A mathematical model for the dynamical transmission of polio is considered,with the aim of investigating the impact of environment contamination.The model captures two infection pathways through both direct human-to-h...A mathematical model for the dynamical transmission of polio is considered,with the aim of investigating the impact of environment contamination.The model captures two infection pathways through both direct human-to-human transmission and indirect human-to-environment-to-human transmission by incorporating the environment as a transition and/or reservoir of viruses.We derive the basic reproduction number R0^env We show that the disease free equilibrium is globally asymptotically stable(GAS)if R0^env<1,while if R0^env>1,there exists a unique endemic equilibrium which is locally asymptotically stable(LAS).Similar results hold for environmental contamination free sub-model(without the incorporation of the indirect transmission).At the endemic level,we show that the number of infected individuals for the model with the environ mental-related contagion is greater than the corresponding number for the environmental contamination free sub-model.In conjunction with the inequality R0<R0^env.Qnv,where R0 is the basic reproduction number for the environmental contamination free sub-model,our finding suggests that the contaminated environment plays a detrimental role on the transmission dynamics of polio disease by increasing the endemic level and the severity of the outbreak.Therefore,it is natural to implement control strategies to reduce the severity of the disease by providing adequate hygienic living conditions,educate populations at risk to follow rigorously those basic hygienic rules in order to avoid adequate contacts with suspected contaminated objects.Further,we perform numerical simulations to support the theory.展开更多
文摘A mathematical model for the dynamical transmission of polio is considered,with the aim of investigating the impact of environment contamination.The model captures two infection pathways through both direct human-to-human transmission and indirect human-to-environment-to-human transmission by incorporating the environment as a transition and/or reservoir of viruses.We derive the basic reproduction number R0^env We show that the disease free equilibrium is globally asymptotically stable(GAS)if R0^env<1,while if R0^env>1,there exists a unique endemic equilibrium which is locally asymptotically stable(LAS).Similar results hold for environmental contamination free sub-model(without the incorporation of the indirect transmission).At the endemic level,we show that the number of infected individuals for the model with the environ mental-related contagion is greater than the corresponding number for the environmental contamination free sub-model.In conjunction with the inequality R0<R0^env.Qnv,where R0 is the basic reproduction number for the environmental contamination free sub-model,our finding suggests that the contaminated environment plays a detrimental role on the transmission dynamics of polio disease by increasing the endemic level and the severity of the outbreak.Therefore,it is natural to implement control strategies to reduce the severity of the disease by providing adequate hygienic living conditions,educate populations at risk to follow rigorously those basic hygienic rules in order to avoid adequate contacts with suspected contaminated objects.Further,we perform numerical simulations to support the theory.
