Mathematics

The recent resurgence of malaria incidence across epidemic regions in South Africa has been linked to climatic and environmental factors. An in-depth investigation of the impact of climate variability and mosquito abundance on malaria parasite incidence may therefore offer useful insight towards the control of this life-threatening disease. In this study, we investigate the influence of climatic factors on malaria transmission over Nkomazi Municipality. The variability and interconnectedness between the variables were analyzed using wavelet coherence analysis. Time-series analyses revealed that malaria cases significantly declined after the outbreak in early 2000, but with a slight increase from 2015. Furthermore, the wavelet coherence and time-lagged correlation analyses identified rainfall and abundance of Anopheles arabiensis as the major variables responsible for malaria transmission over the study region. The analysis further highlights a high malaria intensity with the variabl...

Autoregressive Integrated Moving Average processes (ARIMA) of various orders were presented, with a view to identifying optimal model from a class of models. In this paper, parameters of the models were estimated using Ordinary Least Square (OLS) approach. ARIMA (p, d, q) was formulated for maximum daily temperature data of Ondo and Zaira from January 1995 to November 2005. The choice of autoregressive integrated moving average models of orders p and q was intended to retain any persistence in natural process. To determine the performance of models, Normalized Bayesian Information Criteria was adopted. ARIMA (1, 1, 1) was adequate for modelling maximum daily temperature of Ondo and Zaira, parameters of the model were estimated and redundant variable was removed. Causality and invertiblity behaviour of some optimal models are also presented.

We study the theoretical misclassification probability of linear and quadratic classifiers and examine the performance of these classifiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Résumé. Nousétudions les probabilités théoriques de malclassification de méthodes de classification linéaires et quadratiques. Ensuite, nous examinons les performance de ces méthodes de classifications selon différentes distributions, sur le plan théorique en lesétayant avec deś etudes de simulations. Nous exprimons l'erreur de Bayes pour des distributions de même famille en compétition selon le changement du paramètre de centralisation.

In this paper, stochastic models based on autoregressive integrated moving average models of various orders and its seasonalized versions are presented, with a view to identifying the optimal model for some meteorological outcomes in some cities in Niger Delta region of Nigeria, using Normalized Bayesian Information Criterion as model selection criterion. ARIMA (p, d, q) and seasonal ARIMA (p, d, q)(P, D, Q)[c] are formulated for pressure, cloud, air temperature, relative humidity, wind direction, wind speed, rain amount, and sun hours of Calabar,

The effect of correlation on multivariate rank outlyingness, a result of deviation of multivariate rank functions from property of spherical symmetry, is examined. Possible affine invariant versions of this multivariate rank are surveyed, and outlyingness of affine invariant and non-invariant spatial rank functions under general affine transformation are compared.

Data depth has been described as alternative to some parametric approaches in analyzing many multivariate data. Many depth functions have emerged over two decades and studied in literature. In this study, a nonparametric approach to classification based on notions of different data depth functions is considered and some properties of these methods are studied. The performance of different depth functions in maximal depth classifiers is investigated using simulation and real data with application to agricultural industry.

Autoregressive Integrated Moving Average (ARIMA) processes of various orders are presented to identify an optimal model from a class of models. Parameters of the models are estimated using an Ordinary Least Square (OLS) approach. ARIMA (p, d, q) is formulated for maximum daily temperature data in Ondo and Zaira from January 1995 to November 2005. The choice of ARIMA models of orders p and q is intended to retain persistence in a natural process. To determine the performance of models, Normalized Bayesian Information Criterion is adopted. The ARIMA (1, 1, 1) is adequate for modeling maximum daily temperature in Ondo and Zaira; model parameters are estimated and redundant variables are removed. Causality and the invertibility behavior of some optimal models are also presented.

Recent studies have considered the connections between malaria incidence and climate variables using mathematical and statistical models. Some of the statistical models focused on time series approach based on Box–Jenkins methodology or on dynamic model. The latter approach allows for covariates different from its original lagged values, while the Box–Jenkins does not. In real situations, malaria incidence counts may turn up with many zero terms in the time series. Fitting time series model based on the Box–Jenkins approach and ARIMA may be spurious. In this study, a zero-inflated negative binomial regression model was formulated for fitting malaria incidence in Mopani and Vhembe―two of the epidemic district municipalities in Limpopo, South Africa. In particular, a zero-inflated negative binomial regression model was formulated for daily malaria counts as a function of some climate variables, with the aim of identifying the model that best predicts reported malaria cases. Results fr...

Background Malaria remains a serious concern in most African countries, causing nearly one million deaths globally every year. The review aims to examine the extent and nature of the resurgence of malaria prevalence in South Africa.Method Using the Arksey and O'Malley framework, this scoping review included articles published between the year 2015 and 2018 on the resurgence of malaria prevalence in South Africa. Articles were searched from October 2018 to January 2019 using these electronic databases: CINAHL, Pubmed, Science Direct and SCOPUS. Grey literature from Google Scholar was also hand searched. Key search terms and subject headings such as climate variables; climate changes; climatic factors; malaria resurgence; malaria reoccurrence, and malaria increase over epidemic regions in South Africa were used to identify relevant articles. Articles for selection and characterization were performed by three independent reviewers. Data collected were synthesized qualitatively.Resu...

With the current outbreak of coronavirus disease 2019 (COVID-19), countries have been on rising preparedness to detect and isolate any imported and locally transmitted cases of the disease. It is observed that mode of transmission of the disease varies from one country to the other. Recent studies have shown that COVID-19 cases are not influenced by race and weather conditions. In this study, effect of modes of transmission of COVID-19 is considered with respect to prevalence and mortality counts in World Health Organisation (WHO) regions. Also, a negative binomial model is formulated for new death cases in all WHO regions as a function of confirmed cases, confirmed new cases, total deaths and modes of transmission, with the goal of identifying a model that predicts the total new death cases the best. Results from this study show that there is strong linear relationship among the COVID-19 confirmed cases, total new deaths and mode of transmission in all WHO regions. Findings highlight the significant roles of modes of transmission on total new death cases over WHO regions. Mode of transmission based on community transmission and clusters of cases significantly affects the number of new deaths in WHO regions. Vuong test shows that the formulated negative binomial model fits the data better than the null model.

In this study, we propose classification method based on multivariate rank. We show that this classifier is Bayes rule under suitable conditions. Multivariate ranks are not invariant under affine transformation of the data and so, the effect of deviation from property of spherical symmetry is investigated. Based on this, we construct affine invariant version of this classifier. When the distributions of competing populations have different covariance matrices, minimum rank classifier performs poorly irrespective of affine invariance. To overcome this limitation, we propose a classifier based on multivariate rank region. The asymptotic properties of this method and its associated probability of misclassification are studied. Also, we propose classifiers based on the distribution of the spatial rank and establish some theoretical results for this classification method. For affine invariant version of this method, two invariants are proposed. Many multivariate techniques fail to perfor...

Gross domestic product (GDP) is one of the major ways of detecting the economic growth of a nation and where the GDP is high, the country is actually moving forward. One of the sectors believed to contribute to the Nigerian GDP is the crude oil. Empirical result from existing literature has showed that over dependence on crude oil has almost crippled all other sectors of the economy. Over the years, the high rate of dependence on the crude oil in the Nigeria’s system of government has increased in that, some other sectors of the economy such as agriculture, crude oil, solid minerals, trade, communication, electricity, among others, had not given ardent attention. This paper seeks to analyze GDP from some sectors of Nigerian economy. A dynamic regression model was formulated to analyze Nigerian quarterly GDP data from 1960 to 2010. This study recommends that Government should try as much as possible to look into all other sectors of the economy especially sectors that this paper actu...

Highlights • A revisit to the diagonalized and regularized Hotelling's 2 tests. • Notions of data depth for trimming of mean vectors and covariance matrices. • Comparison of diagonalized and regularized Hotelling's 2 tests with the usual Hotelling's 2 test. • Limitations of diagonalized and regularized Hotelling's 2 tests in high dimension. • Proposal of robust versions of diagonalized and regularized Hotelling's 2 tests in high dimension.

Several multivariate depth functions have been proposed in literature of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant only to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. We extend the notions of maximal depth classifiers for covariance-adjusted, weighted and kernel-based versions of spatial depth. The performance of the classifiers is considered and compared with some existing classification methods using simulated and real datasets.

In this study, we consider some theory of Bayes rule and discriminant analysis to establish asymptotics of linear and quadratic discriminant rules. Effect of deviation from property of spherical symmetry is investigated and optimal performances of discriminant rules are demonstrated using simulation and real life applications.