Is case the following stationary points = (, , , , ): 0 = (5148, 0, 0, 0, 0) , 1 = (3372, 1041, 122, 60, 482) , two = (2828, 1283, 190, 88, 651) . 0 is definitely the steady disease-free equillibrium point (stable node), 1 is definitely an unstable equilibrium point (saddle point), and 2 is a stable endemic equilibrium (steady concentrate). Figure 11 shows the convergence to = 0 or to = 190 based on the initial condition. In Figure 12 is shown an additional representation (phase space) with the evolution with the program toward 0 or to two in line with the initial circumstances. Let us take now the worth = 0.0001683, which satisfies the situation 0 2 . Within this case, the fundamental reproduction quantity has the worth 0 = 1.002043150. We nevertheless have that the situation 0 is fulfilled (34) (33)Computational and Mathematical Methods in Medicine1 00.0.0.0.Figure ten: Bifurcation diagram (solution of polynomial (20) versus ) for the condition 0 . The technique experiences a number of bifurcations at 1 , 0 , and two .300 200 one hundred 0Figure 11: Numerical simulation for 0 = 0.9972800211, = three.0, and = two.5. The technique can evolve to two unique Cecropin B equilibria = 0 or = 190 in accordance with the initial situation.and the system in this case has 4 equilibrium points = (, , , , ): 0 = (5148, 0, 0, 0, 0) , 1 = (5042, 76, 5, three, 20) , 2 = (3971, 734, 69, 36, 298) , three = (2491, 1413, 246, 109, 750) . (35)Computational and Mathematical Solutions in Medicine2000 1500 1000 500 0 0 0 2000 200 400 2000 00 400 3000 3000 0 0 5000 4000 400 4000 00 1 600 800 two 2000 1500 1000 500 three 0 2000 200 two 2000 400 40 1000 1200 1400 3000 300 3000+ ++ +4000 40 4000 0 00 1800 1000 1200Figure 12: Numerical simulation for 0 = 0.9972800211, = three.0, and = two.5. Phase space representation of the system with several equilibrium points.Figure 13: Numerical simulation for 0 = 1.002043150, = 3.0, and = 2.five. The technique can evolve to two various equilibria 1 (stable node) or 3 (steady concentrate) according to the initial condition. 0 and 2 are unstable equilibria.0 is the unstable disease-free equillibrium point (saddle point ), 1 can be a steady endemic equilibrium point (node), 2 is an unstable equilibrium (saddle point), and 3 is a steady endemic equilibrium point (focus). Figure 13 shows the phase space representation of this case. For additional numerical evaluation, we set each of the parameters within the list as outlined by the numerical values offered in Table four, leaving no cost the parameters , , and related for the main transmission price and reinfection prices from the disease. We are going to explore the parametric space of system (1) and relate it for the signs in the coefficients of the polynomial (20). In Figure 14, we consider values of such that 0 1. We are able to observe from this figure that because the primary transmission price with the disease increases, and with it the fundamental reproduction number 0 , the program beneath biological plausible condition, represented in the figure by the square (, ) [0, 1] [0, 1], evolves such PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/21337810 that initially (for lower values of ) coefficients and are each good, then remains positive and becomes damaging and finally each coefficients turn 
into damaging. This transform inside the coefficients signs because the transmission price increases agrees together with the benefits summarized in Table two when the condition 0 is fulfilled. Subsequent, in order to explore a further mathematical possibilities we are going to modify some numerical values for the parameters within the list in a much more extreme manner, taking a hypothetical regime with = { = 0.03885, = 0.015.