One-dimensional discrete-time population models, such as those with logistic or Ricker growth, may exhibit periodic or chaotic dynamics depending on the parameter values. Adding epidemiological interactions into a population model increases its dimension and the resulting complexity of its dynamics. Previous work showed that a discrete susceptible-infectious-recovered (SIR) model with Ricker growth and density-dependent, non-fatal infection exhibits qualitatively similar total population dynamics in the presence and absence of disease. In contrast, a more complicated three-class susceptible-infectious-virus (SIV) system that includes disease-induced mortality does not. Instead, infection in the SIV system shifts the periodic behavior in a manner that distinguishes it from the corresponding disease-free system. Here, we examine a two-class susceptible-infectious (SI) model with Ricker population growth, density-dependent infection, and parameters that tune disease-induced mortality and the capacity of infected individuals to reproduce. We use numerical bifurcation analysis to determine the influence of infection on the qualitative structure of the long-time behavior. We show that when disease is allowed to alter reproduction or disease-induced mortality, infection produces distinctly different bifurcation structures than that of the underlying disease-free system. In particular, it shifts both the location of period-doubling bifurcations and the onset of chaos. Additionally, we show that disease-induced mortality introduces multistability into the system such that a given set of model parameters can produce multiple distinct qualitative behaviors depending upon initial conditions. This work demonstrates that the infection-induced changes in dynamics observed by previous authors do not require the presence of infecting virus particles in the environment. In doing so, our work also advances understanding of the conditions under which discrete epidemiological models exhibit multistability.