Browsing by Author "Lambura, Aristide"
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Item Mathematical modeling for helminths and mycobacterium tuberculosis co-infection(NM-AIST, 2021-10) Lambura, AristideTuberculosis continues to be a life-threatening disease in Sub-Saharan African countries despite the available vaccine whereas soil-transmitted helminth is among the neglected tropical disease that causes threats to pre-school, school-aged children and child-bearing mothers. The infection by helminths increases susceptibility to tuberculosis. Thus, there is a need to investigate the possi bility of co-infection of the two diseases due to its geographical overlap at cellular and population levels. This dissertation presents deterministic mathematical models that are aimed at describing the transmission dynamics of soil-transmitted disease and the co-infection with tuberculosis. The first model that describes the transmission dynamics of soil-transmitted helminth with optimal control is presented. The model was qualitatively analyzed and the threshold that governs the spread of the disease derived. The best control model was developed, and numerical simulations were run using a variety of control measures to determine the most cost-effective method for effectively containing the disease. According to the findings, the most cost-effective method for combating the spread of soil-transmitted helminths is a combination of health education and sanitation. The soil-transmitted helminth model was modified to form the second model for the co-infection with tuberculosis. The qualitative analysis was made to determine the equilibrium points and the conditions for the disease eradication. The impact of helminth infection on tuberculosis and vice-versa were discussed and it was observed that helminth infection enhances tuberculosis in the community. Numerical simulation for the model revealed that the interventions that include a combination of measures for controlling helminth infection, vaccinating the babies with bacille Calmette-Guerin vaccine and the treatment of ´ individuals with active tuberculosis were effective in controlling the spread of the diseases. The last model considered the interaction of the helminth parasites, mycobacterium tuberculosis pathogens, and the immune competence within an individual host. Numerical simulations showed that primary infection by either helminth parasite or Mtb bacteria is unsuccessful within the host when the basic reproduction number is less than the unit.Item Mathematical modeling of vehicle carbon dioxide emissions(Cell Press, 2024-01-02) Mayengo, Maranya; Donald, Pita; Lambura, AristideThe demand for transportation, driven by an increasing global population, is continuously rising. This has led to a higher number of vehicles on the road and an increased reliance on fossil fuels. Consequently, the rise in atmospheric carbon dioxide (𝐶𝑂2) levels has contributed to global warming. Therefore, it is important to consider sustainable transportation practices to meet climate change mitigation targets. In this research paper, a non-linear mathematical model is developed to study the dynamics of atmospheric 𝐶𝑂2 concentration in relation to human population, economic activities, forest biomass, and vehicle population. The developed model is analyzed qualitatively to understand the long-term behavior of the system’s dynamics. Model parameters are fitted to actual data of world population, human economic activities, atmospheric 𝐶𝑂2, forest biomass, and vehicle population. It is shown that increased vehicular 𝐶𝑂2 emissions have a potential contribution to the increase in atmospheric 𝐶𝑂2 and the decline of human population. Numerical simulations are carried out to verify the analytical findings and we performed global sensitivity analysis to explore the impacts of different sensitive parameters on the 𝐶𝑂2 dynamics.Item Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies.(Hindawi, 2020-11-18) Lambura, Aristide; Mwanga, Gasper; Luboobi, Livingstone; Kuznetsov, DmitryA deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin's Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.