http://repository.must.ac.ke/handle/123456789/1453 2026-06-09T20:10:53Z 2026-06-09T20:10:53Z Mirchigan, James Khobocha http://repository.must.ac.ke/handle/123456789/1637 2026-06-09T12:24:04Z 2025-01-01T00:00:00Z

Deterministic and Stochastic Modeling of Clinical Dynamics of HIV-HBV Co-Infection with Optimality Mirchigan, James Khobocha HIV and HBV infections are viral infections with the same route of transmission through sexual intercourse with an infected person and mother-to-child transmission among other means of transmission. Over the decades, these mono infections have led to the deaths of millions of people around the world despite increased access to prevention, diagnosis, treatment, and care. Yet, there have been no conclusive findings in the hunt for HIV/AIDS cure or vaccine. However, the hepatitis B vaccine is available, though not easily acces sible. Consequently, HIV and HBV co-infection is equally a major global health burden that has attracted limited research interest. The interactions and synergistic relationship between these viruses are not well understood and documented. The co-infection presents complex transmission dynamics within a population. Few mathematical models of HIV and HBV co-infection are available that include risk factors and control measures. The effect of variability in predicting infection outcomes is also not captured in deterministic models. In addition, optimality conditions in co-infection models are not explored. This study sought to model HIV and HBV co-infection with optimal control interventions. This study set out to develop and examine a deterministic model of HIV-HBV co-infection, for mulate an optimal control problem for the deterministic model and determine the optimal controls and finally convert the deterministic model into a stochastic model that accounts for variability and uncertainties in infection outcomes. The deterministic model formu lation is based on SI and SIRS epidemic model framework. The theories of calculus are applied to analyze the deterministic model based on reproduction numbers. The thresh old parameter; the basic and control reproduction number is obtained using the Jacobian NGM and survival function approaches. Co-infection-free and endemic equilibrium points are determined and it’s local and global stability analysis established using Routh-Hurwitz criterion and Metzler matrix method respectively. The local sensitivity analysis of the model parameters on R0 and A0 are determined by use of forward normalized sensitivity index method. Using Pontryagin’s Maximum Principle, an optimal control problem is for mulated. The stochastic model is developed by extending the deterministic model using SDEs. The three models are implemented using MATLAB solver based on Runge-Kutta and Euler-Maruyama numerical schemes. The normalized sensitivity analysis of model parameters showed that co-infection transmission rate, β4 and recruitment rate, π con tribute the highest to R0 and A0. Numerical simulations of deterministic model revealed that the combined effect of clinical and non-clinical control interventions led to the re duction in infection rates with time. The effect of HIV and HBV viral loads on infection progression pointed out that the progression is faster at high levels of viral loads. Further, numerical results of optimal controls exhibited a gradual decrease in co-infection of HIV HBV. The sample paths of SDEs showed variations in infection outcomes due to random noise transmission. Thus, this study recommends that focus should be directed towards reducing co-infection rate and vertical transmission to mitigate the co-infection, while re inforcing policies relating to both clinical and non-clinical control interventions at optimal conditions

2025-01-01T00:00:00Z Kirimi, Erick Mutwiri http://repository.must.ac.ke/handle/123456789/1597 2026-04-23T07:39:46Z 2025-01-01T00:00:00Z

Modeling Pulmonary Tuberculosis and Pneumonia Co-Infection Incorporating an Asymptomatic Component and Natural Immunity Kirimi, Erick Mutwiri Pulmonary tuberculosis is one of the leading infectious diseases causing mortality worldwide, and its impact is exacerbated by opportunistic infections such as pneumonia. The lethal synergism between pulmonary tuberculosis and pneumonia contributes to increased mortality in endemic regions. Existing models of pulmonary tuberculosis do not incorporate the screening of asymptomatic infectious individuals, despite their significant contribution to disease transmission within the population. Additionally, these models do not account for the impact of natural immunity in controlling or reducing the spread of infections. The aim of this study was to model pulmonary tuberculosis and pneumonia co-infection, incorporating an asymptomatic infectious component and natural immunity. The study objectives included: formulating a pulmonary tuberculosis model that incorporates an asymptomatic infectious component and natural immunity; formulating a coinfection model that also incorporates an asymptomatic infectious component and natural immunity; determining the reproduction numbers for analyzing the formulated models; and investigating the effects of varying model parameters on the control of pulmonary tuberculosis. A population-based compartmental approach was employed to formulate the models, from which differential equations were derived. The progression from latent infection to pulmonary tuberculosis disease was modeled using Holling’s saturation term to account for natural immunity. The Next-Generation Matrix method was used to determine reproduction numbers, while stability was analyzed using the Routh–Hurwitz criteria, the Castillo–Chávez method, and Lyapunov functions. Sensitivity analyses of the reproduction numbers in relation to the model parameters were conducted using the normalized sensitivity index method. The model equations were solved numerically using fourth- and fifth-order Runge-Kutta methods in MATLAB software to identify effective intervention strategies for significantly reducing disease transmission. Secondary data from National Tuberculosis, Leprosy, and Lung Disease Program (NTLLDP) in Kenya were utilized to perform numerical simulations, with 2022 data serving as the initial conditions. The co-infection model was fitted to NTLLDP prevalence data from 2012 to 2022 using the fminsearch algorithm in MATLAB software to estimate specific parameters. The results predicted that combining vaccination, screening, and treatment for all forms of pulmonary tuberculosis is the most effective intervention for reducing transmission. Enhancing natural immunity, increasing screening rates for latently infected individuals, and improving vaccine efficacy were also shown to reduce the co-infected population. Specifically, a 10% increase in vaccine efficacy was predicted to reduce co-infections by 6.67%, while the same increase in the screening rate for latent infections reduced them by 6.73%. Furthermore, doubling the screening rate for individuals with asymptomatic infectious pulmonary tuberculosis was shown to reduce the population with severe co-infections and those undergoing treatment for severe conditions by 53.2%. These findings offer valuable guidance to healthcare officials in making informed decisions about screening latently infected and asymptomatic infectious tuberculosis patients, thereby contributing to the fight against epidemics of this disease. The results also underscore the importance of accurate diagnosis and effective treatment of tuberculosis and pneumonia co-infections, which contribute to reducing infection transmission. Lastly, the study emphasizes the need to enhance the natural immunity of latently infected individuals to reduce disease progression and transmission.

2025-01-01T00:00:00Z