Dynamical behavior and control strategy of a dengue epidemic model

Khatua, Anupam; Kar, Tapan Kumar

doi:10.1140/epjp/s13360-020-00654-8

Cited by 13 publications

(3 citation statements)

References 29 publications

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“…We see that mathematical modeling plays an important role in quantifying transmission of diseases and formulating control strategies, especially in determining the threshold of disease survival, as well as assessing disease development trends [1][2][3][4][5][6]. In particular, we also see that there has been a lot of research work on mathematical modeling, theoretical analysis, and practical applications of infectious diseases caused by viruses, such as literatures [7][8][9][10][11][12][13][14][15][16][17][18][19][20] and their references. The main research topics include the calculation of the basic reproduction number, the criteria for determining the extinction and persistence of the disease, the generation of branching phenomena and the complexity of dynamics, the fitting of model parameters, model testing and sensitivity analysis, the proposal and analysis of prevention and control measures, as well as the application of mathematical models in the epidemic of some actual viral infections, and so on.…”

Section: Introductionmentioning

confidence: 99%

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Zhang

et al. 2023

Math Methods in App Sciences

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This paper is concerned with the existence and nonexistence of traveling waves of a virus infection model with humoral immunity, cell‐to‐cell transmission, and general nonlinear incidence. Our results show that the existence of traveling wave solutions is determined not only by the basic reproduction number of virus infection and the antibody response reproduction number but also by the critical wave speed . More precisely, we obtain the existence of traveling wave solution connecting infection‐free equilibrium and antibody‐free infection equilibrium for , and and connecting infection‐free equilibrium and antibody‐present infection equilibrium for , and . The existence of traveling wave solution connecting infection‐free equilibrium and antibody‐present infection equilibrium is discussed. Some numerical simulations are carried out to illustrate our analytical results.

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Section: Introductionmentioning

confidence: 99%

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Zhang

et al. 2023

Math Methods in App Sciences

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“…( 2016b ), Hattaf et al. ( 2012 ), Khatua and Kar ( 2020a ), Khatua and Kar ( 2020b ), Khatua et al. ( 2021 ), Mandal 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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“…Mathematical modeling of transmission of infectious disease is being used to understand the emanation procedure and update intervention policies [35] , [36] , [37] . It is also capable of forecasting future scenarios of an outbreak.…”

Section: Introductionmentioning

confidence: 99%

The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India

Das

Khatua

Kar

et al. 2021

Applied Mathematics and Computation

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The ongoing pandemic situation due to COVID-19 originated from the Wuhan city, China affects the world in an unprecedented scale. Unavailability of totally effective vaccination and proper treatment regimen forces to employ a non-pharmaceutical way of disease mitigation. The world is in desperate demand of useful control intervention to combat the deadly virus. This manuscript introduces a new mathematical model that addresses two different diagnosis efforts and isolation of confirmed cases. The basic reproductive number, is inspected, and the model’s dynamical characteristics are also studied. We found that with the condition the disease can be eliminated from the system. Further, we fit our proposed model system with cumulative confirmed cases of six Indian states, namely, Maharashtra, Tamil Nadu, Andhra Pradesh, Karnataka, Delhi and West Bengal. Sensitivity analysis carried out to scale the impact of different parameters in determining the size of the epidemic threshold of . It reveals that unidentified symptomatic cases result in an underestimation of whereas, diagnosis based on new contact made by confirmed cases can gradually reduce the size of and hence helps to mitigate the ongoing disease. An optimal control problem is framed using a control variable projecting the effectiveness of diagnosis based on traced contacts made by a confirmed COVID patient. It is noticed that optimal contact tracing effort reduces effectively over time.

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Dynamical behavior and control strategy of a dengue epidemic model

Cited by 13 publications

References 29 publications

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

Traveling waves for a diffusive virus infection model with humoral immunity, cell‐to‐cell transmission, and nonlinear incidence

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

The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India

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