Dynamical Models of Interactions between Herds Forage and Water Resources in Sahelian Region

Jean Jules Tewa,Alassane Bah,Suares Clovis Oukouomi Noutchie

doi:10.1155/2014/138179

Jean Jules Tewa, Alassane Bah + Show 1 more

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https://doi.org/10.1155/2014/138179

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Abstract

Optimal foraging is one of the capital topics nowadays in Sahelian region. The vast majority of feed consumed by ruminants in Sahelian region is still formed by natural pastures. Pastoral constraints are the high variability of available forage and drinking water in space and especially in time (highly seasonal, interannual variability) and the scarcity of water resources. The mobility is the main functional and opportunistic adaptation to these constraints. Our goal in this paper is to formalize two dynamical models for interactions between a herd of domesticate animals, forage resources, and water resources inside a given Sahelian area, in order to confirm, explain, and predict by mathematical models some observations about pastoralism in Sahelian region. These models in some contexts can be similar to predator-prey models as forage and water resources can be considered as preys and herd’s animals as predators. These models exhibit very rich dynamics, since it predicts abrupt changes in consumer behaviour and disponibility of forage or water resources. The dynamics exhibits a possible coexistence between herd, resources, and water with alternative peaks in their trajectories.

Highlights

It is well known that pastoralism is the name given to the subsistence practice in which people care for and domesticate animals, usually ungulates such as camels, cattle, reindeer, sheep, and goats [1].Pastoralism will continue for the near future in poor nations [2,3,4], especially in Africa, because it is generally an efficient, low energy requiring subsistence base for semiarid regions
We can say that System (2) is well posed, since forage resources R(t), water resources W(t), and the tropical livestock unit of the herd H(t) are always nonnegative quantities
A mathematical model for pastoralism has been considered in order to explain and predict some situations in Sahelian region

Summary

Introduction

It is well known that pastoralism is the name given to the subsistence practice in which people care for and domesticate animals, usually ungulates such as camels, cattle, reindeer, sheep, and goats [1]. Pastoralists make optimum use of the dry lands by practicing a mobile and extensive livestock-keeping system They move according to where and when fodder becomes available and use different herd management strategies such as herd splitting, herd diversification, and herd maximization to ensure that they spread the risk of livestock loss from droughts, diseases, and theft. Climate change has increased the frequency of droughts, floods, and livestock diseases These natural factors only exacerbate the effects of a harsh policy and legal environment that is focused on “modernizing” and settling pastoralists. Alongside support to improve primary and secondary education is the need to strengthen institutions of higher learning and research in pastoral areas of Africa [5] Such institutions require support to conduct research on a range of political, social, and natural science subjects and at levels, which range from local adaptation to regional integration and global trends. This paper is our contribution to this research in pastoral areas of Africa

Model Construction

Mathematical Results and Interpretations in Sahelian Context

Numerical Simulations and Interpretations

Conclusion

Expression of coefficients in Theorem 11

Proof of Theorem Theorem 15