A number of important phenomena in epidemiology can be modeled by systems of ordinary differ- ential equations (ODEs). This paper considers a modified system of ODEs which is nonlinear and describes the MSEIR model. Based on the nonstandard discretization method, we propose a family of explicit schemes to solve numerically the MSEIR model. The proposed schemes preserve the positivity property as well as the requirement of conservation law and boundedness. Numerical tests of new schemes are done. A brief discussion of how the work can be extended is also given.
