# A Generalized Framework for the Estimation of Edge Infection Probabilities
## 6 Conclusions  
In this paper, we explored some theoretical properties and demonstrated the general applicability of the Generalized Inverse Infection Model. Given an unweighted graph and a set of observations on an infection process, the GIIM is able to estimate the edge infection probabilities explaining the input observations. Contrary to existing models, our model is able to handle an arbitrary number of observations; it can be applied to fully, minimally or, potentially, partially observed infection processes. The nature of the observations is not fixed either; in the scope of this study, we experimented with binary and real node infection values, but it is possible to use other values tied to the spread of the infection process within the framework. The underlying infection model may also be customized: we worked with the SI, IC, SIR and SEIR models, but it is also possible to consider other network-based models. The GIIM formulates the inverse infection task as a general optimization problem, and a Particle Swarm Optimization method was suggested as the solution method. Finally, it is possible to further extend the functionality of the model, such as estimating the parameters of the infection model.  
We evaluated the performance of the GIIM on a large variety of artificial infection scenarios. We have shown on trees that, even though the problem is underdetermined, it is possible to find accurate explanations of the infection process. In more general complex networks, we examined the behavior of our method on 108 different inverse infection tasks. Our findings indicate that there is a close relationship between the expected size of the infection and the difficulty of the task, with larger infections being easier to predict. There is a complex interplay between the density of initial infections, the likelihood of the infection spread and the difficulty of the estimation at different time steps. Finally, we experimented with larger networks and a few specific infection scenarios to investigate the scalability of the problem. We can say that the optimization method performs well for almost all of the situations described in this paper.  
The GIIM method's ability to predict edge infection values in real-life scenarios has already been proven in [24; 25]. In this work, we have shown that the model's flexibility and robustness allow it to be applied in wider settings than we have previously seen, paving the way for successful future applications of the model.  
**Author Contributions:** Conceptualization, A.B. and L.G.; methodology, A.B and L.G.; software, A.B.; validation, A.B.; formal analysis, A.B. and L.G.; investigation, A.B. and L.G.; resources, A.B. and L.G.; data curation, A.B.; writing--original draft preparation, A.B. and L.G.; writing--review and editing, A.B. and L.G.; visualization, A.B.; supervision, A.B. and L.G.; project administration, L.G.; funding acquisition, L.G. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Health and Medical Research Council (NHMRC), grant number No. APP1082524.  
**Data Availability Statement:** Data sharing not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.