Abstract
Problem statement: In this study, we present the mathematical model of the transmission dynamics of fowl pox infection in poultry. Approach: It describes the interaction between the susceptible and the infected birds which results in a system of ordinary differential equation. Introducing the control which represents the effort in applying chemoprophylaxis control u1 and treatment control u2 in birds with fowl pox, the system becomes a system of ordinary differential equations with control. Results: Our optimal control problem involves that in which the number of birds with latent and active fowl pox infections and the cost of treatment controls u1 (t) and u2 (t) were minimized subject to the differential Eq. 5-8. This involves the number of birds with active and latent fowl pox respectively as well as the cost of applying chemoprophylaxis control u1 and treatment u2 in birds with fowl pox. Conclusion: Analysing the model using Pontryagin’s Maximum Principle and optimality conditions, optimal effort necessary to reduce the transmission rate of fowl pox in the poultry has been determined. Hence, it is possible to reduce to reduce the rate of transmission.
Highlights
Fowl pox, pox, or avian pox is a relatively slowspreading viral disease characterized by skin lesions or plagues in the pharynx
The model: Mode formulation: Our model describes the for application of optimal control to the epidemiology transmission dynamics of fowl pox infection based on fowl pox transmission dynamics in poultry
Using the optimality condition and by standard control argument involving the bounds on the controls, we obtain the solution of the optimal control problem as control: u1*
Summary
Pox, or avian pox is a relatively slowspreading viral disease characterized by skin lesions or plagues in the pharynx. It is prevalent among chickens, turkey, pigeons, canaries, worldwide. Morbidity is 10-95% and mortality usually 0-50%. The virus can enter the blood stream through the eye, skin wound, or respiratory tracts. Mosquitoes become infected by feeding on birds with fowl pox in their blood stream. There is some evidence that the mosquitoes remain infected for life. Mosquitoes are the primary reservoir and spreaders of fowl pox on poultry ranges. Several species of mosquito can transmit fowl
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