### Cod on the menu? Using mathematical modelling to provide fisheries management advice

In this seminar Dr Nicola Walker, a Fisheries Modeller for Centre for Environment, Fisheries and Aquaculture Science, presented the state-space assessment model (SAM) that is used to assess fish stocks, in this case using North Sea cod as an example. Such models inform scientific advice on the management of fish stocks, with results being derived from evidence including catches, research surveys and life history.

Dr Walker explained the diagnostics for assessing the quality of input data and model fits and highlighted some of the problems facing the assessment of this stock. The North Sea cod made an interesting case study, as this fish is believed to have stock that is below safe biological limits, even though the fishery was certified sustainable just two years ago.

#### Related papers

Nicola D. Walker, Robin Boyd, Joseph Watson, Max Kotz, Zachary Radford, Lisa Readdy, Richard Sibly, Shovonlal Roy, Kieran Hyder, A spatially explicit individual-based model to support management of commercial and recreational fisheries for European sea bass Dicentrarchus labrax, Ecological Modelling, Volume 431, 2020, 109179, ISSN 0304-3800

Roy, S., Walker, N. and Sibly, R. M. (2020) Potential consequences of climate and management scenarios for the northeast Atlantic mackerel fishery. Frontiers in Marine Science, 7. 639. ISSN 2296-7745.

### An extended SIR model for the spread of COVID-19 in different communities

In early 2020 the novel coronavirus Covid-19 began to spread rapidly throughout the world. To understand the impact of the virus, and how to control infections, scientists looked towards data modelling to provide examples of the infection rate and the impact on communities.

In this seminar, Dr Chris Antonopoulos looked at the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop an extended-susceptible-infected-removed (eSIR) model that provides a theoretical framework to investigate its spread within a community. A particular focus of this research has been the time evolution of different populations, and how to monitor diverse significant parameters for the spread of the disease in various communities, represented by countries and the state of Texas in the USA.

Dr Antonopoulos explained that the eSIR model can provide us with insights and predictions of the spread of the virus in communities that recorded data alone cannot. It was interesting to hear that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease.

#### Related papers

Cooper, I., Mondal, A. and Antonopoulos, CG., (2020). A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solitons and Fractals. 139, 110057-110057

Cooper, I., Mondal, A. and Antonopoulos, CG., (2020). Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic. Chaos, Solitons and Fractals. 139, 110298-110298

### K-stability of Fano 3-folds

Dr Anne-Sophie Kaloghiros, a Senior Lecturer at Brunel University, joined us to discuss her work on K-stability of Fano 3-folds.

Fano varieties are geometric shapes which are positively curved. They arise in a wide array of fields from theoretical physics to phylogenetic trees. There are rich interactions between differential geometric and algebro-geometric properties of Fano manifolds (and more generally of Kahler manifolds).

An instance of this phenomenon was conjectured by Yau Tian and Donaldson (and proved by Donaldson, Chen and Sun): they proved that on Fano manifolds the existence of special canonical metrics is equivalent to a stability property. This is an equivalence between properties that are subtle, and still little understood.

In her talk, Dr Kaloghiros explained the algebro-geometric approaches to this problem, as well as recent developments in this area of research and their applications to our understanding of Fano surfaces and 3-folds.

#### Related papers

Ahmadinezhad, H. and Kaloghiros, A-S. (2015) 'Non-rigid quartic 3-folds'. Compositio Mathematica, 152 (5). pp. 955 - 983. ISSN: 1570-5846

Kaloghiros, AS. (2011) 'The defect of Fano 3-folds'. Journal of Algebraic Geometry, 20 (1). pp. 127 - 149. ISSN: 1056-3911