Maji Chandan, Mukherjee Debasis, Kesh Dipak
Department of Mathematics, Vivekananda College, Thakurpukur, 269 D.H. Road, Kolkata, 700063, India.
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata, 700032, India.
J Biol Phys. 2018 Mar;44(1):17-36. doi: 10.1007/s10867-017-9472-5. Epub 2017 Oct 7.
Chronic wasting disease (CWD) is a contagious prion disease among the deer family that has the potential to disrupt the ecosystems where deer occur in abundance. To understand the dynamics of this emerging infectious disease, we consider a simple eco-epidemic model where the host population is infected by CWD. Boundedness of the system is established. The structure of equilibria and their linearized stability are investigated. The persistence condition is discussed. By constructing a suitable Lyapunov function, we discuss the global stability of the endemic equilibrium. Local bifurcation (transcritical) around the boundary equilibria is developed. Sufficient conditions for the existence of Hopf-bifurcation are derived. Further, we have also introduced white type of noise into the system to investigate stochastic stability. This suggests that the deterministic model is robust with respect to stochastic perturbation. Some numerical simulations are performed to validate our results.
慢性消耗病（CWD）是鹿科动物中的一种传染性朊病毒疾病，有可能扰乱鹿大量出没的生态系统。为了理解这种新出现的传染病的动态，我们考虑一个简单的生态流行病模型，其中宿主种群受到慢性消耗病的感染。建立了系统的有界性。研究了平衡点的结构及其线性化稳定性。讨论了持续生存条件。通过构造一个合适的李雅普诺夫函数，我们讨论了地方病平衡点的全局稳定性。发展了围绕边界平衡点的局部分岔（跨临界）。推导了霍普夫分岔存在的充分条件。此外，我们还将白噪声引入系统以研究随机稳定性。这表明确定性模型对于随机扰动是鲁棒的。进行了一些数值模拟以验证我们的结果。
