A novel predictive modeling framework for the spread of infectious diseases using high-dimensional partial differential equations is developed and implemented . A scalar function representing the infected population is defined on a high-dimensional space and its evolution over all the directions is described by a population balance equation (PBE). New infections are introduced among the susceptible population from a non-quarantined infected population based on their interaction, adherence to distancing norms, hygiene levels and any other societal interventions . Moreover, recovery, death, immunity and all aforementioned parameters are modeled on the high-dimensional space . To epitomize the capabilities and features of the above framework, prognostic estimates of Covid-19 spread using a six-dimensional (time , 2D space, infection severity, duration of infection, and population age) PBE is presented . Further, scenario analysis for different policy interventions and population behavior is presented, throwing more insights into the spatio-temporal spread of infections across duration of disease, infection severity and age of the population . These insights could be used for science-informed policy planning.