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- ItemMathematical modelling of the impact of HIV intervention strategies in Kenya(Strathmore University, 2020) Omondi, E. O.Since the identification of the first cases of AIDS almost three and half decades ago, HIV/AIDS continues to inflict major public health and socio-economic challenges. Although various intervention strategies have been employed, cases of new infections are still quite high especially in sub-Saharan Africa. At the end of 2018, nearly 37.9 million people were infected with HIV globally. In Kenya, approximately 1.6 million people are living with HIV with 25,000 deaths resulting from AIDS-related illness yearly. The rise in the cases of infections obviously poses danger in the efforts to contain HIV pandemic. HIV prevention and intervention measures need to be enhanced in order to achieve an HIV free society. In this work, mathematical models for HIV transmission dynamics with focus on the impacts of testing and counselling, PrEP uptake and ART treatment are formulated and analysed. Vital analyses that include positivity, steady states and their stability conditions for the models are precisely established. Numerical results from fitting the models to real-time surveillance data to show the evolution of populations over time are obtained. Through Pontryagin’s maximum principle, qualitative optimal control measure against HIV is established. Results are indicative of the fact that combination of various control measures lead to reduction in cases of new infections. Our findings show that the introduction of PrEP has a positive effect on the limitation of spread of HIV when the coverage is maintained at 40%. Furthermore, a combination of PrEP uptake, condom use and ART treatment is likely to offer the best control measure against HIV infections. It is thus critical to devote more resources to education on HIV preventive measures and treatment programmes. In summary, control of new cases of HIV infections should take into account PrEP uptake and combination of condom use and ART treatment. However, PrEP program coverage and individual-level adherence is very critical. These results have the potential to help in escalating programs against HIV infections in high risk populations by modifying the implementation of current interventions, or by adding new control measures.
- ItemA Dynamic parallel algorithm for derivatives pricing and hedging on GPU-CPU heterogeneous systems(Strathmore University, 2023) Muganda, B. W.The use of artificial intelligence in the financial services industry has the potential to transform the sector through greater efficiencies, cost reductions and better tools to draw intelligence from large datasets. The access to computing power which is scalable, accurate and reliable has consequently become a major requirement for the industry due to increased competition, increased products and complexity in models, increased volume of data, stricter regulatory environment and desire for competitive advantage. In this regard, this research provides methodological solutions that would result in accurate and fast system throughput, cost saving and speed acceleration for a financial institution’s financial engineering system by adoption of heterogeneous CPU-GPU parallel architecture with algorithms which are freshly created by drafting from dynamic copula framework for option pricing. This price estimation of options and the assessment of their risk sensitivities under stochastic dynamics namely: stochastic interest rate, stochastic volatility and jumps for varying strikes, maturity and asset classes is a computationally intensive task given the complex nature of the pricing methodologies applied. Models that are much more fully analytical and less complex for pricing derivatives under stochastic dynamics are desirable for much more accurate pricing, investment portfolio construction and risk analysis; and with it an associated system prototype that would provide real-time results. This thesis formulated dynamic parallel algorithms for derivative security pricing and hedging on GPU-CPU heterogeneous systems. This was achieved through the design and implementation of a real-time derivative pricing system prototype supported by a parallel and distributed architecture. The parallel architecture was implemented using hybrid parallel programming on CPU and GPU in OpenCL C, Python and R to provide computational acceleration. The GPU implementation resulted to a peak speed acceleration of 541 times by reducing compute time from 46.24 minutes to 5.12 seconds with the dynamic models under stochastic volatility and stochastic interest rates improving pricing accuracy by an aggregate of 46.68% over the Black-Scholes framework. This adopted approach in this thesis is of practical importance in the harnessing idle processor power, reducing the financial institution’s computational resources requirements and provision of accurate and real-time results necessary in trading, hedging, risk assessment and portfolio optimization processes. Keywords: Dynamic copula, empirical dependence, stochastic volatility, stochastic interest rates, jumps, hybrid GPU acceleration, parallelism
- ItemDetermining the rational homotopy type of the component of inclusion in the space of continuous mappings from gr(k, n) to gr(k , n + r)(Strathmore University, 2020) Otieno, Paul AntonyThe complex Grassmann manifold Gr(k, n) is the space of k dimensional sub spaces of en. Fork= 1, one gets epn-l, the space of lines in en. There is a natural embedding G(k , n) <-+ G(k, n + r). Moreover, any complex manifold can be embedded in some projective space epN. In particular, there is an embedding Gr(k, n) <-+ epN-l where N = (~) 0 To a simply connected topological space, Sullivan associates in a functional way a commutative differential graded algebra (cdga) henceforth (/\ V, d) which encodes the rational homotopy type of X. This is called a Sullivan model of X . Given that H *(ePn, Q) is the truncated polynomial algebra 1\xj(xn+l ), one gets a Sullivan model of the form (1\(x, y), d) where lxl = 2, jyj = 2n + 1 and dx = 0, dy = xn+l . For k 2: 1, one might use the homeo morphism G(k, n) = U(n)/(U(k) x U(n- k)) to find a Sullivan model. Moreover, iff :X --+ Y is a continuous mapping between CW-complexes, then there is a commutative differential graded algebra ( cdga) morphism ¢ : (1\Vy, d) --+ (1\Vx, d) between Sullivan models of X andY. This is called a Sullivan model of f. In this thesis, we use a Sullivan model of the inclusion Gr(k, n) ~ Gr(k, n+ r) to compute the rational homotopy type of the component of the inclusion in the space of mappings from Gr(k , n) to Gr(k, n + r). Further, we will compute an L00-model of the component of the inclusion i and deduce its Sullivan model, using the generalised cochain Quillen functor. We seek to define a model both Sullivan and Quillen for the component of the inclusion and from it obtain the cohomology algebra and even attempt to determine whether the space is formal or not.
- ItemEstimating a finite population mean under random non-response in two-stage cluster sampling with replacement(Strathmore University, 2020) Bii, Nelson KipronoNon-response is a regular occurrence in sample surveys. Developing estimators when non-response exists may result in large biases when estimating population parameters. In this study, a finite population means estimator has been developed under two-stage cluster sampling with replacement in the presence of random non-response. It is assumed that non-response arises in the survey variable in the second stage of cluster sampling assuming full auxiliary information is known. A weighting method of compensating for non-response has been applied. Kernel density estimation was used and the modified transformation of data method was incorporated in order to address the boundary effects due to the Nadaraya-Watson estimator used in the estimation process. Asymptotic properties of the proposed estimator of the finite population mean have been derived. The performance of the proposed estimator has been compared with other estimators based on bias, mean squared error, and confidence interval lengths using simulated data. The results revealed that the estimator proposed has smaller mean squared error values and shorter confidence interval lengths when compared to other estimators of the finite population mean. The bias results also indicated that the proposed estimator of finite population means performed better than the Nadaraya-Watson and the improved Nadaraya-Watson estimators. The transformed estimator proposed to address boundary bias due to Nadaraya-Watson has also been shown to have smaller values of the bias, smaller mean squared error values, and shorter confidence interval lengths compared to those of the Nadaraya-Watson estimator. The results obtained can be useful in choosing efficient estimators of finite population mean for instance in demographic health sample surveys.
- ItemMathematical models for hepatocytic-erythrocytic dynamics and therapeutic control of Malaria(Strathmore University, 2020) Orwa, T. O.Malaria is a mosquito-borne infectious disease caused by parasites of the genus Plasmodium. Mortality and morbidity due to malaria infection is a serious burden to malaria endemic countries. Despite the many years of prevention and control, malaria cases and mortality are still quite high. In 2018, the World Health Organization (WHO) reported about 219 million cases and 435000 deaths due to malaria globally. The threat of parasite resistance, minimal efficacy of malaria vaccines and the high burden of malaria prevention and control measures offer serious challenge to malaria elimination efforts. Improved therapeutic measures is hence necessary for malaria control and possible eradication. In this study, deterministic in-host malaria models with therapeutic control measures are extended and mathematically analysed. Effects of antimalarial drugs and malaria vaccines on disease severity are established analytically and numerically. Parasite resistance and the effects of competition between different parasite strains are also investigated numerically. Each model is analysed and vital properties such as positivity, existence of steady states and their stability conditions are precisely determined. By Pontryagin’s Maximum Principle, the optimal control therapy measure against P. falciparum malaria is determined. Results indicate that a combination of different malaria vaccine antigens yield better therapeutic outcome compared to individual vaccine antigens. A highly efficacious malaria vaccine (efficacy > 90%) is likely to offer the much needed protection against P. falciparum malaria. Multiple-strain infection is likely to increase parasitaemia and hence the severity and cost of malaria control. Malaria therapeutic control efforts should focus on reducing: the parasite invasion rate, the proportions of merozoites that become gametocytes per dying blood schizont, the average number of merozoites released per bursting blood schizonts and the rate of development of resistance during multiple-strain infections. Moreover, a combination of pre-erythrocytic vaccine antigen, blood schizontocide and gametocytocide drugs is likely to offer the best therapeutic control strategy against P. falciparum malaria. In conclusion, future malaria control efforts should consider efficacious malaria vaccines and vaccine combinations. To reduce development of resistance and morbidity, only efficacious antimalarials such as ACT should be used against P. falciparum malaria. The administration and use of current antimalarial drugs alongside efficacious malaria vaccines is likely to offer the much needed therapeutic combination against P. falciparum. Regular and strict surveillance on quality and standards of antimalarial drugs in medical facilities in malaria endemic countries is therefore very critical. Collectively, results from this study highlights the need for continued investment in malaria drug development and urgent drive to improve the efficacy of malaria vaccine candidates such as RTS,S/AS01.