Mathematical modeling refers to the dire action of describing practical systems, phenomena, or issues with mathematical abstractions and frameworks. Modeling aims at reducing the complexity of systems, whilst maintaining their key properties, so that they can be analyzed, predicted, and decisions made. The chapter is devoted to the modeling of so-called computer viruses and infectious diseases where the main tools of the analysis are the fractional calculus and the fixed point theory. Computer virus spread can be effectively modeled mathematically as a way of gaining insight into this phenomenon and as a means of making predictions about it. They infect, spread and disrupt their host systems in much the same way as biological viruses do and once again this means that mathematical techniques, especially those of epidemiology can be used to analyze their behaviour. Computer viruses are transmitted over the networks via the vulnerability in the systems. To analyze such process, it is common to use models that divide the devices in three states: Susceptible (S), which are vulnerable devices; Infected (I), which are device already infected and Recovered (R), which are devices that have been cleaned or secured against the virus. These classes assist in simplifying and dissecting the manner in which a virus spreads and is finally contained. A popular model is the SIR model which is used to trace how the devices are flowing in and out of the three categories. The model takes parameters like the transmission rate ( \(\beta \) ), where the rate determines how fast the virus spreads, and the recovery rate ( \(\gamma \) ), where the rate determines how well infected devices are recuperated. There is also another simpler model that does not consider recovery and is only concerned with the spread of the virus; the SI model.