A dynamical model to explain outbreaks of Hantavirus infections

J. TREDICCE; J. M. BOYER; M. S. TORRE

Punta del este

Workshop; Dynamics Days Latin America and the Caribbean; 2018

Universidad de la Republica

Simple models for population dynamics have been used in the past to study outbreaks of infections. Usuallythe ecological conditions were considered as parameters remaining constant in time. Here we analyze thepropagation of a virus when the ecological conditions change slowly in time. In particular we consider amodel used to simulate the propagation of Hanta virus in the mice population. We show that a changingparameter varying much slower than the time constants associated with the variables may cause a muchfaster increase in the density of infected mice generating an epidemic of hanta virus. Thus, the ecological process with very long periodical cycle or with low frequency of occurrence, such us the colihue bamboo (Chusquea culeou) bloom, increases the mice density and it may produce an outbreaks of the disease . Theresults obtained also agree with other experimental observations, such as the disappearance of the infection for prolonged periods and its abrupt appearance. This later phenomenon is explained in terms of the critical slowing down resulting from crossing a bifurcation point. We also studied how the variations in time of the parameters induce a chaotic behavior of the variables.