Abstract
ABSTRACTWe develop an age of infection model with heterogeneous mixing in which indirect pathogen transmission is considered as a good way to describe contact that is usually considered as direct and we also incorporate virus shedding as a function of age of infection. The simplest form of SIRP epidemic model is introduced and it serves as a basis for the age of infection model and a 2-patch SIRP model where the risk of infection is solely dependent on the residence times and other environmental factors. The computation of the basic reproduction number , the initial exponential growth rate and the final size relation is done and by mathematical analysis, we study the impact of patches connection and use the final size relation to analyse the ability of disease to invade over a short period of time.
Highlights
Epidemic model of infectious diseases had been extensively investigated by proposing and investigating mathematical models ([4,5,6, 10, 19, 22] and references therein)
Brauer [4] proposed an SIVR epidemic model with homogeneous mixing, which is an extension of the SIR model by the addition of a pathogen compartment V to describe the indirect transmission pathway
We proposed and studied an epidemic model in which infection is transmitted when viruses are shed and acquired through host-source-host in heterogeneous environments
Summary
Epidemic model of infectious diseases had been extensively investigated by proposing and investigating mathematical models ([4,5,6, 10, 19, 22] and references therein). The basic reproduction number and the final size relation was derived and investigated to determine the impact of indirect transmission pathway on disease spread. DAVID the direct transmission pathway ( host–host) They derived the basic reproduction number, final size relation and investigated how residence times influence them. We have based most mathematical results in this paper on the final size relation of epidemic models in an heterogeneous environment This relation had been extensively discussed in [2,3,4, 10, 13] using different models to predict how worst an epidemic could be during a disease outbreak. A Lagrangian method is used to monitor the place of residence of each population at all times [6, 9,10,11] We propose that this may be an alternative way to study disease epidemic in an heterogeneous mixing environment. Note that the same analytic approach, a standard way to analyse disease transmission models will be used in each section
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