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When initially introduced into a susceptible population, a disease may die out or result in a major outbreak. We present a Continuous- Time Markov Chain model for enzootic WNV transmission between two avian host species and a single vector, and use multitype branching process theory to determine the probability of disease extinction based upon the type of infected individual initially introducing the disease into the population -- an exposed vector, infectious vector, or infectious host of either species. We explore how the likelihood of disease extinction depends on the ability of each host species to transmit WNV, vector biting rates on host species, and the relative abundance of host species, as well as vector abundance. Theoretical predictions are compared to the outcome of stochastic simulations. We find the community composition of hosts and vectors, as well as the means of disease introduction, can greatly affect the probability of disease extinction. [ABSTRACT FROM AUTHOR]

When initially introduced into a susceptible population, a disease may die out or result in a major outbreak. We present a Continuous-Time Markov Chain model for enzootic WNV transmission between two avian host species and a single vector, and use multitype branching process theory to determine the probability of disease extinction based upon the type of infected individual initially introducing the disease into the population – an exposed vector, infectious vector, or infectious host of either species. We explore how the likelihood of disease extinction depends on the ability of each host species to transmit WNV, vector biting rates on host species, and the relative abundance of host species, as well as vector abundance. Theoretical predictions are compared to the outcome of stochastic simulations. We find the community composition of hosts and vectors, as well as the means of disease introduction, can greatly affect the probability of disease extinction.

A stochastic continuous-time Markov chain tuberculosis model with fast-slow progression and relapse is established to explore the impact of the demographic variation on TB transmission. At first, the extinction threshold and probability of the disease extinction and outbreak are obtained by applying the multitype Galton-Waston branching process for the stochastic model. In numerical simulations, the probability of the disease extinction and outbreak and expected epidemic duration of the disease are estimated. To see how demographic stochasticity affects TB dynamics, we compare dynamical behaviors of both stochastic and deterministic models, and these results show that the disease extinction in stochastic model would occur while the disease is persistent for the deterministic model. Our results suggest that minimizing the contact between the infectious and the susceptible, and detecting the latently infected as early as possible, etc., could effectively prevent the spread of tuberculosis.

Abstract We construct a Zika transmission model to investigate the effect of postponing pregnancy on the infection intensity. We perform analytical and numerical investigations for deterministic and stochastic analysis to obtain the basic reproductive ratio, endemic state, probability of disease extinction, and the probability of outbreak. The results indicate that by reducing the pregnancy rate the mosquito-to-human ratio increases, and, consequently, the basic reproductive ratio increases. Simultaneously, the probability of disease extinction decreases, and the probability of disease outbreak increases. On the other hand, the endemic state of infected infants initially increases with the decrease of the pregnancy recruitment rate, up to a certain level, and decreases as the recruitment rate of pregnancy tends to zero. This work highlights that postponing pregnancy that gives the individual temporary protection for unexpected infected newborns may increase the population infectivity.

We construct a Zika transmission model to investigate the effect of postponing pregnancy on the infection intensity. We perform analytical and numerical investigations for deterministic and stochastic analysis to obtain the basic reproductive ratio, endemic state, probability of disease extinction, and the probability of outbreak. The results indicate that by reducing the pregnancy rate the mosquito-to-human ratio increases, and, consequently, the basic reproductive ratio increases. Simultaneously, the probability of disease extinction decreases, and the probability of disease outbreak increases. On the other hand, the endemic state of infected infants initially increases with the decrease of the pregnancy recruitment rate, up to a certain level, and decreases as the recruitment rate of pregnancy tends to zero. This work highlights that postponing pregnancy that gives the individual temporary protection for unexpected infected newborns may increase the population infectivity. [ABSTRACT FROM AUTHOR]