Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study was carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

Background: Hepatitis C Virus (HCV) and Human Immunodeficiency Virus (HIV) are both as classified blood-borne viruses since they are transmitted through contact with contaminated blood. Approximately 1.3 million of the 2.75 million global HIV/HCV carriers inject drugs (PWID). HIV co-infection has a harmful effect on the progression of HCV, resulting in greater rates of HCV persistence after acute infection, higher viral levels, and accelerated progression of liver fibrosis and end-stage liver disease. In this study, we developed and investigated a mathematical model for the dynamical behavior of HIV/AIDS and HCV co-infection, which includes therapy for both diseases, vertical transmission in HIV cases, unawareness and awareness of HIV infection, inefficient HIV treatment follow-up, and efficient condom use. Methods: Positivity and boundedness of the model under investigation were established using well-known theorems. The equilibria were demonstrated by bringing all differential equations to zero. The associative reproduction numbers for mono-infected and dual-infected models were calculated using the next-generation matrix approach. The local and global stabilities of the models were validated using the linearization and comparison theorem and the negative criterion techniques of bendixson and dulac, respectively. Results: The growing prevalence of HIV treatment dropout in each compartment of the HIV model led to a reduction in HIV on treatment compartments while other compartments exhibited an increase in populations. In dually infected patients, treating HCV first reduces co-infection reproduction number R ech , which reduces liver cancer risk. Conclusions: From the model's results, we infer various steps that policymakers could take to reduce the number of mono-infected and co-infected individuals.

Despite the intervention of WHO on vaccination for reducing the spread of Hepatitis B Virus (HBV), there are records of the high prevalence of HBV in some regions. In this paper, a mathematical model was formulated to analyze the acquisition and transmission process of the virus with the view of identifying the possible way of reducing the menace and mitigating the risk of the virus. The models' positivity and boundedness were demonstrated using well-known theorems. Equating the differential equations to zero demonstrates the equilibria of the solutions i.e., the disease-free and endemic equilibrium. The next Generation Matrix method was used to compute the basic reproduction number for the models. Local and global stabilities of the models were shown via linearization and Lyapunov function methods respectively. The importance of testing and treatment on the dynamics of HBV were fully discussed in this paper. It was discovered that testing at the acute stage of the virus and chronic unaware state helps in better management of the virus.

Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

Background: Hepatitis C Virus (HCV) and Human Immunodeficiency Virus (HIV) are both classified as blood-borne viruses since they are transmitted through contact with contaminated blood. Approximately 1.3 million of the 2.75 million global HIV/HCV carriers are people who inject drugs (PWID). HIV co-infection has a harmful effect on the progression of HCV, resulting in greater rates of HCV persistence after acute infection, higher viral levels, and accelerated progression of liver fibrosis and end-stage liver disease. In this study, we developed and investigated a mathematical model for the dynamical behavior of HIV/AIDS and HCV co-infection, which includes therapy for both diseases, vertical transmission in HIV cases, unawareness and awareness of HIV infection, inefficient HIV treatment follow-up, and efficient condom use. Methods: Positivity and boundedness of the model under investigation were established using well-known theorems. The equilibria were demonstrated by bringing all differential equations to zero. The associative reproduction numbers for mono-infected and dual-infected models were calculated using the next-generation matrix approach. The local and global stabilities of the models were validated using the linearization and comparison theorem and the negative criterion techniques of bendixson and dulac, respectively. Results: The growing prevalence of HIV treatment dropout in each compartment of the HIV model led to a reduction in HIV on treatment compartments while other compartments exhibited an increase in populations. In dually infected patients, treating HCV first reduces co-infection reproduction number R ech , which reduces liver cancer risk. Conclusions: From the model's results, we infer various steps (such as: campaigns to warn individuals about the consequences of having multiple sexual partners; distributing more condoms to individuals; continuing treatment for chronic HCV and AIDS) that policymakers could take to reduce the number of mono-infected and co-infected individuals.