<![CDATA[We consider Susceptible-Infected-Recovered (SIR) models of infectious disease spread without and with vital dynamics. We recall some existing analytical approximate iterative methods for solving these models. We observe that all these methods solve the models accurately only for points close to the initialisation. These methods produce inaccurate, and even, unrealistic solutions to the SIR models if the time domain is sufficiently large. In this paper, our research objective is to propose an analytical-numerical iterative method, which is able to solve the SIR models accurately on the whole domain. The research method used is quantitative mathematical modelling with simulation. By implementing this analytical-numerical iterative method into a finite number of small consecutive subintervals of the domain, our research results show that the proposed method produces accurate solutions to the SIR models on the whole domain.]]>
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