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 the steady disease-free equillibrium point (steady node), 1 is an unstable equilibrium point (SIS3 site saddle point), and 2 is usually a steady endemic equilibrium (stable concentrate). Figure 11 shows the convergence to = 0 or to = 190 as outlined by the initial situation. In Figure 12 is shown an additional representation (phase space) of your evolution in the method toward 0 or to 2 as outlined by the initial conditions. Let us take now the value = 0.0001683, which satisfies the situation 0 2 . In this case, the basic reproduction number has the worth 0 = 1.002043150. We nevertheless have that the condition 0 is fulfilled (34) (33)Computational and Mathematical Strategies in Medicine1 00.0.0.0.Figure ten: Bifurcation diagram (answer of polynomial (20) versus ) for the situation 0 . The system experiences many bifurcations at 1 , 0 , and 2 .300 200 100 0Figure 11: Numerical simulation for 0 = 0.9972800211, = 3.0, and = two.five. The system can evolve to two different equilibria = 0 or = 190 in accordance with the initial condition.as well as the program within this case has 4 equilibrium points = (, , , , ): 0 = (5148, 0, 0, 0, 0) , 1 = (5042, 76, 5, 3, 20) , two = (3971, 734, 69, 36, 298) , three = (2491, 1413, 246, 109, 750) . (35)Computational and Mathematical Procedures 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 2 2000 1500 1000 500 three 0 2000 200 2 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 = 2.5. Phase space representation with the technique with many equilibrium points.Figure 13: Numerical simulation for 0 = 1.002043150, = 3.0, and = 2.5. The system can evolve to two distinct equilibria 1 (stable node) or three (stable concentrate) according to the initial situation. 0 and 2 are unstable equilibria.0 will be the unstable disease-free equillibrium point (saddle point ), 1 is really a stable endemic equilibrium point (node), two is an unstable equilibrium (saddle point), and three is actually a stable endemic equilibrium point (focus). Figure 13 shows the phase space representation of this case. For additional numerical analysis, we set all the parameters within the list in line with the numerical values offered in Table 4, leaving free the parameters , , and connected towards the principal transmission rate and reinfection rates of your disease. We are going to explore the parametric space of program (1) and relate it towards the signs from the coefficients on the polynomial (20). In Figure 14, we contemplate values of such that 0 1. We are able to observe from this figure that as the key transmission price of your disease increases, and with it the basic reproduction number 0 , the technique 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 constructive, then remains good and becomes damaging and finally both coefficients develop into unfavorable. This modify within the coefficients indicators because the transmission rate increases agrees with the outcomes summarized in Table two when the condition 0 is fulfilled. Next, in an effort to discover one more mathematical possibilities we’ll modify some numerical values for the parameters inside the list in a more intense manner, taking a hypothetical regime with = { = 0.03885, = 0.015.