Microbial disease in coral reefs: An ecosystem in transition

Joydeb  Bhattacharyya; Samares  Pal

doi:10.3934/dcdsb.2016.21.373

Article Contents

2016, Volume 21, Issue 2: 373-398. Doi: 10.3934/dcdsb.2016.21.373

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Microbial disease in coral reefs: An ecosystem in transition

Joydeb Bhattacharyya^1, and
Samares Pal^1,

1.
Department of Mathematics, University of Kalyani, Kalyani-741235

Received: January 2015

Revised: September 2015

Published: March 2016

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Abstract

Infectious disease outbreaks are considered an important factor for the degradation of coral reefs. Reef-building coral species are susceptible to the influences of black band disease (BBD), characterized by cyanobacteria-dominated microbial mat that migrates rapidly across infected corals, leaving empty coral skeletons behind. We investigate coral-macroalgal phase shift in presence of BBD infection by means of an eco-epidemiological model under the assumption that the transmission of BBD occurs through both contagious and non-contagious pathways. It is observed that in presence of low coral-recruitment rate on algal turf, reduced herbivory and high macroalgal immigration, the system exhibits hysteresis through a saddle-node bifurcation and a transcritical bifurcation. Also, the system undergoes a supercritical Hopf bifurcation followed by a saddle-node bifurcation if BBD-transmission rate crosses certain critical value. We examine the effects of incubation time lag of infectious agents develop in susceptible corals after coming in contact with infected corals and a time lag in the recovery of algal turf in response to grazing of herbivores by performing equilibrium and stability analyses of delay-differential forms of the ODE model. Computer simulations have been carried out to illustrate different analytical results.

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Mathematics Subject Classification: Primary: 92B05, 92D25; Secondary: 92D40.

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