ABSTRACT
The risk of dengue virus infection to travelers visiting dengue fever endemic regions was studied through the use of mathematical modeling. A Susceptible-Infected-Recovered (SIR) model is used to describe the transmission of dengue fever (DF) in an endemic region into which tourists enter. The dynamics of a new class of human, the traveler, is incorporated into the systems of first order differential equations in the SIR describing the dynamics of the transmission in the host region. Using standard dynamic analysis methods, the numbers of travelers who become infected with the dengue virus are calculated as a function of the length of time the tourist stays in the region.
Subject(s)
Dengue/epidemiology , Dengue Virus/isolation & purification , Endemic Diseases , Female , Humans , Incidence , Male , Models, Theoretical , Predictive Value of Tests , Risk Assessment , Survival Rate , Thailand/epidemiology , TravelABSTRACT
The possibility of relapse is introduced into a mathematical model for the transmission of Plasmodium vivax malaria. In the model, the human population is divided into four classes: susceptible, infected, dormant and recovered. Loss of immunity by individuals in the recovered class moves these individuals back into the susceptible class. Two equilibrium states are found, a disease-free state and an endemic state. A basic reproduction number Ro is found. Depending on whether Ro is less than or greater than one. the disease free state or the endemic state results. The dependence of Ro on the rate of relapse is determined and the implication of this dependence is identified.
Subject(s)
Animals , Disease-Free Survival , Endemic Diseases , Humans , Malaria, Vivax/immunology , Models, Statistical , Plasmodium vivax/physiology , RecurrenceABSTRACT
The influence of age structure in the susceptible class of the Susceptible-Infected Recovered (SIR) model used to describe the transmission of dengue hemorrhagic fever (DHF) was studied. This was done by first dividing all of the population classes into cohorts and then writing a set of coupled SIR equations for each cohort. The consequences of assuming different behavior of the transmission rates on the age structure in the DHF incidence rates were determined. In order for the predicted incidence rates to be similar to the DHF incidence patterns observed in several provinces in Thailand during the DHF epidemic in 1998, the transmission rates should be age dependent.