A mathematical approach to lethargic crab disease

• Grant number: 07/05265-1
• Support Opportunities: Scholarships abroad - Research
• Start date: January 02, 2008
• End date: February 01, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cláudia Pio Ferreira
• Grantee: Cláudia Pio Ferreira
• Host Investigator: Maria de Lourdes Esteva
• Host Institution: Instituto de Biociências (IBB). Universidade Estadual Paulista (UNESP). Campus de Botucatu. Botucatu , SP, Brazil
• Institution abroad: Universidad Nacional Autónoma de México, Coyoacán (UNAM), Mexico

Abstract

Since 1997 massive mortalities of the mangrove crab, Ulcides cordatus, has been report on Brazilian coast. In 2005, the Grupo Integrado de Aquicultura e Estudos Ambientais (GIA-UFPR) shown that the etiological agent that promove the Lethargic Crab disease (DCL) is a fungus of phylum Ascomycota. Working together with the Departmentof Bioestatística (IBB-UNESP) this group searches now to develop an epidemiological model to describes the disease dynamics and tries to evaluate the most susceptible places for new events of mortality. The first step, is to developed a mathematical model to describe the LCD disease transmission between crabs that belongs to a specific mangrove. In this case, the model is described by a system of ordinary differential equations. An analysis of this model indicates that its presents Hopf bifurcation that allows it to reproduce the cyclical temporal patterns of the disease. Analytical and numerical results for the equilibrium points, stability analysis will be obtained. (AU)