population, who are away at a given time (visiting other villages than their own village).
- $\upsilon \left(t\right)$: anopheles’ density (ratio of the number of female anopheles to the number of humans, at time t).
- $\alpha $: number of bites per female anopheles per night.
- $\beta $: probability that a person bitten by an infectious mosquito becomes infected.
- ${\gamma}_{s}\left(t\right)$, ${\gamma}_{i}\left(t\right)$, ${\gamma}_{p}\left(t\right)$ and ${\gamma}_{a}\left(t\right)$ are rectangular pulse functions.$\gamma \left(t\right)=K=-\mathrm{log}\left(1-c\right)/\Delta $ where c represents coverage and Δ the duration of intervention in weeks.
- ${\gamma}_{s}\left(t\right)$: rate at which susceptible individuals are treated.
- ${\gamma}_{i}\left(t\right)$: rate at which blood-stage infected individuals are treated.
- ${\gamma}_{p}\left(t\right)$: rate at which naturally immune individuals are treated. Naturally immune individuals are assumed RDT positive. Susceptible individuals are RDT negative.
- ${\gamma}_{a}\left(t\right)$: rate at which asymptomatic gametocyte carriers are treated. Asymptomatic gametocyte carriers are assumed RDT positive.
- ${\gamma}_{m}\left(t\right)$: rate at which symptomatic gametocyte carriers are treated. This corresponds to access to care, in periods of no intervention.
- ${\eta}_{a1}$: transition rate from blood-stage infection, to asymptomatic gametocyte carriage.
- ${\eta}_{m1}$: transition rate from blood-stage infection, to symptomatic gametocyte carriage.
- ${p}_{1}$: transition rate from blood-stage infection to premunition.
- ${p}_{2}$: transition rate from premunition to blood-stage infection (loss of premunition).
- δ: transition rate from resistant to susceptible (loss of the protection due to treatment).
- ${\zeta}_{m}$: probability that a mosquito, biting a symptomatic gametocyte carrier, got infected.
- ${\zeta}_{a}$: probability that a mosquito, biting an asymptomatic gametocyte carrier, got infected.
- $\xi $: mortality rate of mosquitoes.
- ${Q}_{kj}$: relative probabilities of travel from remote locations j, to local village k.
- $r\left(t\right)$: rainfall at week t.

**Equation (A1) describes the variations in the proportion of susceptible individuals.**In each village k, individuals leave the susceptible compartment by getting infected. The human infection rate consists of the product of the anopheles density $\upsilon $, the frequency of mosquito bites $\alpha $, the human susceptibility to infection $\beta $ and the effective proportion of infected mosquitoes affecting village k, represented by $i$.

**Equation (A2) describes the variations in the compartment (I) of blood-stage infection.**New infections increased the compartment I by $\upsilon \times \alpha \beta S\times i$. Compartment I was decreased by gametocyte production ($-\left({\eta}_{a1}+{\eta}_{m1}\right)I$) and acquisition of premunition ($-{p}_{1}I$).

**Equation (A3) describes the variations in the compartment (P) of pre-immune.**The compartment increased by receiving individuals acquiring premunition after several blood-stage infections ($+{p}_{1}I$). The compartment decreased when infection was reactivated by loss of immunity ($-{p}_{2}P$) or by interventional treatment ($-{\gamma}_{p}P$).

**Equations (A4) and (A5) describe the variations in the compartments of gametocyte carriers.**Compartments of gametocyte carriers increased by receiving individuals from blood-stage infection ($+{\eta}_{a1}I$ or $+{\eta}_{m1}I$). These compartments could decrease by transition to resistant compartment because of treatment ($-{\gamma}_{a}\times Ga$ ,$-{\gamma}_{m}\times Gm$).

**Equation (A6) describes the variations in the resistant compartment.**This compartment was increased by individuals under treatment effects (usual malaria therapies or interventional drugs), coming from all compartments where an effective malaria treatment had been delivered. This compartment was depleted by the loss of protection ($-\delta R$), beyond drug half-life. Long-acting drugs dihydroartemisinin-primaquine and sulphadoxine-pyrimethamine-amodiaquine were used for MDA/MSAT and SMC, respectively, all yielding protection for about 4 weeks’ duration.

**Equation (A7) describes the variations in the proportion of infective mosquitoes.**The proportion of infective mosquitoes was the product of the frequency of mosquito bites ($\alpha $) and the effective proportion of infected humans (${i}_{m}$). The proportion of infective mosquitoes was decreased by deaths in mosquito population ($-\xi A{i}_{k}$).

**Equation (A8) details the effective proportion of infective mosquitoes in a location k taking account of human mobility.**This proportion is represented by $i=\left(1-m\right)A{i}_{k}+m{\displaystyle \sum}_{jk}^{}{Q}_{kj}A{i}_{j}$. The effective proportion of infected mosquitoes affecting village k is a weighted average of local proportions of infected mosquitoes $A{i}_{k}$ and remote proportions of infected mosquitoes ($A{i}_{j}$). The weights depended on the proportion of human mobility $m$ and also on the relative probabilities of travel from remote locations j to local village k (${Q}_{kj}$).

**Equation (A9) details the effective proportion of infected humans in a location k taking account of human mobility.**This proportion is represented by ${i}_{m}=\left(1-m\right)\left({\zeta}_{a}G{a}_{k}+{\zeta}_{m}G{m}_{k}\right)+m{\displaystyle \sum}_{j\ne k}^{}{Q}_{kj}\left({\zeta}_{a}G{a}_{j}+{\zeta}_{m}G{m}_{j}\right)$ as a weighted average of the local proportion of infected humans $\left({\zeta}_{a}G{a}_{k}+{\zeta}_{m}G{m}_{k}\right)$ and remote proportions of infected humans $\sum}_{j\ne k}{Q}_{kj}\left({\zeta}_{a}G{a}_{j}+{\zeta}_{m}G{m}_{j}\right)$, weekly. The weights depended on the proportion of human mobility ($m$) and on the relative probabilities of travel from remote locations j to local village k (${Q}_{kj}$). The susceptibility of mosquitoes to infection from humans (${\zeta}_{m}$) was assumed ten times higher from symptomatic than from asymptomatic (${\zeta}_{a}$) (expert opinion).

**Equation (A10) represents variations in anopheles’ density with respect to rainfall.**Anopheles density depends on deterministic environmental factors. Among these factors, accumulated rainfall in previous weeks was the most important. lag was the duration (in weeks) between rainfall and mosquito bites. Optimal lag was estimated using sensitivity analysis as the one minimizing the gap between model estimations and observations Figure A1.

**Figure A1.**Goodness of fit of malaria metapopulation model according to the assumed lag between rainfall and mosquito bites. Calibrations were undertaken on 2008 and 2010 transmission seasons. Optimization function computing the sum of squared residuals (SSR) were minimized for 6 weeks lag.

#### Appendix A.2. Model Parameters

Parameter Symbol | Parameter Description | References | Parameter Values | 95% C.I. |
---|---|---|---|---|

$\upsilon $ | Anopheles density in relation to hosts | [27,31] | 0–12 (min–max) | |

$\alpha $ | Mosquito biting rate | [45] | 0.46 bite/anopheles/night | |

$\beta $ | Human susceptibility to infection | [45] | 0.3 | |

EIR | Entomological Inoculation Rate | [46] | 0 to 2.16/per person/year | |

${\zeta}_{m}$ | Mosquito susceptibility to infection from symptomatic humans | [45] | 0.80 | |

${\zeta}_{a}$ | Mosquito susceptibility to infection from asymptomatic humans | Expert opinion | 0.08 $({\zeta}_{a}=0.1{\zeta}_{m}$) | |

${\eta}_{m1}$ | Transition rate from blood-stage parasitemia to symptomatic infection with gametocytemia | [47] | 0.1 days^{−1} | |

${\eta}_{a1}$ | Transition rate from blood-stage parasitemia to asymptomatic infection with gametocytemia | [47] | 0.1 days^{−1} | |

$\delta $ | Transition rate from post-treatment protection, to susceptible | [48,49] | 0.032 days^{−1} | |

$\xi $ | Daily mosquito mortality rate | [45] | 0.18 | |

${p}_{1}$ | Rate of the acquisition of premunition | fitted | 0.0002 days^{−1} | 0.0001–0.00035 days^{−1} |

${p}_{2}$ | Rate of the loss of premunition | fitted | 0.0002 days^{−1} | 0.0001–0.00035 days^{−1} |

${\gamma}_{m}$ | Usual recovery rate by access to care, not related to specific interventions | fitted | 0.37 days^{−1} | 0.20–0.51 days^{−1} |

$m$ | Proportion of people who are away from their home village at a given time | fitted | 0.01 | 0.09–0.2 |

Compartment | Assigned Value | Reference |
---|---|---|

${I}_{0}$ | ${I}_{0}\approx 0$. Proportion of plasmodium falciparum infection in humans, in dry season | [27,45] |

${P}_{0}$ | ${P}_{0}$ = 0.2, Proportion of pre-immune individuals | 0.16 [46] B0.27 [47] 0.23-0.32 [31] |

$G{m}_{0}$ | Proportion of symptomatic malaria in dry season. Average dry season incidence estimated from all the dataset (5years data) | [48] |

$G{a}_{0}$ | Proportion of asymptomatic gametocyte carriers were assumed 10 times lower than symptomatic (expert advice) | $\mathrm{Deduced}\text{}\mathrm{from}\text{}G{m}_{0}$ |

${R}_{0}$ | ${R}_{0}\approx G{m}_{0}$. Continuous access to treatment for symptomatic malaria. | $\mathrm{Deduced}\text{}\mathrm{from}\text{}G{m}_{0}$ |

$A{i}_{0}$ | $A{i}_{0}\approx 0.$ Proportion of female anopheles that carry sporozoites, in dry season | [27,45] |

${S}_{0}$ | ${S}_{0}=1-G{m}_{0}-G{a}_{0}-{R}_{0}-{P}_{0}$ | Calculated |

## Appendix B

#### Appendix B.1. Simulation of Interventions Targeting HT Hotspots

**Figure A2.**Decrease in malaria incidence while targeting one third of HT hotspots in Mbour, Senegal 2008–2012. The y-axis represents intervention efficacy (relative decrease in overall malaria incidence). (

**a**) Unique one-year intervention during rainy season, (

**b**) Repeated interventions on five consecutive rainy seasons, once per year, (

**c**) Unique one-year intervention during the dry season, (

**d**) Repeated interventions on five consecutive dry seasons, once per year.

#### Appendix B.2. Simulation of Interventions Targeting HT Hotspots

**Figure A3.**Mbour zone, Senegal, 2008–2012. Geographical coordinates of the 45 villages circles. Red circles represent connectivity hotspots and gray lines represent main connections between villages.

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**Figure 1.**Mbour zone, Senegal, 2008–2012. The geographical coordinates of the 45 villages are represented by black circles, and moving individuals by gray lines. The thickness of the lines reflects the number of trips.

**Figure 2.**Malaria transmission diagram at a local village $k$. Letter j stands for remote villages. Human compartments are ${S}_{k}$ (susceptible), ${P}_{k}$ (premunition), ${I}_{k}$ (blood-stage infection), $G{a}_{k}$ (asymptomatic carriage of gametocytes), $G{m}_{k}$ (symptomatic carriage of gametocytes) and ${R}_{k}$ (resistance due to treatment). Mosquito compartments are $A{i}_{k}$ (infected mosquitoes) and $A{s}_{k}$ (susceptible mosquitoes). The arrows represent the transition rates between compartments.

**Figure 3.**Sensitivity of model parameters in the malaria metapopulation model, Mbour, Senegal, 2008–2012. Right and left correspond to a parameter increase and decrease, respectively. Black and gray bars respectively represent a increase and decrease in total malaria cases, subsequent to parameter variations.

**Figure 4.**Decrease in malaria incidence while targeting low transmission (LT) hotspots in Mbour, Senegal, 2008–2012. The y-axis represents the relative decrease in malaria incidence for the overall area (45 villages). (

**a**) unique one-year intervention in the rainy season, (

**b**) repeated interventions over five consecutive rainy seasons, once per year, (

**c**) unique one-year intervention in the dry season, (

**d**) repeated interventions over five consecutive dry seasons, once per year. SMC12 corresponds to a theoretical schedule of uninterrupted monthly administration of SMC over 12 months.

**Figure 5.**Malaria incidence in the year following mass drug administration associated with vector control. Various definitions of hotspots were tested. The x-axis represents the percentage of villages included as hotspots. The y-axis represents the decrease in mosquito bites from baseline.

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## Share and Cite

**MDPI and ACS Style**

Sallah, K.; Giorgi, R.; Ba, E.-H.; Piarroux, M.; Piarroux, R.; Cisse, B.; Gaudart, J.
Targeting Malaria Hotspots to Reduce Transmission Incidence in Senegal. *Int. J. Environ. Res. Public Health* **2021**, *18*, 76.
https://doi.org/10.3390/ijerph18010076

**AMA Style**

Sallah K, Giorgi R, Ba E-H, Piarroux M, Piarroux R, Cisse B, Gaudart J.
Targeting Malaria Hotspots to Reduce Transmission Incidence in Senegal. *International Journal of Environmental Research and Public Health*. 2021; 18(1):76.
https://doi.org/10.3390/ijerph18010076

**Chicago/Turabian Style**

Sallah, Kankoé, Roch Giorgi, El-Hadj Ba, Martine Piarroux, Renaud Piarroux, Badara Cisse, and Jean Gaudart.
2021. "Targeting Malaria Hotspots to Reduce Transmission Incidence in Senegal" *International Journal of Environmental Research and Public Health* 18, no. 1: 76.
https://doi.org/10.3390/ijerph18010076