Application of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in Poultry (original) (raw)
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7TH INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION: Mathematics of Quantum Computing
Isolation and fumigation play an essential role in the mechanism of the spread of fowl pox disease. This paper establishes a mathematical model to describe the spread of fowl pox in chicken farms by considering two interventions; isolation intervention to reduce the spread of feathers containing the virus and fumigation intervention to kill fowl pox vectors of adult mosquitoes and their larvae. The model was constructed as a ten-dimensional non-linear ordinary differential equation. Furthermore, analytical and numerical studies were carried out on the constructed model to determine the existence and analyze the disease-free equilibrium point, endemic balance point, basic reproduction number (R 0), and understand the long-term and shortterm dynamics of the constructed model. Based on the carried out analytical and numerical studies, it was concluded that although fumigation and isolation were proven to minimize fowl pox disease, fumigation was more reliable for maximum results.
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SN Computer Science, 2021
Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin's maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method.
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Infectious diseases have remained one of humanity's biggest problems for decades. Multiple disease infections, in particular, have been shown to increase the difficulty of diagnosing and treating infected people, resulting in worsening human health. For example, the presence of influenza in the population is exacerbating the ongoing COVID-19 pandemic. We formulate and analyze a deterministic mathematical model that incorporates the biological dynamics of COVID-19 and influenza to effectively investigate the codynamics of the two diseases in the public. The existence and stability of the disease-free equilibrium of COVID-19-only and influenza-only sub-models are established by using their respective threshold quantities. The result shows that the COVID-19 free equilibrium is locally asymptotically stable when R C < 1, whereas the influenza-only model, is locally asymptotically stable when R F < 1. Furthermore, the existence of the endemic equilibria of the sub-models is examined while the conditions for the phenomenon of backward bifurcation are presented. A generalized analytical result of the COVID-19influenza co-infection model is presented. We run a numerical simulation on the model without optimal control to see how competitive outcomes between-hosts and withinhosts affect disease co-dynamics. The findings established that disease competitive dynamics in the population are determined by transmission probabilities and threshold quantities. To obtain the optimal control problem, we extend the formulated model by including three time-dependent control functions. The maximum principle of Pontryagin was used to prove the existence of the optimal control problem and to derive the necessary conditions for optimum disease control. A numerical simulation was performed to demonstrate the impact of different combinations of control strategies on the infected population. The findings show that, while single and twofold control interventions can be used to reduce disease, the threefold control intervention, which incorporates all three controls, will be the most effective in reducing COVID-19 and influenza in the population.