Mathematical modelling approach of the study of Ebola virus disease transmission dynamics in a developing country

Background: Ebola Virus causes disease both in human and non-human primatesespecially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date. Materials and Methods:We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus ina population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease-endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle's Invariant principle.Results: The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.Conclusions: Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.

A FRACTIONAL ORDER HIV/AIDS MODEL USING CAPUTO-FABRIZIO OPERATOR.

BACKGROUND: HIV is a virus that is directed at destroying the human immune system thereby exposing the human body to the risk of been affected by other common illnesses and if it is not treated, it generates a more chronic illness called AIDS. MATERIALS AND METHODS: In this paper, we employed the fixed-point theory in developing the uniqueness and existence of a solution of fractional order HIV/AIDS model having Caputo-Fabrizio operator. This approach adopted in this work is not conventional when solving biological models by fractional derivatives. RESULTS: The results showed that the model has two equilibrium points namely, disease-free, and endemic equilibrium points, respectively. We showed conditions necessitating the existence of the endemic equilibrium point and showed that the disease-free equilibrium point is locally asymptotically stable. We also tested the stability of our solution using the iterative Laplace transform method on our model which was also shown stable agreeing with the disease-free equilibrium. CONCLUSIONS: Numerical simulations of our model showed clear comparison with our analytical results. The numerical solutions show that given fractional operator like the Caputo-Fabrizio operator, it is less noisy and hence plays a major role in making a precise decision and gives room or opportunity ('freedom') to use data of specific patients as the model can be easily adjusted to accommodate this, as it a better fit for the patients' data and provide meaningful predictions. Finally, the result showed the advantage of using fractional order derivative in the analysis of the dynamics of HIV/AIDS over the classical case.

Rifampicin resistance patterns and dynamics of tuberculosis and drug-resistant tuberculosis in Enugu, South Eastern Nigeria.

INTRODUCTION: Tuberculosis (TB) continues to be a public health problem globally. The burden is further exacerbated in developing countries like Nigeria, by poor diagnosis, management and treatment, as well as rapid emergence of drug-resistant TB. This study was conducted to evaluate the prevalence of drug-resistant TB, determine the rpoB gene mutation patterns of Mycobacterium tuberculosis (MTB) and model the dynamics of multidrug resistant TB (MDR-TB) in Enugu, Nigeria. METHODOLOGY: A total of 868 samples, from patients accessing DOTS services in designated centres within the zone, were screened by sputum-smear microscopy, while 207 samples were screened by Nucleic Acid Amplification (Xpert® MTB/Rif) Test (NAAT). A deterministic model was formulated to study the transmission dynamics of TB and MDR-TB, using live data generated through epidemiological study. RESULTS: The results showed TB prevalence values of 22.1% and 21.3% by sputum-smear and NAAT assays, respectively. Analysis of the rifampicin resistance patterns showed the highest occurrence of mutations (50%) along codons 523 - 527. Factors such as combination therapy, multiple therapy and compliance to treatment had influence on both prevalence and development of TB drug resistance in the population. CONCLUSIONS: This first documentation of Rifampicin resistance patterns in MTB from Nigeria shows that a majority of rpoB gene mutations occurred along codons 523 to 527, contrary to the widely reported codon 531 mutation and that multiple interventions such as combination therapy, with good compliance to treatment are needed to reduce both prevalence and development of TB drug resistance in the population.