Stability and Sensitivity Analysis of the COVID-19 Spread with Comorbid Diseases

Nainggolan, Jonner; Ansori, Moch. Fandi

doi:10.3390/sym14112269

Cited by 5 publications

(5 citation statements)

References 36 publications

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“…37) Finally, since the arithmetic mean is greater or equal to the geometric mean as applied by [22,23,24], it follows that:…”

Section: Global Stability Of Covid-19 Endemic Equilibrium Pointmentioning

confidence: 99%

Mathematical Analysis of COVID-19 model with Vaccination and Partial Immunity to Reinfection

Muli,

Benard Okelo,

Richard Magwanga

et al. 2023

J. Math. Anal. Model.

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COVID-19 is an infectious respiratory disease caused by a new virus, called SARS-CoV-2. Since itsinception, it has been a major cause of deaths and illnesses in the general population across the globe. Inthis paper, we have formulated and theoretically analyzed a non-linear deterministic model for COVID-19transmission dynamics by incorporating vaccination of the susceptible population. The system properties,such as the boundedness of solutions, the basic reproduction number R0, the local stability of disease-freeequilibrium(DFE), and endemic equilibrium (EE) points, are explored. Besides, the Lyapunov function isutilized to prove the global stability of both DFE and EE. The bifurcation analysis was carried out by utilizingthe center manifold theory. Then, the model is fitted with real COVID-19 cumulative data of infected casesin Kenya as from March 30, 2020, to March 30, 2022. Furthermore, sensitivity analysis was performed forthe proposed model to ascertain the relative significance of model parameters to COVID-19 transmissiondynamics. The simulations revealed that the spread of COVID-19 can be curtailed not only via vaccinationof susceptible populations but also increased administration of COVID-19 booster vaccine to the vaccinatedpersons and early detection and treatment of asymptomatic individuals.

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“…37) Finally, since the arithmetic mean is greater or equal to the geometric mean as applied by [22,23,24], it follows that:…”

Section: Global Stability Of Covid-19 Endemic Equilibrium Pointmentioning

confidence: 99%

Mathematical Analysis of COVID-19 model with Vaccination and Partial Immunity to Reinfection

Muli,

Benard Okelo,

Richard Magwanga

et al. 2023

J. Math. Anal. Model.

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show abstract

“…If the fundamental reproduction number is smaller than one, the dynamic model of COVID-19 in China with recruitment growth rate logistics spread internationally, and an asymptotically stable non-endemic equilibrium point [6]. The COVID-19 mathematical model study also took into account comorbid and non-comorbid [7], symptomatic and asymptomatic disorders in Indonesia [8,9].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Sensitivity Analysis of COVID-19 and Tuberculosis Coinfection with Vaccination

Nainggolan,

Ansori

2024

MMEP

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This research combines the COVID-19 and BCG vaccination subpopulations to examine the spread of COVID-19 coinfection and tuberculosis (TB) using a compartmental mathematical model. The model analysis yields the non-endemic and endemic equilibrium points in addition to the basic reproduction number. The vaccination variable in the model can reduce the incidence of COVID-19, TB, and coinfection. A sensitivity analysis using elasticity index is conducted and the result is that the natural death rate parameter is the most influential in relation to the accelerated spread of COVID-19 co-infection with tuberculosis. Additionally, we conduct a timedependent sensitivity analysis to determine how varying parameter values influence each subpopulation. By using this technique, we calculate the sensitivity index after reaching equilibrium of several groups of parameters, and the result is that resusceptible, immunity rate, symptomatic transition rate of TB, COVID-19 recovery rate, and natural death rate are the most influential for each group of parameters on the dynamics of each subpopulation.

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“…It could be concluded that the prevention strategy for dengue infection could prevent COVID-19 infection among 870,000 new cases while controls against dengue and controls against COVID-19 could only considerably reduce the infection. Nainggolan and Ansori [35] studied a model of the spread of COVID-19 in Indonesia. Importance was given to quarantine for infectious persons.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Strategy of a Mathematical Model for the Fifth Wave of COVID-19 Outbreak (Omicron) in Thailand

Lamwong,

Wongvanich,

Tang

et al. 2023

Mathematics

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The world has been fighting against the COVID-19 Coronavirus which seems to be constantly mutating. The present wave of COVID-19 illness is caused by the Omicron variant of the coronavirus. The vaccines against the five variants (α, β, γ, δ, and ω) have been quickly developed using mRNA technology. The efficacy of the vaccine developed for one of the strains is not the same as the efficacy of the vaccine developed for the other strains. In this study, a mathematical model of the spread of COVID-19 was made by considering asymptomatic population, symptomatic population, two infected populations and quarantined population. An analysis of basic reproduction numbers was made using the next-generation matrix method. Global asymptotic stability analysis was made using the Lyapunov theory to measure stability, showing an equilibrium point’s stability, and examining the model with the fact of COVID-19 spread in Thailand. Moreover, an analysis of the sensitivity values of the basic reproduction numbers was made to verify the parameters affecting the spread. It was found that the most common parameter affecting the spread was the initial number in the population. Optimal control problems and social distancing strategies in conjunction with mask-wearing and vaccination control strategies were determined to find strategies to give better control of the spread of disease. Lagrangian and Hamiltonian functions were employed to determine the objective function. Pontryagin’s maximum principle was employed to verify the existence of the optimal control. According to the study, the use of social distancing in conjunction with mask-wearing and vaccination control strategies was able to achieve optimal control rather than controlling just one or another.

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Stability and Sensitivity Analysis of the COVID-19 Spread with Comorbid Diseases

Cited by 5 publications

References 36 publications

Mathematical Analysis of COVID-19 model with Vaccination and Partial Immunity to Reinfection

Mathematical Analysis of COVID-19 model with Vaccination and Partial Immunity to Reinfection

Mathematical Modeling and Sensitivity Analysis of COVID-19 and Tuberculosis Coinfection with Vaccination

Optimal Control Strategy of a Mathematical Model for the Fifth Wave of COVID-19 Outbreak (Omicron) in Thailand

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