School of Science
http://ir-library.mmust.ac.ke:8080/xmlui/handle/123456789/42
2024-03-29T09:50:39ZVECTOR AUTOREGRESSIVE MODEL INCORPORATING NEW INFORMATION USING BAYESIAN APPROACH
http://ir-library.mmust.ac.ke:8080/xmlui/handle/123456789/2527
VECTOR AUTOREGRESSIVE MODEL INCORPORATING NEW INFORMATION USING BAYESIAN APPROACH
Musyoki, Michael Ngungu
The Vector Autoregressive (VAR) Models have been applied extensively in many
fields ranging from finance, economics, machine learning among others. In fact,
the VAR models are the mostly applied among the multivariate time series models
since they have shown to perform well especially when forecasting is done. Many
researchers have fitted the VAR models to the available data so as to come up with
a model that explains the relationship between the variables involved. However,
despite this fact that the VAR models have performed well, there is a concern of
what one should do in the event that new information is received after the model
has been fitted. In this study, an approach is provided of updating the VAR
model instead of fitting a new model whenever new information is received where
the fitted VAR model is treated as the prior, new information or measurements
as the likelihood to get an updated VAR model, the posterior, using the Bayesian
Approach. Thus, updated VAR models of order one, two and three are developed
after which generalization is done to a VAR model of order p. The performance
of the existing VAR model is compared with the updated VAR model from which
it is observed that the model performs well based on the fairly low values of root
mean square error (RMSE) obtained. Furthermore, estimation of parameters is
done using the joint estimation which estimates both the states and the parameters
simultaneously. In the estimation, the estimated parameters converge to
the true parameter value as time evolves. An application is considered where a
penta-variate VAR(1) model is fitted using data for the contribution of five main
sub-sectors of the agriculture sector to the Kenyan economy. The data considered
was obtained from the Kenya National Bureau of Statistics (KNBS) on Statistical
abstract reports from 2000 - 2021. The model was then updated and after comparing
with the initial model, the model was found to perform well based on the
lower values of the RMSE. From the study, it is then concluded that the updated
Vector Autoregressive model performs well based on the Root Mean Square Error
(RMSE). Finally, recommendations are also given regarding future work of updating
other multivariate time series models to assimilate new information obtained
after model fitting is done.
2023-01-01T00:00:00ZWHOLE TRANSCRIPTOME ANALYSIS OF DIFFERENTIALLY EXPRESSED GENES IN NILE TILAPIA (Oreochromis niloticus) SUBJECTED TO CHRONIC STRESS
http://ir-library.mmust.ac.ke:8080/xmlui/handle/123456789/2510
WHOLE TRANSCRIPTOME ANALYSIS OF DIFFERENTIALLY EXPRESSED GENES IN NILE TILAPIA (Oreochromis niloticus) SUBJECTED TO CHRONIC STRESS
Mwaura, John Gitau
Chronic stress is the long-term activation of the stress response system and is a major bottleneck to aquaculture production as it lowers productivity and compromises fish welfare. Several studies have attempted to infer the presence of stress, however, there is paucity of information regarding quantification and the mechanisms by which chronic stress depresses growth. A few studies have attempted to determine which genes are regulated in chronic stress and how chronic stress impacts metabolic pathways. Furthermore, in cultivated Nile tilapia (Oreochromis niloticus L.), only a small number of genes conferring advantageous phenotypes have been identified. The current study investigated the relationship between stress levels and growth performance in relation to the metabolic pathways regulated in response to chronic stress in cultured Nile tilapia. Juvenile Nile tilapia were cultured in the laboratory at different ammonia concentrations and stocking densities for 70 days. Growth performance was determined alongside renowned stress markers: glucose and cortisol levels, followed by RNA sequencing and differential gene expression. Fish in the treatment groups showed negative allometry while the controls showed positive allometric growth. The specific condition factor (Kn) ranged from 1.17 for the controls to 0.93 for the ammonia treatment and 0.91 for the stocking density treatment. Results of this study indicated a positive correlation between the levels of stressors and the indicators of stress i.e. concentrations of blood glucose, plasma cortisol and scale cortisol. There was a significant difference (p<0.05) in the mean plasma cortisol levels between ammonia treatments and the control (p< 0.05 i. e 4.71 ± 0.52 ng/ml and 6.50 ± 0.83 ng/ml) respectively. The cortisol levels increased concomitantly with the concentration of ammonia. There was also a significant difference in the plasma cortisol levels between the low fish stocking densities and the high fish stocking densities. Comparative transcriptome analysis revealed 209 Differentially Expressed Genes (DEGs) (156 up- and 53 down-regulated) in ammonia and 252 DEGs (175 up- and 77 down-regulated) in stocking density treatment. In both treatments, 24 and 17 common DEGs were up- and down-regulated respectively. DEGs were significantly enriched in six pathways associated with muscle activity, energy mobilization and immunity. The heightened muscular activity consumes energy which would otherwise have been utilized for growth. Comparative genomics identified similarities between fishes with common genetic and evolutionary ancestry, allowing for better adaptation to local environmental conditions. Some of the selected genes exhibiting substantial effect on immunity include: Prxs, MMR1 like, ZMYM4-like partial; Stress reactive genes including: PALLD-like gene, LPLBAG6-like and growth-related genes including: NF1x like, PEDF and CL like. Experimental sample, O. niloticus, O. aureas and Danio rerio can hybridize in their natural environments bringing about genetic admixture ancestry that hybridises new genes which confer beneficial phenotypes. These results bring to fore the molecular mechanisms underlying chronic stress’ suppression of growth in cultured Nile tilapia and can inform formulation of breeding programmes targeting stress resistance. The results of this study lays the foundation for the development of fish breeds that are climate-ready and able to weather climate shocks. This will allow Aquaculture to contribute to food and nutrition security in line with SDG2 and improve the economic status of fish farming communities in the Global South.
2023-11-01T00:00:00ZMULTISCALE MODELING OF EBOLA TRANSMISSION DYNAMICS WITH TREATMENT
http://ir-library.mmust.ac.ke:8080/xmlui/handle/123456789/1503
MULTISCALE MODELING OF EBOLA TRANSMISSION DYNAMICS WITH TREATMENT
Oganga, Duncan Otieno
Ebola Virus Disease, (EVD) is a rare and deadly disease with high fatality rates in humans and other primates. It is introduced into the human population through direct contact with the infected hosts which include porcupines, fruit bats, chimpanzees, gorillas, monkeys and forest antelopes. Transmission from one human being to another takes place via direct contact with body fluids of the infected or indirectly via surfaces contaminated by these fluids. Mathematical models have been developed describing between host and within host dynamics of EVD separately. The within host models of EVD have considered mass action incidence rate which does not capture the effect of saturation due to high concentration of Ebola virions. As a result, a within host model incorporating saturated incidence rate and treatment has been developed and analysed. Stability analyses of the model developed show that the Infection Free Equilibrium (IFE) is locally and globally
0 > 1, an Endemic Equilibrium (EE) emerges,
asymptotically stable, if R
0 < 1, and when R
w
w
which is unique and globally asymptotically stable. The effect of treatment has been illustrated using numerical simulations. One of the control strategies of EVD is vaccination. The between host models of EVD incorporating vaccination available in literature assume that the vaccines grant full immunity. This may not be the case since the vaccines are still under development. Consequently, this study has developed and analysed a Susceptible Exposed Infected Recovered (SEIR) model incorporating an imperfect vaccine. Analyses
B
of its equilibrium points have shown that if the basic reproduction number , R
0 < 1,
the disease dies out and if R0B > 1, the disease persists in the population. The impact of vaccination on the disease has also been established. Even though separate models have been used to study immunological and epidemiological dynamics of EVD, studies have shown that for virus infections, the infectivity of the host is directly proportional to the viral load. This therefore calls for the use of a multiscale model to capture this interdependence between scales. Multiscale models of EVD exist. However, they have not considered uninfected cells and infected cells, yet they are major players in the within host dynamics of EVD. This study therefore has formulated a multiscale model of EVD incorporating the uninfected cells, infected cells and the Ebola virions. Analyses of the Disease Free Equilibrium (DFE) and the EE show that the disease dies out if the basic reproduction number R0c < 1 and persists in the population when R0c > 1 respectively. Sensitivity analysis shows that the rate and efficacy of vaccination are the most sensitive parameters. This indicates that effort should be directed towards implementing an effective vaccination strategy to control the spread of the disease. It has also been established through simulations that when treatment efficacy is scaled up, the viral load goes down within a host and consequently, the transmission between hosts is also reduced. The models developed and analysed in this study have a significant impact on the control of EVD.
2021-03-01T00:00:00ZPREDATOR-PREY MODEL WITH LOGISTIC GROWTH FOR CONSTANTAND DENSITY-DEPENDENT DELAYED MIGRATION
http://ir-library.mmust.ac.ke:8080/xmlui/handle/123456789/1450
PREDATOR-PREY MODEL WITH LOGISTIC GROWTH FOR CONSTANTAND DENSITY-DEPENDENT DELAYED MIGRATION
Apima, Samuel Bong’ang’a
Predator-prey models describe the interaction between two species, the prey which serves as a food source to the predator. The migration of the prey for safety reasonsafter a predator attack and the predator in search of food, from a patch to anothermay not be instantaneous. This may be due to barriers such as a swollen river ora busy infrastructure through the natural habitat. Recent predator-prey modelshave either incorporated a logistic growth for the prey population or a time delayin migration of the two species. Predator-prey models with logistic growth thatintegrate time delays in migration of both species have been given little attention. Inthis study, a logistic predator-prey model integrating a time delay in the migration ofboth species is developed and analyzed. The developed model was solved using twoinvariant manifolds; the symmetric manifold and the asymmetric manifold. Analysisof the model shows that when the prey growth rate is less than or equal to theprey migration rate, the two species coexist, otherwise both species become extinct.Numerical simulations show that during migration of the species, a longer time delaymakes the model to stabilize at a slower rate compared to when the time delay isshorter. It is also shown that the prey migration due to the predator density does notgreatly affect the prey density and existence compared to factors, such as logging,bad climatic conditions and limited food resources in a patch, that cause the preyto migrate. In the interest of species conservation, policies should be developed andenacted which address factors which prolong time delays during migration of thespecies by minimizing human activities and settlement in natural habitat.
2020-12-02T00:00:00Z