Applied Mathematics & Information Sciences

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The article presents the stochastic modeling of a particular dynamic of dengue cases for a constant population with an initial number of susceptible and infected members, a time-dependent force of infection and a probability-generating function from which a linear partial differential equation (PDE) of first order is derived whose solution can assign probabilities to each of the states of the model and the transitions between them. The force of infection is estimated numerically based on a dynamic system of ordinary differential equations. The method of characteristics applied to find the analytical solution of the PDE and subsequently the marginal probabilities of the stochastic process are derived analytically. Furthermore, by applying the cumulative generating function, a system of ordinary differential equations is derived, and the numerical solution determines the values of statistical measures over time. Finally a comparison of the results of the simulations is undertaken to understand the probabilistic dynamics of the process of infection in a population.

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