Michael Olaniyi Adeniyi

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.

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.

An SIRS (Susceptible–Infected–Removed-Susceptible) mathematical model for the transmission dynamics of the Transfusion–Transmitted Malaria (TTM) model with optimal control pair u1(t) and u2(t) was developed and studied in this research work. The model Transfusion–Transmitted Malaria disease–free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It is shown that the disease–free equilibrium was locally asymptotically stable if the associated basic reproduction numbers R0 is less than unity while the disease persists if R0 is greater than unity. The global stability of the Transfusion–Transmitted Malaria model at the disease-free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion–Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.

Malaria and Pneumonia are leading causes of serious illness in children and adults worldwide with their death rate and prevalence on the rise. Such alarming statistics may retard the milestones so far achieved in meeting the Millennium Development Goals 4 and 6 whose targets are to improve child survival and reverse the high prevalence of diseases such as pneumonia and malaria respectively. Two sub-models of malaria-pneumonia co-infection namely malaria model and pneumonia model were considered first and then followed by the full malaria-pneumonia co-infection model. The malaria model, pneumonia model and co-infection model basic reproduction numbers denoted by Rm, Rp and Rmp respectively was obtained using the Next Generation Matrix method. The model disease free equilibrium’s local and global stability was analysed using Descartes’ Rule of signs and Comparison method. The bifurcation analysis for the malaria, pneumonia and co-infection models was studied using the Centre Manifold Theory. The sensitivity indices of the model basic reproduction numbers Rm, Rp and Rmp to the parameters in the models were calculated. Optimal control theory was applied using the Pontryagins’ Maximum Principle to investigate optimal strategies for controlling the spread of malaria, pneumonia and co-infection models using insecticide treated bed nets (u1(t)) spraying of mosquitoes insecticides (u2(t)), sanitation (u3(t)), vaccination (u4(t)), anti-malaria drugs (u5(t)), anti-pneumonia drugs (u6(t)), both anti-malaria drugs and anti-pneumonia drugs (u7(t)) as the system time control variables. Numerical simulations using a set of parameter values were provided to validate the analytical results.