Reproduction numbers for infections with free-living pathogens growing in the environment

Abstract

The basic reproduction number R 0 for a compartmental disease model is often calculated by the next generation matrix (NGM) approach. When the interactions within and between disease compartments are interpreted differently, the NGM approach may lead to different R 0 expressions. This is demonstrated by considering a susceptible-infectious-recovered-susceptible model with free-living pathogen (FLP) growing in the environment. Although the environment could play different roles in the disease transmission process, leading to different R 0 expressions, there is a unique type reproduction number when control strategies are applied to the host population. All R 0 expressions agree on the threshold value 1 and preserve their order of magnitude. However, using data for salmonellosis and cholera, it is shown that the estimated R 0 values are substantially different. This study highlights the utility and limitations of reproduction numbers to accurately quantify the effects of control strategies for infections with FLPs growing in the environment.

Understanding the effects of intermittent shedding on the transmission of infectious diseases: example of salmonellosis in pigs

“…The methods and efficacy of decontamination vary across facilities [18]. Bani-Yaghoub et al established an equation relating the decontamination rate to the proportion of free-living Salmonella removed from the environment each day [3]. The relationship is given by…”

Estimating the probability of an extinction or major outbreak for an environmentally transmitted infectious disease

“…Contaminated food, water, soil, surfaces, and fomites are all possible vehicles for indirect transmission [6,10,14,55]. Some free-living pathogens are capable of long-term survival and even growth within the environment [9,45,58,73].…”

“…Epidemic models for the transmission of ETIDs have been developed in previous studies [see e.g. 5,6,12,18,24,26,43,56,57,62,63,71, and references therein] with particular emphasis on E. coli O157:H7 infection [24], salmonellosis [18,26,43,71], and cholera [56,57,62]. In these studies, the basic reproduction number was used to predict disease persistence or extinction.…”

“…In a previous work, an ODE model was developed by Bani-Yaghoub et al [6] for ETIDs which includes host demography, direct and indirect transmission, replication of free-living pathogens, and environmental decontamination. However, the model developed by Bani-Yaghoub did not account for stochasticity in the transmission dynamics which is critical for determining the probability of a major outbreak.…”

“…However, the model developed by Bani-Yaghoub did not account for stochasticity in the transmission dynamics which is critical for determining the probability of a major outbreak. Therefore, based on the assumptions of the deterministic model in [6], we develop a CTMC model which accounts for the random variations that occur in the transmission process. The objectives of our investigation are to: (1) explore the effects of indirect transmission, pathogen shedding by infectious hosts, free-living pathogen replication, and environmental decontamination on the probability of disease extinction or a major outbreak, and (2) demonstrate an analytically tractable method for approximating the probability of disease extinction or a major outbreak initiated by a small number of infectious individuals or a low level of environmental contamination.…”