Theoretical assessment of the impact of environmental contamination on the dynamical transmission of polio

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.

A mathematical model of cholera in a periodic environment with control actions

In this paper,we studied the impact of sensitization and sanitation as possible control actions to curtail the spread of cholera epidemic within a human community.Firstly,we combined a model of Vibrio Cholerae with a gencric SIRS cholera model.Classical control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential equations.Then we presented the theoretical analysis of the model.More precisely,we computed the disease free equilibrium.We derive the basic reproduction number R0 which determines the extinction and the persistence of the infection.We show that the trivial disease-free equilibrium is globally asymptotically stable whenever.R0≤1,while when R0>1,the trivial disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable.Theoretical results are supported by numerical simulations,which further suggest that the control of cholera should consider both sensitization and san itation,with a strong focus on the latter.