Throughout history, infectious diseases, which are illnesses caused by a disease agent that can be transmitted from organism to organism, have had a big impact on the human health and social development. Since the great work of Kermack and McKendrick, modeling an epidemic has been one of the central themes in mathematical biology. The processes of disease transmission are complex and thus nonlinear dynamics are often observed.

One grander purpose of mathematical epidemiology is to predict in populations how diseases transmit between humans or animals in both time and space and find out the effective control and prevention measures which can guide policy decisions. Spatial epidemics systems based on reaction diffusion equations can be used to estimate the formation of spatial patterns on the large scale, the transmission velocity of diseases and reveal the regions where they may run a high risk of disease outbreak. Epidemic systems based on complex networks in which the nodes represent individuals and the links represent various interactions among those individuals and diseases can only spread along the edges of the networks can be used to reflect the heterogeneity of human beings. In this sense, epidemic systems based on reaction diffusion equations and complex networks are suitable for describing the process of epidemiology.

The special issue received many manuscripts from the scholars in these research fields. The topics of these accepted papers are from theoretical studies to applications in real diseases, including global dynamics in complex networks, stability analysis in HIV infection, threshold behavior on multistage epidemic, and mathematical modelling on Ebola in West Africa.

It should be noted that it is not easy to gather all the research work in the fields of nonlinear dynamics in epidemic systems. We know that although more work is needed, this special issue may be seen as a new start for the investigations on nonlinear dynamics in epidemic systems. As a result, we can predict that more and more excellent work on this topic will emerge and it will enjoy a huge boom in the future.

Li Li
Zhen Jin
Sanling Yuan
Kaifa  Wang
Alexander B.  Medvinsky
Bai-Lian Li