Titlebook: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory; Carlos Castillo-Chavez,Sally Blower,

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Infectious Disease Models with Chronological Age Structure and Epidemiological Age Structure,us on the relation between the basic reproductive number, the mean life span, and the mean age at infection. The S-I model, with no recovery, is analyzed completely and partial stability results are obtained for models with mean infective period much shorter than mean life span.

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Global Dynamics of Tuberculosis Models with Density Dependent Demography,r recruitment rate is established with the use of explicit threshold quantities controlling the absolute and relative spread of the disease and the likelihood of extinction or persistence of the total population. The classification of planar quadratic systems helps rule out the existence of closed orbits (limit cycles).

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Global Stability in Some Seir Epidemic Models,. > 1, a unique endemic equilibrium P. is globally asymptotically stable in the interior of the feasible region and the disease will persist at the endemic equilibrium if it is initially present. In this paper, this threshold phenomenon is established for two epidemic models of SEIR type using two recent approaches to the global-stability problem.

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The Global Stability Analysis for an SIS Model with Age and Infection Age Structures,etermining the global dynamics, i.e., the endemic steady-state is globally asymptotically stable if .. > 1, while the disease-free steady-state is globally asymptotically stable if .. ≤ 1. The basic reproductive number is over estimated where the infection age is ignored.

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The Transition Through Stages with Arbitrary Length Distributions, and Applications in Epidemics,period, infectious period without symptoms (the two together usually form the incubation period), infectious period with symptoms, and often an immunity period. With some diseases, HIV/AIDS e.g., the infectious period can be further subdivided according to the progress of the disease.

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Infection Transmission Dynamics and Vaccination Program Effectiveness as a Function of Vaccine Effee risk in the unvaccinated. These risks are sometimes calculated for disease and sometimes for infection. In this paper, we consider only infection. We label this statistic . and the risks in the vaccinated and unvaccinated populations on which it is based as .. and .., respectively: