Stability switching and hydra effect in a predator-prey metapopulation model

Impact of disease on a two-patch eco-epidemic model in presence of prey dispersal

The present model is dealt with prey-predator interactions in two different patches where only prey species are allowed to disperse among the patches. Each of these two patches has different predator population but the predator in Patch-2 only is affected with a disease. The proposed model is biologically welldefined. Also, the feasibility of the equilibrium points and corresponding stability conditions are analysed. It is found that the disease among predator, even in one patch, makes an important role to control the whole system dynamics as it starts to oscillates by regulating the disease transmission rate. Moreover, the disease transmission rate has a stabilizing as well as destabilizing effect on the system dynamics. From the results, it is observed that a high dispersal rate decreases the count of infected predator in a patch in presence of prey dispersal. There is another interesting result: it is observed that the prey dispersal cannot destabilize the coexistence state, i.e., the system which is stable in absence of dispersal remains stable when the prey species disperse between two patches.

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

Modeling and dynamic analysis of novel coronavirus pneumonia (COVID-19) in China

Although novel coronavirus pneumonia (COVID-19) was widely spread in mainland China in early 2020, it was soon controlled. To study the impact of government interventions on the spread of disease during epidemics, a differential equation system is established to simulate the process of virus propagation in this paper. We first analyze its basic properties, basic reproduction number R 0 and existence of equilibria. Then we prove that the disease-free equilibrium (DFE) is Globally Asymptotically Stable when R 0 is less than 1. Through the analysis of the daily epidemic data from January 10, 2020 to March 11, 2020, combined with the implementation of the national epidemic policy, we divide the whole process into three stages: the first stage (natural state), the second stage (isolation state), the third stage (isolation, detection and treatment). By using the weighted nonlinear least square method to fit the data of three stages, the parameters are obtained, and three basic reproduction numbers are calculated, which are:R 01 = 2.6735 ,R 02 = 0.85077 ,R 03 = 0.18249 . Sensitivity analysis of threshold parameters and corresponding graphical results were also performed to examine the relative importance of various model parameters to the spread and prevalence of COVID-19. Finally, we simulate the trend of three stages and verify the theory of Global Asymptotic Stability of DFE. The conclusion of this paper proves theoretically that the Chinese government's epidemic prevention measures are effective in the fight against the spread of COVID-19. This study can not only provide a reference for research methods to simulate COVID-19 transmission in other countries or regions, but also provide recommendations on COVID-19 prevention measures for them.