Many challenges are still faced in bridging the gap between Mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a Susceptible-Infected-Recovered (SIR) model and a Susceptible-Infected-Recovered-Exposed-Deceased (SEIRD) model based on conformable space-time PDEs for the Coronavirus Disease 2019 (COVID-19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficious for obtaining analytical solutions for nonlinear systems of partial differential equations (PDEs) with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID-19 pandemic models with conformable space-time partial derivatives