The Internet of Things (IoT) devices are being widely deployed and have been targeted and victimized by malware attacks. The mathematical modelling for an accurate prediction of malicious spreads of botnets across IoT networks is of great importance. Suppose the spread of IoT botnets can be predicted using mathematical models, the security community can then take the necessary steps to deter an outbreak of botnet attacks and minimize the damage caused by malware. This paper surveys mobile malware epidemiological models to understand the mechanisms and dynamics of malware spread for IoT botnets. We describe the characteristics of IoT botnets based on the Susceptible-Infection-Recovery-Susceptible and Susceptible-Exposed-Infection-Recovery-Susceptible epidemic models. These models extend the traditional SIR (Susceptible-Infection-Recovery) model by adding extra states and parameters specific to the epidemic spread of IoT botnets. We use mathematical modelling to simulate complex spreading processes of IoT botnets and interpret the influence of an epidemic on distributed denial of service attacks. We use MATLAB and R to illustrate the use of a stochastic IoT botnet transmission model in the identification and mitigation of challenges towards minimizing the impact of devastating IoT botnet epidemics.