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Abstract
The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model's parameters. In the time-dependent control case, we use Pontryagin's maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees' productivity, effective education programs and strict adherence to preventive measures should be promoted.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default 1.0
Id Name Initial quantity Compartment Fixed
A AIDS 1800.0 default
EXT EXT 1.0 default
I1 Unaware infected 5400.0 default
I2 Aware infected 4500.0 default
S Susceptible 15300.0 default

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v_1 EXT = S

Q_0
v_10 A = EXT

d*A
v_2 S = I1

(Beta_1*I1+Beta_2*I2)*S
v_3 S = EXT

Mu*S
v_4 I1 = I2

Theta*I1
v_5 I1 = EXT

Mu*I1
v_6 I1 = A

Delta*I1
v_7 I2 = EXT

Mu*I2
v_8 I2 = A

Delta*I2
v_9 A = EXT

Mu*A

Global parameters

Id Value
Beta_1 0.0009
Beta_2 0.00027
Delta 0.3
Mu 0.04
Q_0 3000.0
Theta 0.02
d 1.0

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments