Abstract:
Neglected tropical diseases (NTDs) are a health crisis that is ignored by the developed
world and only starts getting attention when there is an outbreak that kills a large
population. AIDS associated Kaposi sarcoma (AIDS-KS) and Ebola Virus Disease (EVD)
are viral infections which are just two of the many NTDs that require attention. This thesis
presents novel within-host ordinary differential equation (ODE) mathematical models
in conjunction with application of the optimal control theory of AIDS-KS dynamics.
Additionally, we derive an epidemiological system of ODEs to model the transmission
dynamics of EVD in the presence of public health education.
AIDS-KS is caused by KS-associated herpesvirus (KSHV). Although the standard KS
therapy has not changed in twenty years, not all cases of KS will respond to the same
therapy. The goal of current AIDS-KS treatment modalities is to reconstitute the immune
system and suppress HIV replication. We introduce novel within-host ODE mathematical
models that consolidate the effect of both HIV and KSHV load on KS tumor progression by
incorporating low or high viral loads (VLs) into the proliferation terms of the immune cell
populations. Regulation of HIV/KSHV VL and viral reservoir cells is crucial for restoring
a patient to an asymptomatic stage. Therefore, in order to device an optimal treatment
plan, optimal control theory is applied by using Pontryagin’s maximum principle with
control measures such as combined antiretroviral therapy (cART). The objective function
is constituted to minimise the population of infected cells, VL and KS tumor and the
harmful side effects of cART to the patient. The results indicate that the drug treatment
strategies are capable of removing the viral reservoirs faster, consequently reducing the
HIV and KS tumor burden. The predictions of the mathematical models have the potential
to offer more effective therapeutic interventions based on VL and virus-infected cell load,
hence support new studies addressing the superiority of VL over CD4 cell count when
predicting life expectancy of HIV patients.
iv
Public participation in Ebola virus disease (EVD) prevention efforts is essential to
reduce outbreaks. Targeted education through practical health information for specific
populations and sub-populations is essential to combat this disease. We study the
dynamics of EVD in he presence of public health education to assess the role of behavior
change instigated by health education in the dynamics of an outbreak. The intensity of
behaviour change is clear in two outbreaks of EVD that occurred in Sudan just three years
apart. The first occurrence turned into the primary documented outbreak of EVD and
produced a sizable number of infections. The subsequent outbreak delivered far less cases,
apparently on the grounds that the population in the district gained from the primary
episode. We derive a system of ODEs to model these two opposite behaviors, using data
from these two EVD instances to estimate parameters significant to the two opposite
behaviors. We then simulate a future EVD epidemic in Sudan using our model, which
includes two susceptible populations, one of which is more knowledgeable about EVD
than the other. Our results show how a better educated population leads to fewer cases
of EVD and features the significance of ongoing education in public health.
Fungai, S (2024). Neglected tropical diseases: Mathematical modelling and control of within-host and transmission dynamics of viral infections. Afribary. Retrieved from https://track.afribary.com/works/neglected-tropical-diseases-mathematical-modelling-and-control-of-within-host-and-transmission-dynamics-of-viral-infections
Fungai, Shava "Neglected tropical diseases: Mathematical modelling and control of within-host and transmission dynamics of viral infections" Afribary. Afribary, 30 Mar. 2024, https://track.afribary.com/works/neglected-tropical-diseases-mathematical-modelling-and-control-of-within-host-and-transmission-dynamics-of-viral-infections. Accessed 20 Nov. 2024.
Fungai, Shava . "Neglected tropical diseases: Mathematical modelling and control of within-host and transmission dynamics of viral infections". Afribary, Afribary, 30 Mar. 2024. Web. 20 Nov. 2024. < https://track.afribary.com/works/neglected-tropical-diseases-mathematical-modelling-and-control-of-within-host-and-transmission-dynamics-of-viral-infections >.
Fungai, Shava . "Neglected tropical diseases: Mathematical modelling and control of within-host and transmission dynamics of viral infections" Afribary (2024). Accessed November 20, 2024. https://track.afribary.com/works/neglected-tropical-diseases-mathematical-modelling-and-control-of-within-host-and-transmission-dynamics-of-viral-infections