Complex Dynamics and Optimal Treatment of an Epidemic Model with Two Infectious Diseases

Nandi, Swapan Kumar; Jana, Soovoojeet; Mandal, Manotosh; Kar, Tapan Kumar

doi:10.1007/s40819-019-0613-3

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…Moreover, the control space U is also closed and convex region. Hence the optimal control is bounded and therefore there exists an optimal pair (u * 1 , u * 2 ) which minimizes J for t ∈ [0, T ] with the help of the system of differential equation ( 1) [16,20]. Hence the theorem is proved.…”

Section: Optimal Control Problemmentioning

confidence: 86%

“…It is also considered due to limited space capacities or sources [24]. Again, the incidence rate plays a very important role in epidemiological modelling studies [6,12,13,16,20,28]. Authors use the bilinear incidence rate βSI (where the parameter β is transmission rate of infection and the variables S, I are, respectively, the number of susceptible and infected population) where the force of infection f (I) = βI is an increasing function of I and f (I) −→ ∞ as I −→ ∞.…”

Section: Introductionmentioning

confidence: 99%

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Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Ghosh¹,

Majumdar

Ghosh

2021

Math. Model. Nat. Phenom.

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This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

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Section: Optimal Control Problemmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Ghosh¹,

Majumdar

Ghosh

2021

Math. Model. Nat. Phenom.

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“…While Baba and Hincal ( 2018 ) proposed and analyzed an epidemic model for influenza with three strains and they studied the effects of vaccination and awareness, Nandi et al. ( 2019 ) studied the complex dynamical behavior of an epidemic model with two diseases, and also they pointed out the optimal control strategy. Similar kind of research articles on multi-strain models can be found in Li et al.…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate

Khatua

Pal²,

Kar

2022

Iran J Sci Technol Trans Sci

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In this article, we investigate a diffusive two-strain epidemic model with non-monotone incidence rate and virus mutation. The positivity, existence and uniform boundedness of the solutions of the model system are studied. It is found that the system has three equilibrium points, namely the infection-free equilibrium point, the strain-2 endemic equilibrium point and both the strain-1 and strain-2 endemic equilibrium points. The global asymptotic stability analysis of the diffusive model system near all the equilibrium points is carried out by constructing appropriate Lyapunov functional. It is found that the system has no strain-1 endemic equilibrium point possibly due to the virus mutation. So, in this type of diseases, the infection due to strain-1 cannot be persistent in the community.

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Impacts of Media Awareness on a Stage Structured Epidemic Model

Khatua

Kar

2020

Int. J. Appl. Comput. Math

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Complex Dynamics and Optimal Treatment of an Epidemic Model with Two Infectious Diseases

Cited by 4 publications

References 26 publications

Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Global Dynamics of a Diffusive Two-Strain Epidemic Model with Non-Monotone Incidence Rate

Impacts of Media Awareness on a Stage Structured Epidemic Model

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