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- J Mena-Lorca, H W Hethcote
- Journal of mathematical biology
- 1992

Five SIRS epidemiological models for populations of varying size are considered. The incidences of infection are given by mass action terms involving the number of infectives and either the number of susceptibles or the fraction of the population which is susceptible. When the population dynamics are immigration and deaths, thresholds are found which… (More)

- J Mena-Lorca, J X Velasco-Hernandez, C Castillo-Chavez
- IMA journal of mathematics applied in medicine…
- 1999

A mathematical model of the interaction between two pathogen strains and a single host population is studied. Variable population size, density-dependent mortality, disease-related deaths (virulence), and superinfection are incorporated into the model. Results indicate that coexistence of the two strains is possible depending on the magnitude of… (More)

- Jaime Mena-Lorca, Jorge X Velasco-Hernández, Pablo A Marquet
- Mathematical biosciences
- 2006

Simple patch-occupancy models of competitive metacommunities have shown that coexistence is possible as long as there is a competition-colonization tradeoff such as that of superior competitors and dispersers. In this paper, we present a model of competition between three species in a dynamic landscape, where patches are being created and destroyed at a… (More)

- L Q Gao, J Mena-Lorca, H W Hethcote
- Mathematical biosciences
- 1995

Periodic solutions have been found for some infectious disease models of the SI and SEI types. Here four SEI models with either disease-reduced or uniform reproduction are examined to determine the model features that do and do not lead to periodic solutions. The two SEI models with the simple mass action incidence beta XY can have periodic solutions for… (More)

- Eduardo González-Olivares, Betsabé González-Yañez, Jaime Mena-Lorca, Jose D Flores
- Mathematical biosciences and engineering : MBE
- 2013

The main purpose of this work is to analyze a Gause type predator-prey model in which two ecological phenomena are considered: the Allee effect affecting the prey growth function and the formation of group defence by prey in order to avoid the predation. We prove the existence of a separatrix curves in the phase plane, determined by the stable manifold of… (More)

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