Mathematical model for inflammatory response to coronavirus infection with anti-inflammatory treatment intervention

Wiraya, Ario; Mardiyana,; Fitriana, Laila; Triyanto, .; Baharuddin, D. S. Muhammad; Febri, S. Salma

doi:10.1063/5.0106019

Cited by 2 publications

(6 citation statements)

References 18 publications

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“…Equilibrium points represent a state which illustrates a steady phenomenon in a very long time condition. We investigate the equilibrium points of the model by solving dV/dt = dS/dt = dI/dt = 0 [14][15][16] that interprets a static number of each subpopulation over time. Three equilibrium points of the model were found, i.e., the disease-free equilibria, the sterile media endemic equilibria, and the nonsterile media endemic equilibria.…”

Section: Resultsmentioning

confidence: 99%

“…Fluctuation of the number of viruses, susceptible, and infected subpopulations around the equilibrium points are represented by their local stability. We predict the dynamic of each subpopulation starting around the equilibrium point by analyzing the local stability using the linearization method [14][15][16]. We also use MAPLE to compute some results of algebraic operations, so that calculation error is avoided and accuracy of the calculation is obtained.…”

Section: Resultsmentioning

confidence: 99%

“…Based on the theory in [17] and the characteristic equation in (15), we found that fold bifurcation occurs if −Z 3 = 0 which is equivalent to −aR 1 = 0. It is satisfied if R 1 = 0.…”

Section: Codimension-onementioning

confidence: 98%

“…, and Z 3 = aR 1 . We use the characteristic equation in (15) to identify some bifurcations in codimension-one and codimension-two bifurcation. We also use MAPLE again to compute some results of algebraic operations.…”

Section: Bifurcation Analysismentioning

confidence: 99%

“…Proof. Based on the theory in [17] and the characteristic equation in (15), we obtain that Baogdanov-Takens bifurcation occurs when…”

Section: Theorem 7 Bogdanov-takens Bifurcations Occur At the Followin...mentioning

confidence: 99%

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Bifurcation Analysis of the Dynamics in COVID‐19 Transmission through Living and Nonliving Media

Wiraya,

Fitriana,

Triyanto

et al. 2024

Journal of Applied Mathematics

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Transmission of COVID-19 occurs either through living media, such as interaction with a sufferer, or nonliving objects contaminated with the virus. Recovering sufferers and disinfectant spraying prevent interaction between people and virus become the treatment to overcome it. In this research, we formulate a new mathematical model as a three-dimensional ordinary differential equation system representing an interaction between viruses attached in nonliving media, susceptible, and infected subpopulations, including the treatment to investigate its effect. Disease-free, sterile-media endemic, and two nonsterile media endemic equilibriums exist in the model. The nonexistence of sterile-media equilibria interpreting the nonendemic condition is achieved by crossing the branch point bifurcation of the equilibria point as the infected subpopulation recovery rate increases. Continuation of the limit cycle generated at a Hopf bifurcation point as susceptible-coronavirus interaction prevention rate and period increase trigger two saddle-node bifurcations and a branch point bifurcation of cycle. Stable symmetric cycles with decreasing amplitude that make the dynamic of subpopulation easier to control start to be gained at the branch point bifurcation of cycle between the two saddle-node bifurcation points as the prevention rate increases. Some chaotic attractors which describe a complex and unpredictable pattern of the dynamic in the population are also found at inclination flip bifurcation by a continuation of a homoclinic orbit generated near the Bogdanov-Takens bifurcation point as the prevention rate increases while the recovery rate decreases. Increasing the recovery and prevention rate along with avoiding an increase of the prevention rate while the recovery rate decreases becomes the treatment to optimize the effort in overcoming COVID-19 transmission.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Based on the theory in [17] and the characteristic equation in (15), we found that fold bifurcation occurs if −Z 3 = 0 which is equivalent to −aR 1 = 0. It is satisfied if R 1 = 0.…”

Section: Codimension-onementioning

confidence: 98%

Section: Bifurcation Analysismentioning

confidence: 99%

“…Proof. Based on the theory in [17] and the characteristic equation in (15), we obtain that Baogdanov-Takens bifurcation occurs when…”

Section: Theorem 7 Bogdanov-takens Bifurcations Occur At the Followin...mentioning

confidence: 99%

See 3 more Smart Citations

Bifurcation Analysis of the Dynamics in COVID‐19 Transmission through Living and Nonliving Media

Wiraya,

Fitriana,

Triyanto

et al. 2024

Journal of Applied Mathematics

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Global Stability of Disease-Free Equilibria in Covid-19 Spread Through Living and Inanimate Objects Mathematical Model

Wiraya,

Adi,

Fitriana

et al. 2023

BAREKENG: J. Math. & App.

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Covid-19 is a dangerous disease that is easily transmitted, both through living media in the form of interactions with infected human, as well as through inanimate objects in the form of surfaces contaminated with the Coronavirus. Various preventive and repressive efforts have been made to prevent the spread of this disease, such as isolating and recovering the infected human. In this study, the authors construct and analyze a new mathematical model in the form of a three-dimensional differential equations system that represent the interactions between subpopulations of coronavirus living on inanimate objects, susceptible human, and infected human within a population. The purpose of this study is to investigate the criteria that must be met in order to create a population free from Covid-19 by considering inanimate objects as a medium for its spread besides living objects. The model solution that represents the number of each subpopulation is non-negative and bounded, so it is in accordance with the biological condition that the number of subpopulations cannot be negative and there is always a limit for its value. The eradication rate of Coronavirus living on inanimate objects, the recovery rate of infected human, and the interaction rate between susceptible human and infected human such that the population is free from Covid-19 for any initial conditions of each subpopulation were investigated in this study through global stability analysis of the disease-free equilibrium point of the model.

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Mathematical model for inflammatory response to coronavirus infection with anti-inflammatory treatment intervention

Cited by 2 publications

References 18 publications

Bifurcation Analysis of the Dynamics in COVID‐19 Transmission through Living and Nonliving Media

Bifurcation Analysis of the Dynamics in COVID‐19 Transmission through Living and Nonliving Media

Global Stability of Disease-Free Equilibria in Covid-19 Spread Through Living and Inanimate Objects Mathematical Model

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