Mathematics

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https://hdl.handle.net/20.500.14540/131

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Browsing Mathematics by Author "Adhikari, Khagendra"

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    On the Study of Distribution of Primes and Twin Prime Conjecture
    (Faculty of Mathematics, 2016) Adhikari, Khagendra
    The distribution of primes, mainly focusing on the Tchebycheff estimates of prime counting function, Mertens Theorem which are most significant results for distribution of primes have beeen studied in this thesis. Distribution of Twin Primes, Twin Prime Conjecture and some developments towards the Twin Prime Conjecture is also studied. The alternative approaches for the Twin Prime Conjecture has also been studied in this thesis.
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    Transmission Dynamics of COVID-19: Mathematical Models for Effective Controls
    (Institue of science & Technology, T.U., 2023-12) Adhikari, Khagendra; Prof. Dr. Kedarnath Upreti
    The emergence of a pandemic disease often presents unforeseen challenges to the global healthcare system, particularly affecting low and middle-income nations like Nepal. Mathematical modeling of infectious diseases helps to predict and understand the dynamics of the diseases enabling the implementation of efficient public health interventions and resources allocation. This contributes to evidence-based policy decisions to mitigate a pandemic. Despite worldwide efforts and vaccine development, the COVID-19 pandemic has had devastating global impacts varying significantly from one country to another, making country-specific studies essential for a deeper understanding of the disease and its control strategies. This dissertation presents novel mathematical models designed to comprehensively analyze COVID-19 transmission dynamics. Our models have been rigorously validated with multiple datasets, enhancing their reliability and validity. Our mathematical model for the first wave of COVID-19 in higher dimensional systems, characterized by non-linear ordinary differential equations, possesses a significant capability to assess the count of returnees, particularly those crossing the open border between Nepal and India. To estimate the temporal pattern of the returnees, we enhance the system by introducing non-autonomous features. By using the Next Generation Matrix Method, we calculate the Basic Reproduction Number (R_0) and Effective Reproduction number which successfully predict the bifurcating nature of diseases trajectories. By taking advantage of this model, we evaluate the effectiveness of various control measures implemented during the first wave of the pandemic in Nepal. We specifically investigate the impact of three key intervention policies enacted during the first wave of COVID-19 in Nepal: the 1st Lockdown, the 2nd Border Screening and Quarantine, and the 3rd Detection and Isolation. Our findings uncover their effectiveness in the mitigation of COVID-19 transmission in Nepal. In addition, we focus on the Delta variant dominated second wave of COVID-19 in Nepal. We shed light on the transmission dynamics and seroprevalence associated with this highly transmissible variant. Furthermore, we estimate the expected burden on medical resources, including ICU beds and ventilators, in Nepal, providing crucial insights for healthcare preparedness. Additionally, we investigate vaccination programs and the gradual relaxation of lockdown measures as prospective pandemic control methods, which are especially important in resource-limited country like Nepal, where good healthcare management is critical. Our work demonstrates that our mathematical model successfully predicted the seroprevalence during the Delta surge with estimates closely matching the results obtained by the government through a nationwide seroprevalence survey. This finding demonstrates the model's ability, reliability and effectiveness in tracking and understanding disease dynamics, which is crucial for public health planning and response during infectious disease outbreaks. It also highlights the potential for mathematical modeling to complement and authenticate real-world data collection efforts, improving our ability to assess and manage public health crises. We also develop the data-driven models for the estimation of real-time risk of infection and hospitalization during a pandemic. Our probabilistic model for estimation of the risk of infection incorporates susceptible populations, active infectious cases, contact patterns of people, and the effective reproduction number. It offers a more precise description of pandemic's transmission patterns that can be achieved solely through the reproduction number. We also use Maximum Likelihood Function to construct the mathematical model for estimating the rate of the temporal pattern of hospitalization during a pandemic. These models are applied to unique datasets of new COVID-19 cases and hospitalization cases in Nepal including its seven provinces, enabling us to assess disease transmission and efficiently manage healthcare resources to minimize the pandemic's burden. These data-driven models introduce innovative techniques and yield exciting results that advance our understanding of the risk of infection and hospitalization during a pandemic. These findings hold the potential to inform guidelines and strategies for pandemic control, particularly in the face of catastrophic outbreaks. Our biologically realistic models, data integration methods, and probabilistic approaches contribute to the broader scientific fields encompassing life sciences, mathematics, and computational science.