The disease-free equilibrium is locally asymptotically stable whenever the basic reproduction number
is less than one ([R.sub.0a] < 1).
Basic Reproduction Number
for the Multiple Control Model.
In epidemiology, one of the most important parts, basic reproduction number
, [R.sub.0] is obtained by the next generation method.
In Figure 3, when the basic reproduction number
[R.sub.0] > 1, we examine the impact of d on the evolution of infection prevalence, which is defined as the proportion of infected peers with respect to the total number of the peers.
The basic reproduction number
[R.sup.0] for (3) is given by
By calculating we can know that the basic reproduction number
of SIWR model [R.sub.0SIWR] = [alpha] + [[beta].sub.1] + [[beta].sub.2]/[alpha] + [mu] = 2.2 > 1, and there exists positive equilibrium point [E.sup.+.sub.SIWR] = (0.454,0.171,0.171,0.374); the basic reproduction number
of SIR model SIR model [R.sub.0SIR] = [alpha] + [[beta].sub.2]/[alpha]+[mu] = 1.6 > 1, and there exists a positive equilibriumpoint [E.sup.+.sub.SIR] = (0.625,0.15,0.225) .Apparently, [R.sub.0SIR] < [R.sub.0SIWR] succeed (theorem2).
In the following part, we will give two examples to show changes of equilibria with the basic reproduction number
[R.sub.0] by numerical simulation when [a.sub.2] = 0 and [a.sub.2] = 0.
We know that the basic reproduction number
of the model [R.sub.0] is proportional to the total number of the host tree population available as oviposition sites for the vector beetles and the number of vector population and host infectious rates a and vector infectious rate p, respectively.
I also investigated that the basic reproduction number
for this model and On the basis of basic reproduction number
[R.sub.0], the Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) are established.
From every epidemiological model one can compute an epidemiological quantity called basic reproduction number
After that, we determine the basic reproduction number
and steady states of the model.
We begin by computed the basic reproduction number
[R.sub.0] of model (2).