Application of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virus

Abstract

In this study, an optimal control theory was applied to a nonautonomous model for Newcastle disease transmission in the village chicken population. A notable feature of this model is the inclusion of environment contamination and wild birds, which act as reservoirs of the disease virus. Vaccination, culling, and environmental hygiene and sanitation time dependent control strategies were adopted in the proposed model. This study proved the existence of an optimal control solution, and the necessary conditions for optimality were determined using Pontryagin’s Maximum Principle. The numerical simulations of the optimal control problem were performed using the forward–backward sweep method. The results showed that the use of only the environmental hygiene and sanitation control strategy has no significant effect on the transmission dynamics of the Newcastle disease. Additionally, the combination of vaccination and environmental hygiene and sanitation strategies reduces more number of infected chickens and the concentration of the Newcastle disease virus in the environment than any other combination of control strategies. Furthermore, a cost-effective analysis was performed using the incremental cost-effectiveness ratio method, and the results showed that the use of vaccination alone as the control measure is less costly compared to other control strategies. Hence, the most effective way to minimize the transmission rate of the Newcastle disease and the operational costs is concluded to be the timely vaccination of the entire population of the village chicken, improvement in the sanitation of facilities, and the maintenance of a hygienically clean environment.

Poultry health constraints in smallholder village poultry systems in Northern Ghana and Central Tanzania

“…Studies show that seasonality of outbreaks is influenced by changes in climatic conditions leading to stress, which predisposes birds to the disease, and hot, dry and windy periods, which encourage airborne spread of the virus ( 27 ). Several studies in sub-Saharan Africa settings have shown the substantial losses due to NCD in village poultry systems ( 28–30 ) resulting from high mortalities ( 11 ). Dankwa et al ( 31 ) in their study of Northern Ghana show recurrent outbreaks of NCD in November and January and resulting losses of flocks.…”

Optimal control analysis of hepatocytic-erythrocytic dynamics of Plasmodium falciparum malaria

“…Consider an optimal problem of system (1) , subject to initial conditions of state variable and boundary condition of control variables u i ( t ) ∈ U for i = 1, …, 4 . There exists an optimal solution such that if the following necessary conditions in ( Chuma, Mwanga, & Masanja, 2019 ) are satisfied: Control set U and the corresponding state variables are nonempty, Control set U is convex and closed, The right hand side of the state system is bounded by the linear function in the state and control variables, The integrand of the objective function is convex, and There exist constant numbers q 1 , q 2 > 0 and ξ > 1 such that the integrand of the objective function is bounded below by . …”

Optimal Control in Two Strain Pneumonia Transmission Dynamics

“…where A 1 , A 2 , and A 3 are the weight constants associated with the number of susceptible individuals, the number of individuals infected with drug-sensitive strain, and the number of individuals infected with drug-resistant strain while B 1 , B 2 , B 3 , and B 4 present relative cost weight which is associated with control measures u 1 , u 2 , u 3 , and u 4 , respectively. The control variables in the objective functional are in quadratic form because we assume that costs are nonlinear in nature which is a convex function as applied by [17,[33][34][35]. The aim is to minimize the objective functional such that the optimal control satisfy…”