Our research and methods are diverse with the common thread being the use of mathematical models for understanding questions from the sciences and other real-world questions. Our research goals are to use, and where necessary develop, the theoretical and analytical tools necessary for understanding these systems. In particular, we have applied these tools to the following African issues:
Natural systems modeling group
Diseases are always a concern in Africa. Multifaceted approaches are necessary to their control and mathematical models can be useful in the approaches used. (See for example Collins and Duffy, 2021; Mugabi et al., 2021a,b; Duffy and Collins, 2019).
Managing ecosystems are crucial to the wellbeing of our future on earth. Central to this aim is an understanding of how and in what way species persist. Mathematical dynamical systems models can assist in understanding and also guide ecosystem management. (See for example, Duffy and Collins, 2021; Duffy, O’Connor and Collins, 2018; Dai, Zhang, Xu, Duffy and Guo, 2017; Duffy and Collins, 2016). We have investigated the importance of animal movement on ecosystem function, especially with regard to elephants.
Investigation of specific ecological systems using models
Leader: Prof. Kevin Duffy
Example: Models on how elephants move around reserves
Research in food security
Food security is a growing concern worldwide and in the arid conditions of Africa particularly important. We have developed a decision support tool to assist small farm holders with these decisions (See for example, Manjengwa, Chitja and Duffy, 2016; Duffy and Masere, 2015; Masere and Duffy, 2014). We are also linking these results to nutritional needs.
Human growth exerts enormous pressures on societies and the environment. Here we explore models of the impacts of population growth on cities. We also consider the importance of energy needs and impacts created by humans. (See for example, Collins, Simelane and Duffy, 2019; Ebhota and Tabakov, 2020).
Physical systems modeling group
Theoretical and mathematical physics
Multi-disciplinary studies in the application of non-linear and non-Hermitian approaches to various phenomena and systems that arise in classical and quantum physics, biology and optics (see for example any of Paliathanasis, 2021, Zloshchastiev, 2021, Govender, 2021).
This summary represents an overview of our work. The projects all involve levels of applied mathematical sophistication and the staff and students working on them benefit from the interrelated communication resulting from the approaches.