Compartmental models that dynamically divide the host population in categories such as susceptible, infected and immune constitute the mainstream of epidemiological modelling. Effectively such models treat infection and immunity as binary variables. We constructed an individual based stochastic model that considers immunity as a continuous variable and incorporates factors that bring about small changes in immunity. The small immunity effects (SIE) comprise cross immunity by other infections, small increments in immunity by sub clinical exposures and slow decay in the absence of repeated exposure. The model makes qualitatively different epidemiological predictions including repeated waves without the need for new variants, dwarf peaks (peak and decline of a wave much before reaching herd immunity threshold), symmetry in the upward and downward slopes of a wave, endemic state, new surges after variable and unpredictable gaps, new surge after vaccinating majority of population. In effect the SIE model raises alternative possible causes of the universally observed dwarf and symmetric peaks and repeated surges, observed particularly well during the Covid-19 pandemic. We also suggest testable predictions to differentiate between the alternative causes for repeated waves. The model further shows complex interactions of different interventions that can be synergistic as well as antagonistic. The model suggests that interventions that are beneficial in the short run can also be hazardous in the long run.