Rich dynamics of a simple delay host-pathogen model of cell-to-cell infection for plant virus

Figure 1.  Increasing $ \tau $ changes the stability of the positive equilibrium, which gives rise to a stable orbit. For this simulation, we use $ r = 0.3,K = 10^3,\beta = 0.1,\delta = 0.0001 $ and $ \tau $ varies from $ 1 $ to $ 80 $. We plot $ \tau $ over a viable region. For smaller value of $ \tau $, either the condition for the theorem is not satisfied or the positive steady does not exist. The switching between a stable positive steady state and a stable orbit takes place around $ \tau \approx 50.5 $

Figure 2.  Corresponding examples for Figure 1. (a) $ \tau = 50 $, the oscillation is damping toward the positive steady state. (b) $ \tau = 51 $, the oscillation is stable

Figure 3.  For this simulation, we start with the following values $ r = 0.3,K = 10^3,\beta = 0.1,\delta = 0.0001 $ and $ \tau = 51 $. (a) increasing the infection rate $ \beta $ can have a destabilizing effect on the endemic equilibrium; however, as $ \beta $ increases, $ S $ and $ I $ approach closely to 0. (b) Decreasing the death rate $ \delta $ can be destabilizing as well. (c) The growth rate $ r $ can be both stabilizing or destabilizing as it varies. As $ r $ decreases, it can result in mutual extinction. (d) shows additional details of Figure 1 and 2. Note that varying the carrying capacity $ K $ only changes the size but not the stability

Figure 4.  Parameter fitting result for the cell-to-cell transmission model. The description of each experiment is given in subsection 1.2 and additional details can be found in Kendig et al. [26]

Figure 5.  Comparison of data fitting between mass action model and ratio-dependent model. The description of each experiment is given in subsection 1.2 and additional details can be found in Kendig et al. [26]