Mathematics

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Browsing Mathematics by Subject "Adult-child vaccination"

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    Dynamics of Transmission and Control of Measles
    (Institute of Sciecne and Technology, 2024-08) Pokharel, Anjana; Prof.Dr. Kedar Nath Uprety
    The emergence and re-emergence of infectious diseases have become a global problem. Measles is a highly contagious human viral disease whose outbreaks frequently occur in many countries, including Nepal, despite the availability of vaccines partly due to the lack of compliance with vaccination. While the National Immunization Program is in place in Nepal, the frequent occurrence of measles in Nepal remains a major cause of child morbidity and mortality. Mathematical modeling for infectious diseases aids in forecasting and comprehending the dynamics of such diseases, facilitating the deployment of effective public health interventions and the allocation of resources. In this work, we developed a novel transmission dynamics model in the form of system of nonlinear ordinary differential equations to evaluate the effects of monitored vaccination programs on individuals who have skipped the regular vaccination program, aiming to control and eliminate measles properly. Our model was validated by Nepal's yearly incidence case data from 2000 to 2019. We calculated the vaccinated reproduction number, Rv, using the Next Generation Matrix method. We also computed the effective reproduction number of measles in Nepal. We performed model analyses to establish the global asymptotic stability of the disease-free equilibrium point for Rv<1 and the uniform persistence of the disease for Rv>1. Moreover, we performed model simulations to identify monitored vaccination strategies for successfully controlling measles in Nepal. Additionally, using the model, we analyzed the long-term dynamics of the epidemic. Our model demonstrates that the monitored vaccination programs can help control the potential resurgence of the disease. Due to the nationwide lockdown enforced by the government of Nepal during the COVID-19 pandemic, the scheduled immunization program was disrupted. As a result, amid the ongoing lockdown, measles outbreaks, including fatal cases, have been reported in several districts of Nepal. Moreover, measles cases in adult groups, albeit small in number, indicate that the previously neglected adult group may need to be brought into vaccine coverage to achieve the WHO’s goal of measles eradication around the world. To examine the role of measles-infected adult groups and to evaluate combined adult-child vaccination programs for eradication, we develop a further extended transmission dynamics model describing measles cases in adults and children. We validated the new model using measles outbreak cases in Nepal from November 24, 2022, to March 10, 2023. Detailed analyses of our model provide the vaccination reproduction number, conditions for measles eradication or persistence, and the role of contact network size. Furthermore, our results highlight that while children are the primary targets for measles outbreaks, a small infection in adults may act as a reservoir for measles, posing obstacles to eradication. Moreover, our model predicts that while impactful controls can be achieved by children-focused vaccines, a combined adult-child vaccination program may help ensure the eradication of the disease.