Simulation Model for Dynamics of Dengue with Innate and Humoral Immune Responses

Perera, Sunethra; Perera, S. S. N.

doi:10.1155/2018/8798057

Cited by 14 publications

(6 citation statements)

References 32 publications

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“…Therefore, determining the intervals at which the model parameters are sensitive is crucial. In similar lines to the sensitivity analysis done in [43], in this section we carry out sensitivity analysis of the model parameters. As each parameter is varied, we plot the infected population, the mean infected population, and the mean squared error as a function of time.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Chhetri

Vamsi

Sanjeevi

2022

Differ Equ Dyn Syst

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COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable when R 0 < 1 , and when R 0 is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.

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Section: Sensitivity Analysismentioning

confidence: 99%

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Chhetri

Vamsi

Sanjeevi

2022

Differ Equ Dyn Syst

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“…In this context, the invivo mathematical modelling studies can be extremely helpful in understanding the efficacy of the drug/medicine administered. These studies can also help in understanding the behaviour of cytokines, chemokines and immune system response of the body towards this virus [24,26]. The results of these studies can suggest the optimal drug regime for treating Covid-19.…”

Section: Introductionmentioning

confidence: 97%

Crucial Inflammatory Mediators and Efficacy of Drug Interventions in Pneumonia Inflated COVID-19: An Invivo Mathematical Modelling Study

Chhetri,

Vamsi,

Bhagat

et al. 2020

Preprint

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The virus SARS-COV-2 caused disease COVID-19 has been declared a pandemic by WHO. Currently, over 210 countries and territories have been affected. Careful, well-designed drugs and vaccine for the total elimination of this virus seem to be the need of the hour. In this context, the invivo mathematical modelling studies can be extremely helpful in understanding the efficacy of the drug interventions. These studies can also help understand the role of the crucial inflammatory mediators and the behaviour of immune response towards this novel coronavirus. Motivated by these facts, in this paper, we study the invivo dynamics of Covid-19. We initially model and study the natural history, the course of the infection and its dynamics. We then validate the model by generating two-parameter heat plots that represent the characteristics of Covid-19. We also do the sensitivity analysis to identify the sensitive parameters of the system. Lastly, we study the efficacy of drug interventions for Covid-19 by formulating an Optimal Control Problem. The outcomes of these studies are multi-fold. The system admits two steady states: the disease-free equilibrium and the infected equilibrium. The dynamics of the system show that the disease takes its course to one of these steady states based on the reproduction number R 0 . The system undergoes a transcritical bifurcation at R 0 = 1. From the sensitivity analysis, it is seen that the burst rate of the virus particles and the natural death rate of the virus are the sensitive parameters of the system. Results from the optimal control studies suggest that the antiviral drugs that target viral replication and the drugs that enhance the immune system response both reduce the infected cells and viral load when taken individually. However, it is observed that these drugs yield the best possible results when administered together. Hence, it is concluded that the optimal control strategy would be to use the combination of both these drugs which not only help in patient's recovery but also reduce the side effects caused to the patient because of the minimal/optimal dosage administered. The results obtained here are inline with some of the clinical findings for Covid-19. This invivo modelling study involving the crucial biomarkers of Covid-19 is the first of its kind and the results obtained from this can be helpful to researchers, epidemiologists, clinicians and doctors who are working in this field.

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“…During the recent years, several mathematical models have been developed which describe within-host DENV primary infection [9][10][11][12][13][14][15][16][17]. ese models are based on the virus dynamics model introduced by Nowak and Bangham [18].…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of Secondary DENV Infection with Diffusion

Ełaiw

Alofi

2021

Journal of Mathematics

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During the past eras, many mathematicians have paid their attentions to model the dynamics of dengue virus (DENV) infection but without taking into account the mobility of the cells and DENV particles. In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. The model includes five nonlinear PDEs describing the interaction among the target cells, DENV-infected cells, DENV particles, heterologous antibodies, and homologous antibodies. In the beginning, the well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive three threshold parameters which govern the existence and stability of the four equilibria of the model. We study the global stability of all equilibria based on the construction of suitable Lyapunov functions and usage of Lyapunov–LaSalle’s invariance principle (LLIP). Last, numerical simulations are carried out in order to verify the validity of our theoretical results.

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Simulation Model for Dynamics of Dengue with Innate and Humoral Immune Responses

Cited by 14 publications

References 32 publications

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Crucial Inflammatory Mediators and Efficacy of Drug Interventions in Pneumonia Inflated COVID-19: An Invivo Mathematical Modelling Study

Global Dynamics of Secondary DENV Infection with Diffusion

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