School of Physical Sciences (Phys-Sciences) Collections

Permanent URI for this collection

http://10.29.1.53:4000/handle/10570/194

Browse

Recent Submissions

Now showing 1 - 5 of 233
  • Item
    Long-range contact process: theory and applications
    (Makerere University, 2025) Namugera, Frank
    We consider a general class of contact processes on a d-dimensional integer lattice (Zd), allowing for long-range interactions. By adapting classical renormalization arguments, we extend well-known results for the case where the infection parameter has a finite range to this more general setting under certain assumptions on the decay rate. Particularly, we show that a supercritical process remains supercritical after truncation of the interaction parameter at a sufficiently large distance. Further, for families of parameters satisfying this latter truncation property, we conclude that the probability of the process never to recover is continuous. To further assess the impact of long-range dynamics on complex networks, we extend this concept into environments that incorporate aging, cooperation, and competing strain models. Using discrete-time nonlinear dynamical systems, we show that contagion dynamics are highly sensitive to both environmental randomness and long-range couplings in both cooperative and competitive models. Furthermore, statistical analyses reveal that the epidemic survival significantly depends on the spatial decay exponent (α) and the scale-free graph exponent (γ). Particularly, these exert pronounced, nonlinear, and time-dependent effects on the survival of competing strains. Finally, by means of a mean-field analysis, we demonstrate that the survival function in a contact process with aging model depends on three exponents: the spatial decay exponent (α), the recovery exponent (δ), and the infectivity exponent (γ). We show that (α) predominantly controls the threshold behavior. However, as spatial interactions become increasingly localized, the temporal exponents (δ , γ) play a dominant role. In particular, slower recovery (δ < 1) enhances memory effects and spatial correlations, promoting infection persistence and lowering the critical contagion rate (λc), whereas faster recovery suppresses local clustering and raises the threshold. These results reveal how non-Markovian temporal dynamics and long-range spatial coupling interact to shape critical behavior in epidemic processes on complex networks.
  • Item
    Regime-switching approaches for dynamic risk and dependence modeling of insurance claim frequency and severity
    (Makerere University, 2025) Afazali, Zabibu
    This study advances dynamic risk and dependence modeling in general insurance by applying regime-switching approaches that aim to accurately capture nonlinear, asymmetric, time-varying structures and regime shifts in claim frequency and severity, limitations often overlooked by traditional methods such as Pearson correlation, static copulas, and single-regime models. The Local Gaussian Correlation (LGC) framework is used to analyze monthly and weekly insurance severity data from Kenya and Norway. By combining LGC with Hidden Markov Models (LGC-HMM), the study reveals time-varying dependencies across different lines of business. Diagnostic checks using Auto Correlation Functions (ACFs) confirm the validity of the framework. Furthermore, comparisons of Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) show that LGC-HMM models achieve higher accuracy and exhibit asymmetric diversification benefits. For Claim Frequency modeling, weekly motor insurance data from Uganda, covering periods before, during, and after COVID-19, are analyzed using the Regime-Switching Integer-Valued Generalized Autoregressive Conditional Heteroskedasticity (RS-INGARCH) framework, estimated via the Extended Hamilton-Gray algorithm. Among the lag options, RS-INGARCH(1,1) is chosen for its simplicity and effectiveness. A similar analysis with Kenyan motor insurance data enhances regional generalizability. Comparisons with INAR(1) and INGARCH models indicate that RS-INGARCH provides improved in-sample fitting and out-of-sample forecasting, supported by appropriate residual diagnostics using ACFs and Ljung-Box tests. The findings highlight the need for regime-switching models to manage volatility and structural changes in insurance claims. The LGC-HMM framework aids dependence analysis, while RS-INGARCH enhances claim frequency modeling. Together, these approaches offer insurers and regulators valuable tools for solvency monitoring and riskbased decision-making, especially in developing markets facing uncertainty from regulatory reforms and systemic shocks like the COVID-19 pandemic.
  • Item
    Assessment of direct hydrocarbon indicators for prospect mapping in the Semliki Basin, Western Uganda
    (Makerere University, 2025) Namukowa, Kaloli
    This study evaluated Direct Hydrocarbon Indicators (DHIs) for prospect mapping in the Semliki Basin, Western Uganda, using seismic attributes, structural interpretation and petrophysical evaluation techniques. The research focused on delineating seismic reflection anomalies and validating them against structural interpretations and reservoir property estimations. Seismic attributes of RMS (Root Mean Square) amplitude and sweetness were applied to enhance the detection of amplitude anomalies and identified eight bright Spots (A-H) across the study area. Structural mapping confirmed that several anomalies are aligned with potential hydrocarbon traps, including anticline structures and fault-related traps. Genetic inversion techniques also provided quantitative estimates of reservoir properties (volume of shale, effective porosity, and water saturation). Bright Spots B, C, D, and H demonstrate significant hydrocarbon potential due to their association with structurally trapped Formations and moderate reservoir qualities. Anomaly C emerges as the most promising candidate, characterized by a well-defined flat Spot interpreted as a fluid contact within an anticlinal configuration. On the other hand, anomalies A, E, F, and G show limited hydrocarbon potential due to poor reservoir quality and limited structural support.
  • Item
    Groundwater flow modelling of micro-catchments in Tilenga Area, Western Uganda
    (Makerere University, 2025) Businge, Ambrose
    Groundwater resources in the Tilenga area in western Uganda are anticipated to face unprecedented stress from oil and gas projects due to increased abstractions alongside projected climate change and population growth. This study addresses the critical gap left by basic water balance models in use by developing a robust numerical groundwater flow model. Hydrostratigraphic analysis of 42 boreholes delineated a semi-confined aquifer system with thickness raging 5-117 m (mean of 48 m), overlain by an aquitard of thickness ranging 3 to 68 m (mean of 22.5 m). The hydraulic properties were; transmissivity in range of 32.5-361 m2/d (mean of 111 m²/d), storativity of 1.4x10-8 to 3.0x10-1 (mean of 3.3x10-2), hydraulic conductivity of 0.56-3.88 m/d (mean of 1.5 m/d), specific yield of 0.026 -0.046 (mean of 0.035) and specific storage of 1.5x10-10 - 4.0x10-3 1/m (mean of 4.4 x 10-4 1/m). The static water levels range from 617 to 681 masl (mean of 623.2 masl) with flow in the north-westerly direction. Recharge rates ranged from 49 to 435 mm/a (mean of 203.5 mm/a) with 6-37.8% of annual precipitation (mean of 20%) with short time lag of 1-2 days between heavy rainfall events and water-level rises. Recharge rate was estimated using the water table fluctuation method. A 100 m thick single layer model with grids of 150 x 150 m was generated using MODFLOW- 2005 code with Lake Albert as a constant head boundary and the rest as no-flow boundaries. It was calibrated in steady state conditions with 53 wells converging with a mean absolute error of 0.167 m and the root-mean-square error of 1.180 m against a target of ±2 m with a coefficient of regression of 0.9929. Transient calibration was done by history matching of 16 daily water level measurements for close to 2 years with a coefficient of regression of 0.539. The model was highly sensitive to recharge and hydraulic conductivity in the eastern part of the area causing 0.15% and 0.065% change in model outputs, respectively. The model water budget revealed inflows of 21,356.8 m3/d from rainfall recharge and the lake with outflows of 21,356.6 m3/d from the abstraction wells and the lake. Four stressing scenarios were projected from 2024 to 2050. Projecting baseline conditions revealed a decline of groundwater table in range of 0.21 m (near the lake) to 2.52 m (at the CPF). Population growth scenario showed a rise of 1.0 m near the lake and 9.78 m at the CPF. For the abstraction rate increase scenario, a decline of 0.27 m was observed at 50% increment while over 20.5 m decline was observed at 200%, a 300% increment caused mining out of aquifers near the CPF. For recharge rate reduction scenario, an average decline of 0.4 m was observed at 5% reduction with 4 m decline at 50% reduction. Key recommendations include establishing weather stations and a consistent and automated groundwater monitoring network.
  • Item
    Hydrogeochemical factors influencing external corrosion of petroleum pipelines in Tilenga Area, Western Uganda
    (Makerere University, 2025) Nuwagaba, Allan
    The integrity of petroleum pipelines is critical for the safe and efficient transportation of hydrocarbons, yet external corrosion remains a significant threat, particularly in buried pipelines. This study investigates the hydrogeochemical factors influencing the external corrosion of petroleum pipelines in the Tilenga area of western Uganda, a region which is planned as a hub for oil and gas production. The research aims to identify key soil and shallow groundwater parameters that contribute to pipeline corrosion and to develop a soil corrosivity index (SCI) to guide mitigation and monitoring strategies by pipeline operators. Field activities involved the excavation of 82 trial pits to a depth of 3.0 meters below ground level (mbgl) and drilling of 17 boreholes to 10.0 mbgl. Apparent soil resistivity was measured using the Wenner four-electrode method at trial pit locations. Hydrogeochemical properties included texture, pH, moisture content, organic matter, chlorides, sulphates, and carbonates were analysed following standard procedures for sampling and laboratory analyses, and quality control. The results revealed that apparent soil resistivity ranged from 3.2 Ωm to 3,465.8 Ωm, with lower resistivity values correlating with higher moisture content and clayey soils, indicating increased corrosivity. The pH of the soil and groundwater varied from 4.9 to 6.9, with acidic conditions (pH <5.5) observed in specific locations, further exacerbating corrosion risks. Chloride and sulphate concentrations were generally below critical thresholds of 500 ppm and 150 ppm, respectively, however, exhibited seasonal variability, with higher concentrations exceeding thresholds (3%) recorded during dry periods. Developing SCI was by integrating seven key factors: pH, soil organic matter, sulphate and carbonate content, moisture content, soil texture, and resistivity. The SCI classified the study area into four corrosivity levels: non-corrosive (0–10), partially corrosive (11–20), corrosive (21–30), and severely corrosive (31–40). Spatial analysis highlighted that approximately 18% of the pipeline routes in Buliisa district, particularly along the NGR02-NGR01-CPF flowlines, are prone to moderate to severe corrosion primarily due to clay-rich soils, high moisture, and low apparent resistivity. The findings underscore the importance of site-specific corrosion risk assessments prior to pipeline installation. Recommendations include the use of protective coatings, cathodic protection systems, and regular monitoring, especially in identified high-risk zones. The SCI model provides a practical tool for pipeline operators to enhance the longevity and safety of petroleum transportation systems in the Tilenga region and similar hydrogeochemical environments globally.