write (iv),(v) and (vi)

Consider the model with the flow diagram in Figure 2, where all parameters are non-negative. The disease has a latent period (L) after which a fraction of latent individuals proceeds to an infective stage (I), while the remaining fraction proceeds to an asymptomatic stage (A). Assume that after recovery, the individual is no longer infected nor infectious. (i) Write down the corresponding system of ordinary differential equations. Describe the parameters and explain in detail how the equations are obtained. (ii) Show that the total population size is constant. (iii) Reduce the model into a model with four compartments only. Justify the reduction of the model. (iv) Find the biologically feasible region D and establish the well-posedness of the model. (v) Show that the model has a continuum of disease free equilibria. (vi) Investigate the possibility of an outbreak using the next generation matrix approach. (vii) Identify and explain the role of the latent period and asymptomatic infections in the reproductive number. (viii) Solve the model numerically for the parameter values =0.01,=0.1,= 0.5,p=0.75,k=0.75,=0.1,=0.2 and initial values s(0)=10,l(0)= 1,i(0)=0,a(0)=0. Interpret the solution curve obtained. Figure 2: Schematic diagram of the model for Mr Barnabas Konanani and Mr