Control measures of malaria transmission in Rwanda based on SEIR SEI mathematical model

This research paper investigated the dynamics of malaria transmission in Rwanda using the nonlinear forces of infections which are included in SEIR-SEI mathematical model for human and mosquito populations. The mathematical modeling of malaria studies the interaction among the human and mosquito populations in controlling malaria transmission and eventually eliminating malaria infection. This work investigates the optimal control strategies for minimizing the rate of malaria transmission by applying three control variables through Caputo fractional derivative. The optimal control problems for malaria model found the control parameters which minimize infection. The numerical simulation showed that the number of exposed and infected people and mosquito population are decreased due to the control strategies. Finally, this work found out that the transmission of malaria in Rwanda can be minimized by using the combination of controls like Insecticide Treated bed Nets (ITNs), Indoor Residual Spray (IRS) and Artemisinin based Combination Therapies (ACTs)

Solving an optimal control problem of hepatitis B virus dynamics: Efficacy of fuzzy logic strategy

This work aims at using fuzzy logic strategy to solve a hepatitis B virus (HBV) optimal control problem. To test the efficacy of this numerical method, we compare numerical results with those obtained using direct method. We consider a patient under treatment during 12 months where the two drugs are taken as controls. The results are rather satisfactory. In particular, the reaction of HBV to drugs can be modeled and a feedback can be approximated by the solution of a linear quadratic problem. The drugs reduce the risk of HBV. Furthermore, results of both numerical methods are in good agreement with experimental data and this justifies the efficacy of fuzzy logic strategy in solving optimal control problems

Mathematical modelling of the effects of peer-educators’ campaign on the dynamics of HIV/AIDS in Rwanda

In this paper, we analyse the effects of peer-educator’s campaign on the dynamics of HIV. We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which help to account for a time delay due to incubation period of infective before developing AIDS. The sex-structured HIV/AIDS model divides the population into two subpopulations, namely; females and males. Both disease Free equilibrium and the endemic equilibrium points for the model are determined and their stability are examined. The model is extended to assess the effect of peer- educational campaigns in slowing or eradicating the epidemic. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of each intervention in a community. The models are numerically analyzed to assess the effectiveness of the treatment free measure, namely; peer educational campaign on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters of Rwanda. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of educational campaigns as a preventive strategy in a heterosexually active populationMathematics Subject classifications (MSC 2010): 34D20, 34K60, 92D25, 34K25, 34K28Keywords: Population dynamics, Stability, Basic reproductive numbers, Equilibriu

Impact of Imperfect Vaccine, Vaccine Trade-Off and Population Turnover on Infectious Disease Dynamics

Vaccination is an essential tool for the management of infectious diseases. However, many vaccines are imperfect, having only a partial protective effect in decreasing disease transmission and/or favouring recovery of infected individuals and possibly exhibiting a trade-off between these two properties. Furthermore, the success of vaccination also depends on the population turnover, and the rate of entry to and exit from the population. We here investigate by means of a mathematical model the interplay between these factors to predict optimal vaccination strategies. We first compute the basic reproduction number and study the global stability of the equilibria. We then assess the most influential parameters determining the total number of infected over time using a sensitivity analysis. We derive conditions for the vaccination coverage and efficiency to achieve disease eradication, assuming different intensities of population turnover (weak and strong), vaccine properties (transmission and/or recovery) and the trade-off between the latter. We show that the minimum vaccination coverage increases with lower population turnover decreases with higher vaccine efficiency (transmission or recovery) and is increased/decreased by up to 15% depending on the vaccine trade-off. We conclude that the coverage target for vaccination campaigns should be evaluated based on the interplay between these factors.</jats:p

Analysis of risk factors that influence stunting among Rwandan children under the age of five

In East Africa, 39% of all children were stunted in 2016. Rwanda reported the second highest rate at 37.7%. Globally, deaths from malnutrition stand at 45% of child deaths, creating an economic handicap for all countries. According to the World Health Organization's (WHO) goal to reduce malnutrition by 3.9% per year, all countries must define appropriate strategies. Although related research has been conducted in Rwanda, the issue of malnutrition prevails. This study assesses stunting with multiple factors, with the aim of revealing the system-wide impact of food insecurity on malnutrition. Secondary data from the Rwanda Demographic and Health Survey (RDHS) 2014-2015 were used. Variables were classified into five categories, namely the community, environment, socio-development, media, and proximate factors. To assess the risk factors for stunting, a mixed-effect logistic regression was applied and an association between different factors and stunting was determined. The prevalence of stunting was 37.7%, the average was relatively still high, compared to the global prevalence of 21.3% in 2019, and the city of Kigali comprised the lowest prevalence (22.7%) while the highest prevalence was observed in the Western Province (44.6%). The place of residence and altitude were found to be statistically significant community and environmental factors. Wealth index and parental education level were considered socio-demographic risk factors. All media factors were associated with stunting and in proximate factors, the Body Mass Index (BMI) of the mother, duration of breastfeeding, age and weight of the child at birth, sex, and birth order were statistically significant factors. In addition, infection, diarrhoea, and parasitic infection were also associated with stunting. Ensuring sustainable food security in households should go hand in hand with all strategies for eliminating all forms of malnutrition since stunting is observed in most regions where there are cases of food insecurity. Educating children is key to reducing stunting since the parents need nutrition education to better take care of their children. Public policy throughout the country should aim to improve the living standards of people. Generally, all concerned institutions accompanied with policies to eradicate malnutrition and industries providing nutrients should be promoted

Prediction of the Prevalence of Hypertension and Associated Risk Factors in Rwanda Using Gibbs Sampling Method

In Rwanda, the prevalence of hypertension was 15.3% in 2015. At present, there are no accurate predictions of the prevalence of hypertension and its trend over time in Rwanda to assist decision makers in making plans for prevention and more effective interventions. This study used the Gibbs sampling method in combination with the Markov Chain Monte Carlo approach to predict the prevalence of hypertension and its associated risk factors in Rwanda over a period of ten years. The data were from World Health Organization (WHO) reports. The findings showed that the prevalence of hypertension is estimated to reach 17.82% in 2025, with tobacco use, being overweight or obese, and other risk factors having a respective prevalence of 26.26%, 17.13%, 4.80%, and 33.99%, which shows the increase and, therefore, measures for prevention to be taken. Therefore, to prevent and reduce the prevalence of this disease, the government of Rwanda should take appropriate measures to promote a balanced diet and physical exercise

Prediction of Stunting Among Under-5 Children in Rwanda Using Machine Learning Techniques

Objectives: Rwanda reported a stunting rate of 33% in 2020, decreasing from 38% in 2015; however, stunting remains an issue. Globally, child deaths from malnutrition stand at 45%. The best options for the early detection and treatment of stunting should be made a community policy priority, and health services remain an issue. Hence, this research aimed to develop a model for predicting stunting in Rwandan children. Methods: The Rwanda Demographic and Health Survey 2019-2020 was used as secondary data. Stratified 10-fold cross-validation was used, and different machine learning classifiers were trained to predict stunting status. The prediction models were compared using different metrics, and the best model was chosen. Results: The best model was developed with the gradient boosting classifier algorithm, with a training accuracy of 80.49% based on the performance indicators of several models. Based on a confusion matrix, the test accuracy, sensitivity, specificity, and F1 were calculated, yielding the model’s ability to classify stunting cases correctly at 79.33%, identify stunted children accurately at 72.51%, and categorize non-stunted children correctly at 94.49%, with an area under the curve of 0.89. The model found that the mother’s height, television, the child’s age, province, mother’s education, birth weight, and childbirth size were the most important predictors of stunting status. Conclusions: Therefore, machine-learning techniques may be used in Rwanda to construct an accurate model that can detect the early stages of stunting and offer the best predictive attributes to help prevent and control stunting in under five Rwandan children

Mathematical Modelling of Glucose-Insulin System and Test of Abnormalities of Type 2 Diabetic Patients

This paper presents a mathematical model of glucose-insulin dynamics which is specific for type 2 diabetic patients. The general modelling is obtained by simplification of a global compartmental model by John Thomas Sorensen. The model parameters are estimated using nonlinear optimization and data collected in Rwanda for type 2 diabetic patients. In order to identify and evaluate possible abnormalities of type 2 diabetic patients, the Sampling Importance Resampling (SIR) particle filtering algorithm is used and implemented through discretization of the developed mathematical model. This process is done by clamping insulin and glucose concentrations at around clinical trial values as proposed by Defronzo. Furthermore, for detecting potential abnormalities in type 2 diabetic patients, we compare our results with results obtained from a simulation of the mathematical model for healthy subjects. The proposed mathematical model allows further investigation of the dynamic behavior of glucose, insulin, glucagon, stored insulin, and labile insulin in different organs for type 2 diabetic patients

African pollen database inventory of tree and shrub pollen types

African pollen data have been used in many empirical or quantitative palaeoenvironmental reconstructions. However, the pollen types used in these studies were not controlled and standardised, preventing the precise understanding of pollen-plant and pollen-climate relation that is necessary for the accurate quantification of continental scale climate change or ecological processes in the past. This paper presents a summary of the progress made with the African Pollen Database (APD) inventory of plant diversity from pollen data extracted from 276 fossil sites and more than 1500 modem samples, with a focus on tropical tree pollen types. This inventory (1145 taxa) gives, for each pollen taxon whose nomenclature is discussed, information on the habit, habitat and phytogeographical distribution of the plants they come from. Special attention has been paid to pollen types with similar morphology, which include several plant species or genera, whose biological or environmental parameters can differ considerably