Abstract. The recent broad interest on ratio-dependent based predator functional response calls for detailed qualitative study on ratio-dependent predator-prey differential systems. A first such attempt is documented in the recent work of Kuang and Beretta(1998), where Michaelis-Menten-type ratio-dependent model is studied systematically. Their paper, while contains many new and significant results, is far from complete in answering the many subtle mathematical questions on the global qualitative behavior of solutions of the model. Indeed, many of such important open questions are mentioned in the discussion section of their paper.Through a simple change of variable, we transform the Michaelis-Menten-type ratiodependent model to a better studied Gause-type predator-prey system. As a result, we can obtain a complete classification of the asymptotic behavior of the solutions of the MichaelisMenten-type ratio-dependent model. In some cases we can determine how the outcomes depend on the initial conditions. In particular, open questions on the global stability of all equilibria in various cases and the uniqueness of limit cycles are resolved. Biological implications of our results are also presented.

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We studied the severe acute respiratory syndrome (SARS) outbreak in Taiwan, using the daily case-reporting data from May 5 to June 4 to learn how it had spread so rapidly. Our results indicate that most SARS-infected persons had symptoms and were admitted before their infections were reclassified as probable cases. This finding could indicate efficient admission, slow reclassification process, or both. The high percentage of nosocomial infections in Taiwan suggests that infection from hospitalized patients with suspected, but not yet classified, cases is a major factor in the spread of disease. Delays in reclassification also contributed to the problem. Because accurate diagnostic testing for SARS is currently lacking, intervention measures aimed at more efficient diagnosis, isolation of suspected SARS patients, and reclassification procedures could greatly reduce the number of infections in future outbreaks.

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Abstract. The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1) competitive exclusion; 2) total extinction, i.e., collapse of the whole system; 3) coexistence in the form of positive steady state; 4) coexistence in the form of oscillatory solutions; and 5) introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed.