Stability analysis for a class of discrete schistosomiasis models with general incidence

Guiro, Aboudramane; Ngom, Daouda; Ouedraogo, Dramane

doi:10.1186/s13662-017-1174-6

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…In this section, we study the global dynamics for R 0 > 1.We make this additional assumption as in (Guiro, Ngom, Ouedraogo, 2017).…”

Section: Stability Of the Endemic Equilibrium Formentioning

confidence: 99%

Global Analysis of SIRS Epidemic Model With General Incidence Function and Incomplete Recovery Rates Stochastical Model

Ouedraogo¹,

Traoré²,

Guiro³

2020

JMR

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In this paper, deterministic and stochastic models are developped for a class of SIRS epidemic models. Firstly, The conditions for the existence, local and global stability of the disease-free equilibrium and endemic equilibrium are obtained. Secondly, we built the stochastic model. The populations are computationally simulated under various conditions. Comparisons are made between the deterministic and stochastic model.

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“…In this section, we study the global dynamics for R 0 > 1.We make this additional assumption as in (Guiro, Ngom, Ouedraogo, 2017).…”

Section: Stability Of the Endemic Equilibrium Formentioning

confidence: 99%

Global Analysis of SIRS Epidemic Model With General Incidence Function and Incomplete Recovery Rates Stochastical Model

Ouedraogo¹,

Traoré²,

Guiro³

2020

JMR

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“…One could mention few of them. Models with general incidence rate were published in Yan-Fang et al (2016) and Guiro et al (2017). Some within hosts and/or multi-hosts models could be found in Chiyaka and Garira (2009), Nelson et al (2009), Diaby et al (2014), , Ding et al (2015), Shan et al (2011), Chiyaka et al (2010 and Zhang et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Prevalence-based modeling approach of schistosomiasis: global stability analysis and integrated control assessment

2021

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A system of nonlinear differential equations is proposed to assess the effects of prevalencedependent disease contact rate, pathogen's shedding rates, and treatment rate on the dynamics of schistosomiasis in a general setting. The decomposition techniques by Vidyasagar and the theory of monotone systems are the main ingredients to deal completely with the global asymptotic analysis of the system. Precisely, a threshold quantity for the analysis is derived and the existence of a unique endemic equilibrium is shown. Irrespective of the initial conditions, we prove that the solutions converge either to the disease-free equilibrium or to the endemic equilibrium, depending on whether the derived threshold quantity is less or greater than one. We assess the role of an integrated control strategy driven by human behavior changes through the incorporation of prevalence-dependent increasing the prophylactic treatment and decreasing the contact rate functions, as well as the mechanical water sanitation and the biological elimination of snails. Because schistosomiasis is endemic, the aim is to mitigate the endemic level of the disease. In this regard, we show both theoretically and numerically that: the reduction of contact rate through avoidance of contaminated water, the enhancement of prophylactic treatment, the water sanitation, and the removal of snails can reduce the endemic level and, to an ideal extent, drive schistosomiasis to elimination.

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“…Nowadays, in order to study the continuous time SIR and SIRS epidemic models, many various discrete dynamical model have been constructed and then, dynamical properties have been considered in many papers such as ( [9,5,11,12,13]). The fact that the epidemiological data are usually collected in discrete time units, such as daily, weekly or monthly, makes the discrete model a natural choice to describe a disease transmission.…”

Section: Introductionmentioning

confidence: 99%

Global stability for a discrete SIR epidemic model with delay in the general incidence function

Guiro¹,

Ouedraogo²,

Ouedraogo³

2019

IJAMR

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In this paper, we construct a backward difference scheme for a class of general SIR epidemic model with general incidence function f. We use the step size h > 0, for the discretization. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, under the conditions that function f satisfies some assumptions. The global stabilities of equilibria are obtained. If the basic reproduction number R0<1, the disease-free equilibrium is globally asymptotically stable. If R0>1, the endemic equilibrium is globally asymptotically stable.

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Stability analysis for a class of discrete schistosomiasis models with general incidence

Cited by 6 publications

References 14 publications

Global Analysis of SIRS Epidemic Model With General Incidence Function and Incomplete Recovery Rates Stochastical Model

Global Analysis of SIRS Epidemic Model With General Incidence Function and Incomplete Recovery Rates Stochastical Model

Prevalence-based modeling approach of schistosomiasis: global stability analysis and integrated control assessment

Global stability for a discrete SIR epidemic model with delay in the general incidence function

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