Mathematical Modeling, R0, and the Importance of Uncertainty

Abstract

Mathematical modeling of infectious disease transmission dynamics can never represent all features of those dynamics. Its goal must be to represent all those features which are salient for the purpose of making particular inferences that are relevant to public health decisions. The way to identify these features is through an inference robustness assessment, a continuous cycle in which we realistically relax simplifying assumptions, determine whether our inferences are robust to that relaxation, and then, based on the answer to that question, either gather additional data or relax additional assumptions.

In this dissertation, I examine the consequences of realistically relaxing particular simplifying assumptions about the transmission dynamics of two very different pathogens, HIV and poliovirus. I show that key inferences about these systems are not robust to such relaxation, and highlight some ways in which additional data might be gathered in order to constrain the plausible parameter space. Chapters II and III of this dissertation deal with the effects of episodic risk in HIV transmission systems; Chapters IV through VI cover the effects of waning in poliovirus transmission systems.

The per-act probability of sexual transmission of HIV is especially high during early HIV infection (EHI). Any behavioral pattern that increases the expected number of sex acts early in HIV infection will naturally interact with this. One such pattern is episodic risk. In this dissertation, I examine how episodic risk can greatly affect both the role of EHI in sustaining HIV transmission and the relative ease of controlling transmission through Universal Test and Treat measures. Inferences made on the basis of observations about the degree of risk heterogeneity at a given point in time are shown not to be robust to uncertainty in the degree to which risk heterogeneity is episodic, rather than static.

Only a minute fraction of poliovirus infections result in the acute flacid paralysis (AFP) for which poliovirus is notorious. Nevertheless, AFP surveillance remains the backbone of efforts to detect circulating poliovirus. Consequently, the circulation of poliovirus in the absence of paralytic cases may be said to be ``silent" with respect to our primary means of detecting it. Silent circulation that is sustained beyond the Global Polio Eradication Initiative's standard of 3 years without a detected polio case in order to certify a country polio-free has the potential to seriously jeopardize eradication efforts.

The potential for such sustained silent circulation is increased by a high prevalence of partial immunity to poliovirus infection. Even very low levels of immunity are sufficient to effectively eliminate the risk of developing paralysis upon exposure to virulent strains of poliovirus. There is substantial evidence that even full immunity can wane sufficiently over time to make (non-paralytic) infection possible again. Although the importance of including waning in models of poliovirus transmission is increasingly recognized by prominent modelers in the field, this inclusion has often failed to take adequate account of our level of uncertainty as to the speed and depth of that waning. In this dissertation, I present evidence that important inferences about the potential for sustained silent circulation are not robust to that uncertainty.

On a methodological note, in Appendix A, I present an effective reproduction number analogue to the Next-Generation Matrix basic reproduction number. In Chapter VI, I present a hybrid deterministic-stochastic approach for efficient simulation of dynamics during silent circulation.