Modelagem matemática da doença do caranguejo letárgico via ondas viajantes

Abstract

O caranguejo-uçá, Ucides cordatus, tem fundamental importância para os manguezais, seu ambiente natural, realizando a decomposição de matéria orgânica, e também sendo um importante biomonitor de áreas críticas. Sua comercialização é considerada a atividade econômica mais importante relacionada a manguezais, e essencial para o sustento das comunidades ribeirinhas. Desde 1997, têm sido observados eventos de mortandade das populações dessa espécie, com redução de até 85% das coletas. Em tais eventos, os caranguejos doentes apresentavam sintomas comuns, entre eles, uma considerável dificuldade de locomoção, e consequentemente, dificuldade de retornar às suas tocas. Por essa razão, esta enfermidade foi chamada de Doença a do Caranguejo Letárgico (DCL). Em 2005, comprovou-se que o agente causador da DCL é o fungo patogênico Exophiala cf psycrophila, um fungo do Filo Ascomycota...

The mangrove crab, Ucides cordatus, plays a crucial role in a variety of ecosystem processes in its environment, such as nutrient cycling, and it is a biomonitor of critical areas. Moreover, it is an important component in the economy of several underprivileged communities that depend on it for their subsistence. Beginning in 1997, massive mortalities of U. cordatus have been report by crabcollectors, such as 85% reduction in collection rates in some regions. Crabs in areas of high mortality share several common symptoms, such as lethargy, poor motor control and inability to return to the upright position when turned upside down. Hence, this pathology is called Lethargic Crab Disease (LCD). Finally, in 2005, there were several evidences showing that LCD is caused by a fungus of Phylum Ascomycota, Exophiala cf psycrophila. The DCL fungus is not easily found among the periods in which the mortalities occur, been detected only into the mangrove crab U. cordatus, all asymptomatic. There is also no evidence of the presence of this fungus in the soil or plant samples of the mangrove. As a result, the initial hypothesis is that the disease spreads among the estuaries through dispersal of the fungus by the sea. Based on the epidemiology of the LCDdisease,we construct amathematical model using a system of partial differential equations, considering diffusion and advection processes, to describe the dispersion of the disease through the mangrove complexes. The aim of this work is to find travelling waves solutions for the developed model, that connect two equilibrium points. For this, we analyse the characteristic polynomial fromthe jacobianmatrix evaluated at one of equilibrium points, the disease-free equilibrium, and present results about the necessary conditions for the existence of travelling wave solution, numerical simulations and finally, estimate the minimum value... (Complete abstract click electronic access below)