Modeling Ebola Virus Disease transmissions with reservoir in a complex virus life ecology

Tsanou Berge; Samuel Bowong; Jean Lubuma; Martin Luther Mann Manyombe; Tsanou Berge; Samuel Bowong; Jean Lubuma; Martin Luther Mann Manyombe

doi:10.3934/mbe.2018002

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 1: 21-56. doi: 10.3934/mbe.2018002

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Modeling Ebola Virus Disease transmissions with reservoir in a complex virus life ecology

1.
Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67 Dschang, Cameroon
2.
Department of Mathematics and Computer Science, University of Douala, P.O. Box 24157 Douala, Cameroon
3.
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
4.
Department of Mathematics, Faculty of Sciences, University of Yaounde 1, P.O. Box 812 Yaounde, Cameroon

Received: 14 September 2016 Accepted: 31 March 2017 Published: 01 February 2018
MSC : 34A34, 92D30, 65D30

We propose a new deterministic mathematical model for the transmission dynamics of Ebola Virus Disease (EVD) in a complex Ebola virus life ecology. Our model captures as much as possible the features and patterns of the disease evolution as a three cycle transmission process in the two ways below. Firstly it involves the synergy between the epizootic phase (during which the disease circulates periodically amongst non-human primates populations and decimates them), the enzootic phase (during which the disease always remains in fruit bats population) and the epidemic phase (during which the EVD threatens and decimates human populations). Secondly it takes into account the well-known, the probable/suspected and the hypothetical transmission mechanisms (including direct and indirect routes of contamination) between and within the three different types of populations consisting of humans, animals and fruit bats. The reproduction number $\mathcal R_0$ for the full model with the environmental contamination is derived and the global asymptotic stability of the disease free equilibrium is established when $\mathcal R_0 < 1$. It is conjectured that there exists a unique globally asymptotically stable endemic equilibrium for the full model when $\mathcal R_0>1$. The role of a contaminated environment is assessed by comparing the human infected component for the sub-model without the environment with that of the full model. Similarly, the sub-model without animals on the one hand and the sub-model without bats on the other hand are studied. It is shown that bats influence more the dynamics of EVD than the animals. Global sensitivity analysis shows that the effective contact rate between humans and fruit bats and the mortality rate for bats are the most influential parameters on the latent and infected human individuals. Numerical simulations, apart from supporting the theoretical results and the existence of a unique globally asymptotically stable endemic equilibrium for the full model, suggest further that: (1) fruit bats are more important in the transmission processes and the endemicity level of EVD than animals. This is in line with biological findings which identified bats as reservoir of Ebola viruses; (2) the indirect environmental contamination is detrimental to human beings, while it is almost insignificant for the transmission in bats.
- Ebola,
- zoonotic disease,
- reservoir,
- environmental transmission,
- stability,
- simulation
Citation: Tsanou Berge, Samuel Bowong, Jean Lubuma, Martin Luther Mann Manyombe. Modeling Ebola Virus Disease transmissions with reservoir in a complex virus life ecology[J]. Mathematical Biosciences and Engineering, 2018, 15(1): 21-56. doi: 10.3934/mbe.2018002

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Abstract

We propose a new deterministic mathematical model for the transmission dynamics of Ebola Virus Disease (EVD) in a complex Ebola virus life ecology. Our model captures as much as possible the features and patterns of the disease evolution as a three cycle transmission process in the two ways below. Firstly it involves the synergy between the epizootic phase (during which the disease circulates periodically amongst non-human primates populations and decimates them), the enzootic phase (during which the disease always remains in fruit bats population) and the epidemic phase (during which the EVD threatens and decimates human populations). Secondly it takes into account the well-known, the probable/suspected and the hypothetical transmission mechanisms (including direct and indirect routes of contamination) between and within the three different types of populations consisting of humans, animals and fruit bats. The reproduction number $\mathcal R_0$ for the full model with the environmental contamination is derived and the global asymptotic stability of the disease free equilibrium is established when $\mathcal R_0 < 1$. It is conjectured that there exists a unique globally asymptotically stable endemic equilibrium for the full model when $\mathcal R_0>1$. The role of a contaminated environment is assessed by comparing the human infected component for the sub-model without the environment with that of the full model. Similarly, the sub-model without animals on the one hand and the sub-model without bats on the other hand are studied. It is shown that bats influence more the dynamics of EVD than the animals. Global sensitivity analysis shows that the effective contact rate between humans and fruit bats and the mortality rate for bats are the most influential parameters on the latent and infected human individuals. Numerical simulations, apart from supporting the theoretical results and the existence of a unique globally asymptotically stable endemic equilibrium for the full model, suggest further that: (1) fruit bats are more important in the transmission processes and the endemicity level of EVD than animals. This is in line with biological findings which identified bats as reservoir of Ebola viruses; (2) the indirect environmental contamination is detrimental to human beings, while it is almost insignificant for the transmission in bats.

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