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Anopheles funestus and Anopheles gambiae are malaria vector mosquitoes. Knowing their resting behavior is important for implementing control methods. The aim of this study was to investigate the resting behaviour of the two malaria mosquitoes. The study was conducted in Kilombero River Valley and mosquitoes were collected using indoor and outdoor traps from 2012-2015. Poisson mixed models were used to quantify the impact of environment variables on resting behaviour. A log ratio rate between the type of trap and its interaction with environmental variables was used to determine if there was a change over time in the resting behaviour. A total of 4696 mosquitoes were resting indoors of which 57% were A. funestus and 43% were A. gambiae. Similarly, a total of 12,028 mosquitoes were resting outdoor of which 13% were A. funestus and 87% were A. gambiae. Temperature was significant and affected the resting behaviour of A. funestus. Humidity, saturation deficit and temperature were significant variables influencing the resting behaviour of A. gambiae. A. funestus was resting indoor while A. gambiae was resting outdoor over time generally. The findings of this study on the effects of environmental variables and the variations in the resting behaviour of A. gambiae and A. funestus could be used as a guide to implementing appropriate intervention measures such as indoor residential spraying (IRS), insecticide treated nets (ITNs) and mosquito repellents.

Mosquitoes are insects that can cause morbidity and mortality through the diseases they can carry. Beck-Johnson et al. [

Mosquitoes feed on a range of different host vertebrates and some species have developed a characteristic host preference, feeding preferentially from humans, mammals other than human and birds [

Understanding the biology and behavior of Anopheles mosquitoes can help understand how malaria is transmitted [

Kreppel et al. [

In the study of Mayagaya et al. [

Kabula et al. [

Count data refers to observations that can potentially take any non-negative integer value [

The Poisson model can be considered as the standard model for count data [

f ( y i , μ i ) = μ i y i e − μ i y i ! , y ≥ 0 y is an integer, (1)

where E ( Y i ) = μ i and V a r ( Y i ) = μ i .

Hence, the Poisson distribution is characterized by a linear relationship between its variance and mean. To model μ i using explanatory variables x r , the log link function is used, although other choices are also available. More specifically, we write

log ( μ i ) = β 0 + ∑ r = 1 p x i r β r , (2)

where;

• β 0 is the model intercept.

• β r are the regression coefficients which regulate the effects of the explanatory variables x r .

• log ( . ) = log e ( . ) computes the natural logarithm.

If the variance of the data is greater than the mean, the Poisson assumption is questionable. We refer to this case as over-dispersion. Ignoring over-dispersion can lead to invalid inferences on the regression relationship [

These models are only defined by specification of their mean, variance and a dispersion parameter k [

We point out that a distributional form for the variable Y i is not required for fitting of the model and making inference on μ i . If k = 1, we recover the identity relationship between the mean and the variance of the Poisson model. Another advantage of the quasi Poisson model is it can be fitted using the same algorithms for the Poisson model [

The negative binomial model is obtained by assuming that the mean μ i of the Poisson model is Gamma distributed [

f ( y i ; μ i , k ) = Γ ( y i + k ) Γ ( k ) × Γ ( y i + 1 ) × ( k μ i + k ) k × ( 1 − k μ i + k ) y i (3)

where k is the dispersion parameter. The symbol Γ denotes the gamma function and is defined as Γ ( y + 1 ) = y ! . The mean and variance of Y i are now E ( Y i ) = μ i and V a r ( Y i ) = μ i + μ i 2 k . The Poisson model is recovered as a limiting case for k → ∞ .

This model is an extension of the standard Poisson model by the inclusion of the random effects in the linear predictor. One example is given by the random intercept model which is obtained as follows. Let Z i for i = 1 , 2 , 3 , ⋯ , n denote random variables, having joint multivariate Gaussian distribution with mean 0 and covariance matrix Σ Z . We then assume that Y i , conditionally on Z i are mutually independent Poisson variables with mean μ i such that,

log ( μ i ) = β 0 + ∑ r = 1 p x i r β r + Z i , (4)

It can be shown that this model has larger variance than the standard Poisson model. This model can also be further extended by allowing the regression coefficients β r to vary across the observations. In Equation (4), β r would then be replaced by β i r (assumed to follow a Guassian distribution with some appropriate mean and variance). More importantly, this model assumes that the effect of x r on the response is not homogeneous but might depend on both measured and unmeasured variables.

The main difference of the outlined modelling approach with respect to the previous models, is that over-dispersion is accounted for by specification of the conditional mean of Y i for given latent variables (or random effects) Z i and/or β i r . Quasi-poisson and negative binomial models, instead, allow for over-dispersion through the parameter k which regulate the relationship between the marginal mean and variance of Y i . These two different approaches are then used to answer substantially different research questions. The former approach is useful when it is of interest to model the different sources of heterogeneity inherent to the data. The latter techniques are instead more appropriate when inference should be drawn on the general population. For these reasons, we consider Poisson mixed models to be more suitable to address the specific objectives of the present analysis.

The collection of the malaria vector, A. funestus and A. gambiae mosquitoes were collected in four villages of Kilombero River Valley by the use of indoor and outdoor traps over four years from 2012 to 2015. Each village was visited several times over the four years and each time, mosquitoes were trapped inside and outside the houses. Different houses were chosen each time a visit was made to the villages and collected mosquitoes over four (4) nights in each house. Information on temperature, humidity and saturation deficit were also collected from each visited household. To catch mosquitoes inside required a different trap than to catch them outside. Traps were set in the evening at 6 pm and emptied in the morning at 6 am. For every inside trap there are 10 outside traps.

The variables of interest used in this study were determined according to the study objectives and are shown in

The collected data were subjected to verification for consistency, uniformity and accuracy with the researcher in charge. Data were then exported and analyzed in the R software environment [

Let U t ∼ N ( 0 , σ u 2 ) and V t ∼ N ( 0 , σ v 2 ) be independently and identically distributed. Let Y i t denote the monthly counts of mosquitoes at village i at time t . We then assume that conditionally on U t and V t , Y i t are mutually independent Poisson variables with mean η i t μ i t where η i t is the number of traps used to catch the mosquitoes. Using a log link-function, we then write

log ( μ i t ) = α 0 + β 0 T d t + γ 0 T x i t + η t δ i t + μ t , (5)

η t = α 1 + β 1 T d t + V t , (6)

where,

• x i t is vector of dummy variables identifying each of the four villages;

• d t is a vector of environmental variables;

• δ i t is a binary indicator of the type of trap, taking value 1 if outdoor and 0 if indoor;

• U t is a random intercept which accounts for extra-Poisson variation induced by unmeasured explanatory variables;

• V t is a random effect accounting for unmeasured explanatory variables which affect the log-ratio between the rate of mosquitoes outdoor and indoor;

• η t corresponds to the log ratio between the rate of indoor and outdoor mosquitoes at time t.

Variable | Description of variable |
---|---|

V c | The village visited (KID = Kidugalo, MIN = Minepa, LUP = Lupiro and SAG = Sagamaganga) |

T m | The type of mosquito trapped i.e. Ag = A. gambiae and Af = A. funestus. |

T p | Indicates the type of trap used that is in = Indoor and out = Outdoor. |

T r | The difference between the maximum and minimum temperature recorded in degree Celsius. |

H r | Average relative humidity per month. |

S d | Average monthly saturation deficit measured in pressure vapor. |

M d | The density is the number of monthly mosquito counts per trap in the study area and is given by mosquito counts divided by number of traps. |

The standard error is computed by utilizing the formulation,

Standard error = Standard deviation Sample size

To understand how the resting behaviour of mosquitoes changes over time, we use Equation (6) which corresponds to the log-ratio between the rate of indoor and outdoor mosquitoes and therefore, represent our target for inference. The variable selection procedure was to start with a full model including interactions with all environmental variables and type of trap, i.e. indoor or outdoor. Then, the variables with a p-value greater than 5% (i.e. considering a 95% confidence level) are removed from the model. The process is repeated until all the variables have p-values less than 5%.

We now look at the total number of mosquitoes collected by type of mosquito and trap in the study area, that is, for A. funestus and A. gambiae.

In

For both A. funestus and A. gambiae, we observe a similar pattern in the resting behaviour outdoor while the pattern seems different indoors. In almost all the villages, A. funestus was mostly caught indoor while A. gambiae was caught primarily resting outdoor. This implies that A. funestus is likely to be more exposed to insecticide treated nets (INTs) and other chemicals applied to the walls such as indoor residual spraying (IRS). However, for A. gambiae mostly resting outdoor reduces the risk of exposure to chemicals and bites humans and animals outside.

In order to quantify the association between mosquito abundance and environmental factors and trap location, we carried out the analysis separately for A. funestus and A. gambiae.

The first model considered was for A. funestus. After applying the variables selection procedure described in Section 3.2, only temperature range showed a significant association. The final model is shown in

Parameter | Estimate | Std.Error | P value |
---|---|---|---|

α 0 | 0.3265 | 0.2810 | 0.2451 |

LUP | −0.2733 | 0.0576 | 2.09e−06 |

MIN | −0.4816 | 0.0496 | 2e−16 |

SAGE | −0.5815 | 0.0682 | 2e−16 |

T p ( o u t ) | −0.9108 | 0.2697 | 0.0007 |

T r | 0.0991 | 0.0188 | 1.36e−07 |

T p ( o u t ) : T r | −0.1971 | 0.0302 | 6.81e−11 |

The coefficient of Lupiro village indicates that the mosquito density is 0.7609 times the density of A. funestus mosquitoes in Kidugalo village. The density of A. funestus mosquitoes in Minepa village is 0.6178 times the density of mosquitoes in Kidugalo village. In Sagamaganga, the A. funestus mosquito density is 0.5591 times that in Kidugalo village. 40% of the density of A. funestus mosquitoes were caught outdoor implying that 60% were caught indoor. The percentage change in the A. funestus density is by 10% for every 1˚C increase in the temperature range. The interaction effect between temperature and type of trap was significant. This suggests that the effect on the density of A. funestus resting outdoors is a change by 0.8211 compared to resting indoors for every 1˚C change in temperature range.

Temperature is an important environmental factor affecting the resting behavior of A. funestus. We observe a significant relationship between temperature and the density of A. funestus. This implies that, a higher temperature range explains the change in the resting behaviour of A. funestus. It suffices to note that temperature is dependent on several factors such as location of the village, surroundings and structure of the buildings in the area.

We now carry out diagnostic checks of the residuals.

We can observe in

We now look at the model for A. gambiae. In the final model, temperature range, humidity range and saturation deficit showed a significant association with mosquito density. Also, there were interactions between humidity range and saturation deficit with type of trap. The estimates are given in

Parameter | Estimate | Std.Error | P value |
---|---|---|---|

α 0 | −1.2632 | 0.3990 | 0.0016 |

LUP | 1.2866 | 0.0596 | 2e−16 |

MIN | 1.7102 | 0.0524 | 2e−16 |

SAG | 0.5019 | 0.0494 | 2e−16 |

T r | −0.8404 | 0.0297 | 2e−16 |

H r | 0.1349 | 0.0125 | 2e−16 |

S d | 2.8338 | 0.2172 | 2e−16 |

H r : T p ( o u t ) | 0.0675 | 0.0116 | 6.17e−09 |

S d : T p ( o u t ) | −0.9438 | 0.2234 | 2.39e−05 |

The coefficient of Lupiro village indicates that the mosquito density is 3.6205 times the density of A. gambiae mosquitoes in Kidugalo village. The density of A. gambiae mosquitoes in Minepa village is 5.5301 times the density of mosquitoes in Kidugalo village. In Sagamaganga, the A. gambiae mosquito density is 1.6519 times that in Kidugalo village. The A. gambiae mosquito density decreases by 0.4315 for every 1˚C increase in the temperature range. The change in the density of A. gambiae mosquitoes is 1.1444 for a 1 unit change in the average relative humidity range. A one unit change in the average monthly saturation density changes the density of A. gambiae mosquito by 17.01. The effects of the density of A. gambiae mosquitoes resting outdoors is 1.0698 times the density resting indoors for a unit change in the average relative humidity range. The effect on the density of A. gambiae mosquito resting outdoor is a change in the density by 0.3891 compared to resting indoors for a unit change in the average monthly saturation deficit.

All environment variables were statistically significant in explaining the suitability of the environment in the resting behaviour of A. gambiae. An increase in the average relative humidity implies more A. gambiae mosquitoes resting outdoor. [

We now check for model fit by carrying out a diagnostic plot of residuals.

As can be seen from the correlogram plot in

We now compare the resting behavior of A. funestus and A. gambiae by village and use of Equation (6) for the log ratio between the rate of indoor and outdoor mosquitoes. The analysis is based on a comparison of the abundance of A. funestus and A. gambiae trapped indoor and outdoor. When the value of the log ratio is zero i.e. η t = 0 , there is no difference in the log ratio between the mosquitoes resting indoors and outdoors. When η t > 0 implies that the log ratio of mosquito density outdoor is greater than the density indoor and conversely when η t < 0 .

We start by looking at the log ratio rate between indoor and outdoor resting of A. funestus mosquitoes. The log ratio relationship is shown in

As can be seen in

same pattern. Also, we observe that in all villages there are no clear signs of any shift in the resting behaviour of A. funestus mosquitoes from indoor to outdoor.

Investigating the resting behavior of A. funestus mosquito over time found that it was mostly resting indoor. There were no clear variations in the resting behaviour of A. funestus in all the four villages as observed in

Now, we consider the log ratio rate of A. gambiae mosquito resting indoors and outdoors. The plot is shown in

Similarly, it can be seen from

The density of A. gambiae mosquitoes in all the villages was mostly more abundant outdoor over time. This can be attributed to the fact that A. gambiae breeds in places such as rice fields, puddles, sunlit pools and bites both human and animals. For instance, the shift in the resting behavior in some of the villages can be explained by malaria control programs. In Minepa and Lupiro, the main activities are cultivation of rice and thus, A. gambiae is mainly breeding in such fields. While in Sagamaganga and Kidugalo, they have a lot of cattle and therefore this explains the shift in the resting behavior of Anopheles to biting animals outdoor.

We conclude that A. gambiae and A. funestus show a remarkable temporal variation in their resting behaviour. A. funestus was the most abundant malaria vector indoor while A. gambiae was more abundant outdoor in the study area. The finding is in agreement with the results of [

The authors would like to express their gratitude to Ifakara Health Institute for providing the data.

The authors declare no conflicts of interest regarding the publication of this paper.

Moyo, E., Munachoonga, C., Lubumbe, D., Banda, A., Ngunyi, A. and Jere, S. (2019) Modelling of the Abundance of Malaria Mosquitoes Using Poisson Mixed Model. Journal of Applied Mathematics and Physics, 7, 2492-2507. https://doi.org/10.4236/jamp.2019.710169