Mathematical analysis of a time delay visceral leishmaniasis model

Gandhi, Velmurugan; Al-Salti, Nasser; ELmojtaba, Ibrahim M.

doi:10.1007/s12190-019-01315-5

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Treatment of Trichomoniasis vaginalis infections may aid in the battle against HIV/AIDS epidemic to a lesser extent, according to Bhunu et al [28], considering the high cost of antiretroviral drugs in underdeveloped nations, as well as the importance of Trichomoniasis, vaginalis infections in HIV transmission. Gandhi et al [29] have discussed dynamical features of a VL framework with time delay and specified stability conditions, as well as the occurrence of Hopf bifurcation. The delayed system experiences Hopf bifurcation, periodic solution, and once in chaos may likewise happen, [30,31,34,35,36].…”

Section: Introductionmentioning

confidence: 99%

A Mathematical modelling for co-infection dynamics of Japanese encephalitis-Dengue and influence of JE Vaccine on Dengue disease

Dwivedi,

Keval,

Baniya

2024

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A non-linear deterministic mathematical model has been described with the co-infection dynamics of Japanese encephalitis(JE) and dengue disease, incorporating the JE vaccine. A basic reproduction number is discussed to study transmission potential of the co-infection model. In co-infection model, disease-free equilibrium points of Japanese encephalitis and dengue, along with endemic, are presented in system and investigated their stability with the help of their specified method. Our analysis suggests that vaccination against Japanese encephalitis positively affect control of co-infection. By using Center Manifold Theory, the model undergoes backwards bifurcation phenomenon and this has been occurred when basic reproduction number is smaller than unity. It is shown that by taking simultaneous preventive steps, the basic reproduction number of co-infection can be reduced to less than one after eliminating both infections. Sensitivity analysis has been performed to determine which parameters significantly affect disease dynamics. The effects of these parameters on transmission of disease were investigated using a numerical simulation. According to the findings, we obtain that JE-dengue co-infection can be managed with use of JE vaccine, also minimize JE transmission rate rapidly.

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Section: Introductionmentioning

confidence: 99%

A Mathematical modelling for co-infection dynamics of Japanese encephalitis-Dengue and influence of JE Vaccine on Dengue disease

Dwivedi,

Keval,

Baniya

2024

Proyecciones (Antofagasta)

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“…In 2020, Coffeng et al predicted the impact of reduced detection delays and increased population coverage on observed visceral leishmaniasis cases using a mathematical model [2]. In 2020, Gandhi et al discussed the delayed visceral leishmaniasis model's dynamical characteristics and presented the steady states' global stability [3]. Zamir et al formulated well known mathematical model with the help of deterministic techniques [4].…”

Section: Introductionmentioning

confidence: 99%

New Trends in the Modeling of Diseases Through Computational Techniques

Althobaiti¹,

Raza²,

Nasir³

et al. 2023

Computer Systems Science and Engineering

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The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance. The handling strategies of real-world problems are artificial neural networks (ANN), evolutionary computing (EC), and many more. An estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually, with only 25% to 45% reported to the World Health Organization (WHO). It remains one of the top parasitic diseases with outbreak and mortality potential. In 2020, more than ninety percent of new cases reported to World Health Organization (WHO) occurred in ten countries: Brazil,

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“…The delayed system experiences Hopf bifurcation, periodic solution and once in chaos may likewise happen, [11,14,19,21,22,25,26,28]. Gandhi et al, [18] have discussed the dynamical characteristic of a VL framework with time delay and established criteria for stability and the presence of Hopf bifurcation. Kumar et al, [23] have constructed the SIR pandemic model with the deterministic time-delayed system.…”

Section: Introductionmentioning

confidence: 99%

The impact of time delay in the transmission of Japanese encephalitis without vaccination

Baniya

Keval

2021

Proyecciones (Antofagasta)

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In the manuscript, the influence of time delay on the transmission of Japanese encephalitis model without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the JE virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steady-states and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensure the asymptotic stability of relating equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a ”Hopf bifurcation”. Moreover, we infer an express equation to decide the stability and direction of ”Hopf bifurcation” at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. In addition, larger values of virus transmission rate from an infected mosquito to susceptible individuals and the natural mortality of humans of a model affect the existence of ”Hopf bifurcation”. Finally, to understand some analytical outcomes, the delay framework is simulated numerically.

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Mathematical analysis of a time delay visceral leishmaniasis model

Cited by 3 publications

References 25 publications

A Mathematical modelling for co-infection dynamics of Japanese encephalitis-Dengue and influence of JE Vaccine on Dengue disease

A Mathematical modelling for co-infection dynamics of Japanese encephalitis-Dengue and influence of JE Vaccine on Dengue disease

New Trends in the Modeling of Diseases Through Computational Techniques

The impact of time delay in the transmission of Japanese encephalitis without vaccination

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