# Eight challenges for network epidemic models

Pellis, Lorenzo, et al. “Eight challenges for network epidemic models.” *Epidemics* 10 (2015): 58-62.

Networks are representations of complex systems in which components interact. In these models, components are represented as nodes with the interactions between them as edges. Network models have been used to model infection diseases. In the models the nodes can represent individuals, groups of individuals, or locations where individuals are connected. In this paper, the authors consider the nodes of networks as individuals and the edges as acquaintances between them. They then outline eight challenges for network epidemic models.

1. Understanding the effect of heterogeneity on parameter estimation and epidemic outcome

Specific quantities of an outbreak, such as reproductive number, probability and size of an outbreak, duration of an outbreak and peak incidence, and how they relate to each other and heterogeneity in susceptibility and degree is relatively unexplored. Also, understanding how heterogeneities affect parameter estimation and biases on estimations of epidemic predictions.

2. Developing analytical methods to generate and study epidemics on static unweighted complex networks

Although analytical results have be found for some networks, these often make strong unrealistic assumptions.

3. Developing analytical methods to model weighted and dynamic networks and epidemic thereon

The links within real networks are often not all identical and may not remain static. We lack a mathematical framework that handles a broad range of realistic networks.

4. Incorporating waning immunity in network epidemic models

On static random networks, much of the results rely on the assumption of permanent immunity. This significantly increases the analytical tractability. Quantities such as the reproductive number and the probability and size of an outbreak can be determined from branching processes.

5. Developing and validating approximation schemes for epidemics on networks

There are some methods to approximate these results. However, these are often limited to sets of differential equations.

6. Clarifying the impact of network properties on epidemic outcome

Understanding of how network characteristics such as clustering and degree correlation have on the reproductive number of the parasite, the probability of a large outbreak, and the size of an outbreak is lacking. These are lacking because of the shortage of analytical results.

7. Strengthening the link between network modeling and epidemiologically relevant data

As more data becomes available, the analytical and computational toolkit. Using data-driven analytical methods, would help with enhancing deterministic modeling behavior. Modeling also plays an important role in guiding data collection.

8. Designing network-based interventions

Understanding the structure of the network is vital to implementing an optimal strategy. However, without knowing the complete network strategies are often hard to develop and implement.