Defining the role of T-cell avidity and killing efficacy in forming immunological response(s), leading to relapse-remission and autoantibody release in autoimmune type 1 diabetes (T1D), remains incompletely understood. Using competition-based population models of T- and B-cells, we provide a predictive tool to determine how these two parametric quantities, namely, avidity and killing efficacy, affect disease outcomes. We show that, in the presence of T-cell competition, successive waves along with cyclic fluctuations in the number of T-cells are exhibited by the model, with the former induced by transient bistability and the latter by transient periodic orbits. We hypothesize that these two immunological processes are responsible for making T1D a relapsing-remitting disease within prolonged but limited durations. The period and the number of peaks of these two processes differ, making them potential candidates to determine how plausible waves and cyclic fluctuations are in producing such effects. By assuming that T-cell and B-cell avidities are correlated, we demonstrate that autoantibodies associated with the higher avidity T-cell clones are first to be detected, and they reach their detectability level faster than those associated with the low avidity clones, independent of what T-cell killing efficacies are. Such outcomes are consistent with experimental observations in humans and they provide a rationale for observing rapid and slow progressors of T1D in high risk subjects. Our analysis of the models also reveals that it is possible to improve disease outcomes by unexpectedly increasing the avidity of certain subclones of T-cells. The decline in the number of -cells in these cases still occurs, but it terminates early, leaving sufficient number of functioning -cells in operation and the affected individual asymptomatic. These results indicate that the models presented here are of clinical relevance because of their potential use in developing predictive algorithms of rapid and slow progression to clinical T1D.
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