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Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R 0 , the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for R 0 are(More)
Epidemiological models with nonlinear incidence rates lambda IpSq show a much wider range of dynamical behaviors than do those with bilinear incidence rates lambda IS. These behaviors are determined mainly by p and lambda, and secondarily by q. For such models, there may exist multiple attractive basins in phase space; thus whether or not the disease will(More)
Infection by one strain of influenza type A provides some protection (cross-immunity) against infection by a related strain. It is important to determine how this influences the observed co-circulation of comparatively minor variants of the H1N1 and H3N2 subtypes. To this end, we formulate discrete and continuous time models with two viral strains,(More)
Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the(More)
Calculations revealed that approximately a third of the reported cases of gonorrhea in women during 1973-1975 were discoveries of the screening program. Theoretical models and epidemiologic data showed that the prevalence of gonorrhea adjusts rapidly to changes in social behavior, medical treatment, and control programs, that prevalence oscillates(More)
Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (birth and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are(More)
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)
The vaccination program for pertussis (whooping cough) in the United States consists of giving multiple doses of pertussis vaccine to young children. A demographic model with a steady-state age distribution is used as a basis for building an epidemiologic model for the transmission of pertussis. This age-structured model includes vaccination of infants and(More)
A predator-prey model with logistic growth in the prey is modified to include an SIS parasitic infection in the prey with infected prey being more vulnerable to predation. Thresholds are identified which determine when the predator population survives and when the disease remains endemic. For some parameter values the greater vulnerability of the infected(More)
Approximately one million adult pertussis cases occur annually in the US, and infants still die from pertussis. Computer simulations were used to predict the impact of vaccination of children, adults and/or adolescents, and household members of newborns (cocoon strategy). Childhood vaccination greatly reduced cases in children, but increased the incidence(More)