Modelling the outbreak of infectious disease following mutation from a non-transmissible strain.

Modelling the outbreak of infectious disease following mutation from a non-transmissible strain. Theor Popul Biol. 2018 Aug 27;: Authors: Chen CY, Ward JP, Xie WB Abstract In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the past. We use simple mathematical models to describe this process with the aim to better understand the emergence of an epidemic resulting from such a mutation and the extent of measures that are needed to control it. The feared outbreak of a human-human transmissible form of avian influenza leading to a global epidemic is the paradigm for this study. We extend the SIR approach to derive a deterministic and a stochastic formulation to describe the evolution of two classes of susceptible and infected states and a removed state, leading to a system of ordinary differential equations and a stochastic equivalent based on a Markov process. For the deterministic model, the contrasting timescale of the mutation process and disease infectiousness is exploited in two limits using asymptotic analysis in order to determine, in terms of the model parameters, necessary conditions for an epidemic to take place and timescales for the onset of the epidemic, the size and duration of the epidemic and the maximum level of the infected individuals at one time. Furthermore, the basic reproduction number R0 is determined from asymptot...
Source: Theoretical Population Biology - Category: Biology Authors: Tags: Theor Popul Biol Source Type: research