Simulations of rubella vaccination strategies in China.

Many infants whose mothers have rubella infections during their first trimester of pregnancy have birth defects called congenital rubella syndrome (CRS). China does not routinely vaccinate against rubella in the public sector, but may need to start as its 'one child per couple' policy changes the population age distribution and the dynamics of rubella epidemiology, so that the incidence of rubella in pregnant women increases. Computer simulations with demographic transitions and rubella transmission dynamics predict that, with no or limited rubella vaccination, CRS incidence in China in the 30 years after 2020 will be more than twice the level in 2005.

Competing species models with an infectious disease.

The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number R(1) determines the asymptotic behavior, so that the disease dies out if R(1) 1. Because the disease-reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition.

Species coexistence and periodicity in host-host-pathogen models.

Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In contrast, the models formulated using the frequency-dependent (standard) incidence have the behavior of a classic endemic model, since below the threshold, the disease dies out, and above the threshold, the disease persists and the infectious fractions approach an endemic equilibrium.

A predator-prey model with infected prey.

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 prey allows the predator population to persist, when it would otherwise become extinct.

Adolescent and adult pertussis vaccination: computer simulations of five new strategies.

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 in adolescents and adults.

Using computer simulations to compare pertussis vaccination strategies in Australia.

High levels of notified pertussis in adolescents and adults, persisting severe disease (hospitalization and deaths) in infants despite high childhood immunization coverage, together with the availability of adult-formulated pertussis vaccines, have made alternate strategies for vaccine control of pertussis an important issue in Australia. An age-structured computer simulation model was used to compare the likely effects of adopting different vaccination strategies in Australia on pertussis transmission by age group over a 50 year time period. Epidemiological parameters and vaccination coverage in Australia were estimated from previous pertussis modeling studies and existing data.

Effects of quarantine in six endemic models for infectious diseases.

Thresholds, equilibria, and their stability are found for SIQS and SIQR epidemiology models with three forms of the incidence. For most of these models, the endemic equilibrium is asymptotically stable, but for the SIQR model with the quarantine-adjusted incidence, the endemic equilibrium is an unstable spiral for some parameter values and periodic solutions arise by Hopf bifurcation. The Hopf bifurcation surface and stable periodic solutions are found numerically.