Upadhyay Ranjit Kumar, Roy Parimita, Venkataraman C, Madzvamuse A
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad- 826 004. Jharkhand, INDIA.
School of Mathematics, Thapar University, Patiala-147004, Punjab, INDIA.
Math Biosci. 2016 Nov;281:98-119. doi: 10.1016/j.mbs.2016.08.014. Epub 2016 Sep 14.
In the present paper, we propose and analyze an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.
在本文中，我们提出并分析了一个具有扩散项的生态流行病学模型，以研究被猞猁种群捕食的兔子种群的动态。对所提出的兔 - 猞猁模型的解进行了存在性、有界性、稳定性和分岔分析。结果表明，在存在扩散的情况下，该模型具有表现出图灵不稳定性的潜力。数值结果（有限差分法和有限元法）揭示了混沌波的存在，这似乎是疾病传播的一种主导模式。我们还通过霍普夫分岔分析展示了时空模式形成的机制，这可能是理解生态流行病学系统复杂时空动态的一个潜在候选因素。讨论了渐近传播率对兔种群中疾病根除的影响，这反过来又提高了伊比利亚猞猁的存活率。
