Dynamic Model for the Epidemiology of Diarrhea and Simulation Considering Multiple Disease Carriers

Diarrhea is responsible for killing around 525,000 children every year, even though it is preventable and treatable. This research focuses on both houseflies’ roles and humans’ roles in carrying pathogens causing diarrhea as multiple disease carriers. Both human and fly compartmental models are simulated with five diseases control strategies in order to identify the epidemic dynamics. The framework considers the life cycle of flies modeled into eggs, larvae, pupae, susceptible flies, and carrier flies, while the human system follows a compartment model as susceptible, infected, recovered, and back to susceptible again (SIRS). The relationships are modeled into an ordinary differential equation-based compartmental system. Then, the control parameters of the compartmental framework are analyzed. In order to propose effective control methods, five control strategies are considered: (1) elimination of flies’ breeding site, (2) sanitation, (3) installation of UV light trap, (4) good personal and food hygiene, and (5) water purification. Then, overall, ten control scenarios using the five control strategies are analyzed. Among them, effective control solutions considering various dynamic epidemiology are provided with the simulations and analyses. The proposed framework contributes to an effective control strategy in reducing the number of both flies and infected humans, since it minimizes the spread of the disease and considers cost-effectiveness.

Stochastic Modeling of Compartmental Systems with Pipes

An approach to the construction of a stochastic model of population dynamics distributed over a compartmental system with pipes is proposed. Population dynamics is described in terms of a multidimensional random process of birth and death, supplemented by taking into account point distributions reflecting different types of particles. In this model, the belonging of a particle to a certain type is determined by the time of its transition between compartments. The duration of particle transitions through the pipes are not random, but are set as parameters of the environment in which the population develops. Graph theory is used for formalization and compact representation of the model. On the basis of the Monte Carlo method the algorithm of numerical simulation of population dynamics is constructed. The results of computational experiments for a system consisting of five compartments are presented.