1
|
Abstract
Salton Sea (a destination resort) is to be saved from being converted into a skeleton-filled wasteland. The critical amount of water flowing into the sea to maintain its level and salinity has been diverted since January 2018. This will lead to shrinking volumes and increasing salinities. Ecological consequences and public health impacts of altered conditions will be phenomenal. We design and analyze a minimal eco-epidemiological model to figure out future journey of this sea; a way station for fish-eating migratory birds. The mathematical model has been assembled in terms of prey-predator interaction. The salient feature of the proposed model is its seasonally varying contact rate which represents rate of conversion of susceptible fishes into infectives. We have analytically investigated the global stability, disease persistence and periodic solutions of the proposed model system. Susceptible prey-induced periodic solution is globally asymptotically stable when [Formula: see text], otherwise unstable and hence disease persists for [Formula: see text]. Global stability and Hopf bifurcation (HB) analysis help us extract parameter values to explore the dynamical behavior of the model system. Two-dimensional parameter scans and bifurcation diagrams reveal that the model displays propensity towards chaotic dynamics, which is associated with extinction-sized population densities. In the presence of stochastic external forces, this implies extinction of most of the fish species. This, in turn, suggests that resident birds will have to migrate to other destinations. The fish-eating migratory birds will be forced to switch over to invertebrates. Ecological consequences and public health impacts of this transition would be severe. Conservation groups are solicited to draw attention of the government to avert this impounding danger. It is important to plan for an ecosystem-wide transition such that impacts on birds and on human inhabitants living adjacent to the shrinking and salinizing sea are minimized.
Collapse
Affiliation(s)
- Ranjit Kumar Upadhyay
- Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India
| | - Sarita Kumari
- Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India
| | - Sangeeta Kumari
- Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826004, Jharkhand, India
| | - Vikas Rai
- Department of Mathematics, Eritrea Institute of Technology, Mai Nefhi, Asmara, Eritrea, North East Africa, Africa
| |
Collapse
|
2
|
Bate AM, Hilker FM. Preytaxis and Travelling Waves in an Eco-epidemiological Model. Bull Math Biol 2018; 81:995-1030. [DOI: 10.1007/s11538-018-00546-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Accepted: 11/28/2018] [Indexed: 01/21/2023]
|