<p>The main body of this thesis deals with three related concepts pertaining to vaccination strategies for childhood infectious disease. Chapter 2 deals with the implications of reversion in the Oral Polio Vaccine on global polio eradication programs. Chapter 3 explores the phenomenon of contact or secondary vaccination in the use of live-attenuated virus vaccines. Chapter 4 explores the importance of demographic stochasticity in pulse vaccination campaigns. largely focusing on measles dynamics. Abstracts for each chapter are given below.</p><p>Poliomyelitis vaccination via live Oral Polio Vaccine (OPV) suffers from the inherent problem of reversion: the vaccine may, upon replication in the human gut, mutate back to virulence and transmissibility resulting in circulating vaccine derived polio viruses (cVDPVs). We formulate a general mathematical model to assess the impact of cVDPVs on prospects for polio eradication. We find that for OPV coverage levels below a certain threshold, cVDPVs have a small impact in comparison to the expected endemic level of the disease in the absence of reversion. Above this threshold, the model predicts a small but significant endemic level of the disease, even where standard models predict eradication. In light of this, we consider and analyze three alternative eradication strategies involving a transition from continuous OPV vaccination to either continuous Inactivated Polio Vaccine (IPV), pulsed OPV vaccination, or a one-time IPV pulse vaccination. Stochastic modeling shows continuous IPV vaccination is effective at achieving eradication for moderate coverage levels, while pulsed OPV is effective if higher coverage levels are maintained. The one-time pulse IPV method may also be a viable strategy, especially in terms of the number of vaccinations required and time to eradication, provided that a sufficiently large pulse is practically feasible. More investigation is needed rq?;arding the frequency of revertant virus infection resulting directly from vaccination, the ability of IPV to induce gut immunity, and the potential role of spatial transmission dynamics in eradication efforts.</p> <p>Viruses contained in live-attenuated vims vaccines (LAVV) can be transmitted between individuals, resulting in secondary or contact vaccinations. This fact has been exploited successfully in the use of the Oral Polio Vaccine (OPV) to better control wild polio viruses. In this work we analyze general LAVV vaccination models for infections that confer lifelong immunity. We consider both standard (continuous) vaccination strategies and pulse vaccination programs (where mass vaccination is carried out at regular intervals). For continuous vaccination, we provide a complete global analysis of a very general compartmental ordinary differential equation LAVV model. We find that the threshold vaccination level required for eradication of wild virus depends on the basic reproduction numbers of both the wild and vaccine viruses, but is otherwise independent of the distributions of the durations in each of the sequence of stages of disease progression (e.g., latent, infectious, etc.). Furthermore, even for vaccine viruses with reproduction numbers below one. which would naturally fade from the population upon cessation of vaccination, there can be a significant reduction in the threshold vaccination level. The dependence of the threshold vaccination level on the virus reproduction numbers largely generalizes to the pulse vaccination model. For shorter pulsing periods there is negligible difference in threshold vaccination level as compared to continuous vaccination campaigns. Thus, we conclude that current policy in many countries to employ annual pulsed OPV vaccination does not significantly diminish the benefits of contact vaccination.</p><p> In the last two decades, many countries have implemented pulse vaccination for infectious diseases (mass vaccination campaigns repeated annually or at other regular intervals). Based on deterministic mathematical models, previous work has shown that the total expected cost of control or eradication (measured by the number of vaccine doses required) is identical for pulse vaccination (with any pulse interval) and for traditional, continuous vaccination. We reconsider this problem using stochastic epidemic models (both by direct simulation and by employing a moment closure approximation). We focus on measles and show that demographic stochasticity has a large impact on the relative success of pulse and continuous vaccination programs, even for well-mixed populations as large as 10 million.</p> / Thesis / Doctor of Philosophy (PhD)

Many important factors affect the spread of childhood infectious disease. To understand better the fundamental drivers of infectious disease spread, several researchers have estimated seasonal transmission coefficients using discrete-time models. This research addresses several shortcomings of the discrete-time approaches, including removing the need for the reporting interval to match the serial interval of the disease using infectious disease data from three major cities: New York City, London, and Bangkok. Using a simultaneous approach for optimization of differential equation systems with a Radau collocation discretization scheme and total variation regularization for the transmission parameter profile, this research demonstrates that seasonal transmission parameters can be effectively estimated using continuous-time models. This research further correlates school holiday schedules with the transmission parameter for New York City and London where previous work has already been done, and demonstrates similar results for a relatively unstudied city in childhood infectious disease research, Bangkok, Thailand.