| dc.description.abstract | 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 | en_US |
