Abstract
ABSTRACTStochastic epidemic models with two groups are formulated and applied to emerging and re-emerging infectious diseases. In recent emerging diseases, disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals. In some re-emerging infectious diseases, disease spread is attributed to waning immunity in susceptible hosts. We apply a continuous-time Markov chain (CTMC) model to study disease emergence or re-emergence from different groups, where the transmission rates depend on either the infectious host or the susceptible host. Multitype branching processes approximate the dynamics of the CTMC model near the disease-free equilibrium and are used to estimate the probability of a minor or a major epidemic. It is shown that the probability of a major epidemic is greater if initiated by an individual from the superspreader group or by an individual from the highly susceptible group. The models are applied to Severe Acute Respiratory Syndrome and measles.
Highlights
In the twenty-first century, one of the biggest threats to public health is the spread of infectious diseases [35]
Disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals
Recent emerging diseases have been attributed to highly infectious individuals, called superspreaders, who spread the disease to a large number of people [25]
Summary
In the twenty-first century, one of the biggest threats to public health is the spread of infectious diseases [35]. In a two-group model applied to spread of SARS [26], transmission between patients in a hospital and outside visitors were analysed in terms of the final epidemic size. Edholm et al [13] developed a continuoustime Markov chain (CTMC) two-group model for superspreaders and non-superspreaders They applied their stochastic model to MERS and Ebola, performed extensive numerical simulations, and used branching process approximations to compare disease epidemics initiated by superspreaders to non-superspreaders. We apply these models to potential SARS [26] and measles epidemics [11]. The sensitivity of R0 and the probability estimates to group size and transmission and recovery rates are investigated
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