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

Department of Mathematics, Faculty of Science and Technic, University Cheikh Anta Diop, Dakar, Senegal

Department of Computer Engineering, National Advanced School of Engineering, University Cheikh Anta Diop, Dakar, Senegal

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S. Bowong

http://orcid.org/0000-0001-8909-1225

Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P. O. Box 24157 Douala, Cameroon

IRD, Sorbonne University, UHHISCO, F-93143, Bondy, France

Team GRIMCAPE, Yaounde, Cameroon

The African Center of Excellence in Information, and Communication Technologies (CETIC), University of Yaounde 1, Cameroon

E-mail Address: sbowong@gmail.com

Corresponding author.

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, and

J. J. Tewa

National Advanced School of Engineering, University of Yaounde I, P. O. Box 8390 Yaounde, Cameroon

IRD, Sorbonne University, UHHISCO, F-93143, Bondy, France

Team GRIMCAPE, Yaounde, Cameroon

The African Center of Excellence in Information, and Communication Technologies (CETIC), University of Yaounde 1, Cameroon

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https://doi.org/10.1142/S1793524519500128Cited by:3 (Source: Crossref)

Abstract

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 $ℛ_{0}^{env}$ . We show that the disease free equilibrium is globally asymptotically stable (GAS) if $ℛ_{0}^{env} < 1$ , while if $ℛ_{0}^{env} > 1$ , 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 environmental-related contagion is greater than the corresponding number for the environmental contamination free sub-model. In conjunction with the inequality $ℛ_{0} < ℛ_{0}^{env}$ , where $ℛ_{0}$ 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.

Keywords:

AMSC: 34A34, 34D23, 34D40, 92D30

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