Spreading processes are ubiquitous in nature and societies, e.g. spreading of diseases and computer virus, propagation of messages, and activation of neurons. Computer viruses cause an enormous economic loss. Moreover, many illnesses/diseases still causing a serious threat to public health. For example, the outbreaks of circulating influenza strains cause millions of illness and deaths worldwide every year. Pronounced outbreaks of flu usually occur during winter. This recognized timing allows public health agencies to organize their flu-related mitigation and response activities to prepare for the winter flu season. Although the general wintertime peak of influenza incidence in temperate regions can be easily forecast, the specific intensity, duration, and time of individual local outbreaks are quite changeable. Even after an outbreak has begun, it is still difficult to predict the future characteristics of the epidemic curve. If the diseases/viruses outbreak characteristics could be reliably predicted, the public health response will be better coordinated.The goal is to develop a fast and accurate epidemic model to estimate, fit and forecast the spreading of an epidemic on a defined network. The aim is to conduct a study over viruses spreading phenomena both theoretically and numerically, then create a general model/algorithm that can be easily applied to different diseases and computer viruses. In this master thesis, we propose a new approach which can be used on real illness/viruses data (such as influenza) to estimate and forecast the epidemic more accurately. The approach is to use a model-inference system combining the network science, susceptible-infected-recovered-susceptible (SIRS) model, statistical filtering techniques and gradient descent. We are able to fit and estimate with a relatively low error compared to other algorithms. Moreover, we forecast the out-breaker with a high accuracy, four weeks before the true out-breaker on synthetic epidemic data. The model is evaluated on a regular graph, Erdös-Rényi graph, Watts-Strogatz small-world graph, & Barabási-Albert graph. Furthermore, the model is carried out on real-world epidemic data (influenza data) for four countries (the Netherlands, Germany, Belgium and the United Kingdom), from the years 2012 to 2017.