Pengendalian Optimal Model Epidemi Flu Burung pada Unggas-Manusia dengan Pengobatan pada Manusia dan Depopulasi pada Unggas

Pengendalian optimal terhadap penyebaran flu burung melalui pendekatan model epidemi flu burung pada unggas dan manusia dilakukan dengan menggunakan prinsip Pontryagin. Pengendalian ini bekerja dengan menambahkan variabel kendali pada model matematika dan mengoptimalkan fungsional objektif. Variabel kendali yang ditambahkan pada model berupa pengobatan pada subpopulasi manusia yang terinfeksi dan depopulasi pada subpopulasi unggas yang terinfeksi. Tujuan dari pengendalian ini yaitu untuk meminimumkan jumlah subpopulasi manusia yang terinfeksi dan jumlah subpopulasi unggas yang terinfeksi serta biaya yang diperlukan selama pengobatan dan depopulasi. Model diselesaikan secara numerik menggunakan metode Runge-Kutta. Sementara proses pengendalian diselesaikan secara numerik dengan bantuan toolbox DOTcvpSB pada bahasa pemrograman Matlab. Setelah dibandingkan dengan hasil simulasi numerik model epidemi flu burung tanpa kendali, hasil simulasi numerik model epidemi flu burung dengan kendali menunjukkan bahwa pengobatan mampu menurunkan jumlah subpopulasi manusia yang terinfeksi hampir 100%. Begitu juga dengan depopulasi yang mampu menurunkan jumlah subpopulasi unggas yang terinfeksi hampir 100%. Sehingga dengan kata lain penyebaran virus flu burung dapat dikendalikan dengan baik jika dilakukan depopulasi pada unggas yang terinfeksi dan pengobatan pada manusia yang terinfeksi.Kata kunci: depopulasi, flu burung, kendali optimal, model epidemi, pengobatan, Pontryagin

OPTIMAL CONTROL OF INFLUENZA A DYNAMICS IN THE EMERGENCE OF A TWO STRAIN

This paper examines the influenza spread model by considering subpopulation, vaccination, resistance to analgesic/antipyretic drugs + nasal decongestants. Based on the studied model are determined, non-endemic, endemic stability points and the basic reproduction number. In the model studied, control is given in an effort to prevent contact of individuals infected with influenza and susceptible (u1), and control treatment for infected individuals in an effort to accelerate the recovery of infected individuals (u2). In the numerical simulation, using the control u1 the number of infected individuals subpopulation decreased compared to that without control. The number of individual recovered subpopulations using the u2 control increased more than that without the control

Fuzzy modeling for the spread of influenza virus and its possible control

In this paper, we analyze a model of Influenza spread with an asymptotic transmission rate, wherein the disease transmission rate and death rate are considered as fuzzy sets. Comparative studies of the equilibrium points of the disease for the classical and fuzzy models are performed. Using the concept of probability measure and fuzzy expected value, we obtain the fuzzy basic reproduction number for groups of infected individuals with different virus loads. Further, a basic reproduction number for the classical and the fuzzy model are compared. Finally, a program based on the basic reproduction value of disease control is suggested and the numerical simulations are carried out to illustrate the analytical results

Modelling the outbreak of infectious disease following mutation from a non-transmissible strain

In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the past. We use simple mathematical models to describe this process with the aim to better understand the emergence of an epidemic resulting from such a mutation and the extent of measures that are needed to control it. The feared outbreak of a human–human transmissible form of avian influenza leading to a global epidemic is the paradigm for this study. We extend the SIR approach to derive a deterministic and a stochastic formulation to describe the evolution of two classes of susceptible and infected states and a removed state, leading to a system of ordinary differential equations and a stochastic equivalent based on a Markov process. For the deterministic model, the contrasting timescale of the mutation process and disease infectiousness is exploited in two limits using asymptotic analysis in order to determine, in terms of the model parameters, necessary conditions for an epidemic to take place and timescales for the onset of the epidemic, the size and duration of the epidemic and the maximum level of the infected individuals at one time. Furthermore, the basic reproduction number is determined from asymptotic analysis of a distinguished limit. Comparisons between the deterministic and stochastic model demonstrate that stochasticity has little effect on most aspects of an epidemic, but does have significant impact on its onset particularly for smaller populations and lower mutation rates for representatively large populations. The deterministic model is extended to investigate a range of quarantine and vaccination programmes, whereby in the two asymptotic limits analysed, quantitative estimates on the outcomes and effectiveness of these control measures are established