### INTRODUCTION

*Anopheles*mosquitoes; thus, ITN coverage is one of the most commonly used and cost-effective malaria control strategies [3]. The use of ITNs has been reported to increase the protection of people in malaria endemic zones from 29% in 2010 to 50% in 2017. A significant increase in accessibility to ITN was also reported during the same period [1]. In most sub-Saharan African countries, ITN delivery is either subsidized or given free to populations at high-risk of malaria [4].

### MATERIALS AND METHODS

### Study area

### Sample design

### Malaria rapid testing and microscopy on thick blood smears

*Plasmodium falciparum*, the causative agent of malaria. The SD Bioline Malaria Ag P.f (Standard Diagnostic Inc.) test qualitatively detects the histidine-rich protein II (HRP-II) antigen of

*P. falciparum*in human whole blood. In addition to the SD Bioline Ag P.f. (Standard Diagnostic Inc.) rapid test, a thick smear was prepared on a slide for 75% of the households where malaria rapid diagnostic tests (RDTs) were performed. These blood smears were dried and packed carefully in the field, assigned barcode labels corresponding to the Biomarker Questionnaire, and then transported to the state-level laboratory, where they were stained. There were 18 designated staining sites in the states (1 site for each 2 states). The stained slides were then transferred to the Primary Testing Laboratory (ANDI Centre of Excellence for Malaria Diagnosis, Lagos University Teaching Hospital, Nigeria). Microscopy to determine malaria infection was carried out at this laboratory. External quality control was conducted on a selected proportion of the slides at the Secondary Testing Laboratory at the University of Calabar Teaching Hospital [15]. The diagnoses were stratified according to age, sex, and location.

### Spatial map

### Data likelihood and variable description

*C*={

*c*

_{1},…,

*c*}. These data were merged with the geographical dataset supplied by DHS, which housed data on ITN coverage, environmental factors and other socioeconomic factors already aggregated at the cluster level. After deleting inconsistent entries, information from the remaining 1,325 clusters was used for the study. The response variable was the prevalence of malaria, which was defined as a binomial experiment where n independent trials corresponded to the total number of people tested in each cluster while the number of people who tested positive for malaria is the number of successes. The covariates were ITN coverage, aridity, rainfall, maximum temperature, and proximity to water.

_{n}*X*=(

*X*

_{1},…,

*X*) and a spatial structure component

_{k}*ϕ*=(

*ϕ*,…

_{k}*ϕ*) in a spatial generalized linear mixed model, as given in equation 1.

_{k}*C*are represented by

_{k}*ϕ*captures the remaining spatial autocorrelation after the effect of the independent variables had been factored into the model. Furthermore, in the context of the generalized model,

_{k}*Y*is a member of an exponential family (in this case binomial) with a distribution

_{k}*f*(

*y*|

_{k}*μ*) and a mean level of

_{k}*E*(

*Y*)=

_{k}*μ*. The function

_{k}*g*(.) is an invertible link function that relates the expected values of the response variable to the linear predictor, while

*β*=(

*β*

_{0},…..,

*β*

_{p}) are unknown regression parameters. This study adopted the logit link function with a data likelihood model given as;

*n*and

_{k}*θ*are the number of trials in the

_{k}*k*

_{th}area and the probability of success in a single trial, respectively. As is customary in Bayesian analysis, a multivariate Gaussian prior with a mean

*μ*=0 and a diagonal variance matrix

_{β}*∑*=100,000 was assumed for

_{β}*β*.

*ϕ*~

*N*(0,

*T*

^{2}

*Q*

^{-1}), where

*Q*is a precision matrix. This matrix controls the spatial autocorrelation structure of the random effects and is based on a non-negative symmetric

*n*×

*n*neighborhood

*W*. This is defined as a binary representation such that

*w*=1 if the areal units (

_{kj}*C*,

_{k}*C*) share a common border (denoted k-j), and is 0 otherwise. This specification forces (

_{j}*ϕ*,

_{k}*ϕ*) relating to geographically adjacent areas (that is, where

_{j}*W*=1) to be autocorrelated, whereas the random effects relating to non-contiguous clusters (

_{ij}*W*=0) are conditionally independent given the values of the remaining random effects. A Leroux prior [10] is specified as a set of n univariate full conditional distributions

_{ij}*f*(

*ϕ*|

_{k}*ϕ*) for

_{–k}*k*=1,…,

*n*(where

*Ø*)=(

_{–k}*ϕ*

_{1},….

*ϕ*

_{1–k},

*ϕ*

_{k+1},….

*ϕ*). This can be expressed mathematically as:

_{n}*ρ*, and a uniform prior is assigned for the unit interval of 0 and 1. Similarly, τ

^{2}is a variance parameter that measured unstructured random effects and was assigned a uniform prior on the interval from 0 to 1,000.

*DIC*=

### Environmental variables

### RESULTS

^{2}=0.130; 95% CrI, 0.106 to 0.158) also indicated that the prevalence of malaria is not the same across the clusters, as is commonly assumed in non-spatial generalized linear mixed models.

### DISCUSSION

*Anopheles*mosquitoes and malaria parasites [25-27]. Rural areas are also more likely to face challenges in terms of poor housing, poor knowledge of malaria transmission, negative health practices, and poor malaria management due to difficulties in accessing health facilities [24,28].

*Anopheles gambiae*(a common vector of the malaria parasite in Nigeria) to xeric habitats has been reported [36]. The latter factor may overshadow the effects of aridity in Nigeria.