Visceral leishmania model

Boukhalfa, Fatima; Helal, Mohamed; Lakmeche, Abdelkader

doi:10.1051/itmconf/20150401007

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…In 2017, Boukhalfa et al presented a mathematical model which describes the dynamics of visceral leishmaniasis in the dog population. They observed the effect of primary reproduction numbers and showed global stability using the Lyapunov function [1]. 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].…”

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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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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“…There are many scholars who have adopted differential equation models to describe the transmission dynamics of leishmaniasis [14][15][16][17][18]. Ghaves and Hernandez [19] developed a model of the transmission dynamics of CL with incidental host populations of the parasite and host populations and calculated the threshold conditions for persistent infection.…”

Section: Introductionmentioning

confidence: 99%

Transmission dynamics of visceral leishmaniasis with PKDL and periodic delays

Wang

Fan

et al. 2023

Math Methods in App Sciences

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We consider the transmission of visceral leishmaniasis in three populations: humans, dogs and sandflies. To investigate the effects of spatial heterogeneity and temporal periodicity on disease transmission, a nonlocal periodic reaction-diffusion equation model is developed. We introduce the basic reproduction number R 0 and establish the global dynamics. Numerical simulations show that (i) R 0 is overestimated in the absence of spatial heterogeneity; (ii) R 0 is underestimated without considering the effect of temporal seasonality; and (iii) shortening periodic delays of visceral leishmaniasis reduces the risk of disease transmission.

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“…Almeida et al ( [11]) proposed a mathematical model of the immune systems response in CL. In 2017, Boukhalfa et al ( [8]) proposed a mathematical model to describe the dynamics of visceral leishmaniasis in the dog population, and this study identifies the key parameters that play a key role on the disease dynamics, and thereby contributing in the design of effective control strategies. Coffeng et al ( [9]) investigated the detection, control and impact of visceral leishmaniasis VL in the Indian subcontinent.…”

Section: Introductionmentioning

confidence: 99%

Global stability of a diffusive Leishmaniasis model with direct and indirect infection rate

Yang

2023

J. Math. Computer Sci.

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Visceral leishmaniasis (VL), or black fever (kala-azar), is a fatal parasitic disease that infects a hosts internal organs. According to the World Health Organization (WHO), leishmaniasis is a major public health problem that has been neglected, and the control measures in various seriously infected areas have not been successful. Therefore, in order to analyze and control the spread of leishmaniasis, we establish a diffusive model with direct and indirect infection rate. Firstly, we prove the uniform bounds of solutions of the system, and analyze the sensitivity of the parameters. Secondly, sufficient conditions for the existence of the disease-free equilibrium and the endemic equilibrium are given, respectively. In addition, the stability of the model is studied in local and global sense by using the Routh Hurwitz criterion and Lyapunov theory, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R 0 1 and the endemic equilibrium is globally asymptotically stable when the basic reproduction number R 0 > 1. Finally, the theoretical results of the diffusive Leishmaniasis model with direct and indirect infection rate are verified by simulation. The results show that direct or indirect infection rates may affect the prevalence of the disease.

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Visceral leishmania model

Cited by 3 publications

References 5 publications

New Trends in the Modeling of Diseases Through Computational Techniques

New Trends in the Modeling of Diseases Through Computational Techniques

Transmission dynamics of visceral leishmaniasis with PKDL and periodic delays

Global stability of a diffusive Leishmaniasis model with direct and indirect infection rate

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