Stability analysis of a schistosomiasis model with delays

Guiro, Aboudramane; Ouaro, Stanislas; Traoré, Ali

doi:10.1186/1687-1847-2013-303

Cited by 11 publications

(19 citation statements)

References 17 publications

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“…18 This approach has been used also in previous studies on other schistosomiasis models. 23,24 We use a human population of size H ¼ 1000 individuals with a life expectancy of 70 yr (l H ¼ 4 Â 10 À5 /day). The life expectancy of adult parasites is 5 yr 19,25 (l P ¼ 5.5 Â 10 À4 /day).…”

Section: B Parameter Estimationmentioning

confidence: 99%

The temporal patterns of disease severity and prevalence in schistosomiasis

Ciddio

Mari

Gatto

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra- and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility.

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Section: B Parameter Estimationmentioning

confidence: 99%

The temporal patterns of disease severity and prevalence in schistosomiasis

Ciddio

Mari

Gatto

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…As far as models of co-infection are concerned, we found only two studies (Okosun and Smith 2017;Mushayabasa and Bhunu 2011). While a couple of people devoted their works on mathematical models with delays or with periodic environment (Yingke et al 2017;Lin and Zhicheng 2014;Zhang et al 2014;Guiro et al 2013;Shan et al 2011;Yun and Yuanguo 2016;Wu and Feng 2002;Castillo-Chavez et al 2008), very few researchers investigated the spatial dynamics of schistosomiasis Milner and Zhao 2008;Mari et al 2017;Shan et al 2014), and optimal control models (Ding et al 2015;Shan et al 2011;Ding et al 2017). Since none of these above-mentioned existing works have taken into account the role of human behavior on schistosomiasis, we spare the reader of their respective findings, because we want to remain focus on that newly incorporated transmission feature of the disease.…”

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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“…Chiyaka & Garira [4] investigated the host-parasite dynamics of schistosomiasis, Ishikawa et al [12] and Gurarie et al [7] considered the effect of a mass treatment program with snail control, while Chiyaka et al [13] observed that treatment eliminates the mature worms and active macrophages over a period of time with declining T-cell immune responses in the human body. The importance of public awareness campaigns was examined by Guiro et al [14] and Yingke et al [15], where Guiro et al [14] used two general non-linear incidence functions and distributed delay. Diaby et al [16] carried out a stability analysis of schistosomiasis dynamics, while Musa et al [17] promoted the use of vaccination, and Ronoh et al [18] considered the impact of environmental transmission in humans.…”

Section: Introductionmentioning

confidence: 99%

The Role of Non-pharmacological Interventions on the Dynamics of Schistosomiasis

Abokwara

Madubueze

2021

J. Math. Fund. Sci.

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Schistosomiasis is a neglected tropical disease affecting communities surrounded by water bodies where fishing activities take place or people go to swim, wash and cultivate crops. It poses a great risk to the health and economic life of inhabitants of the area. This study was carried out to evaluate the impact of public health education and snail control measures on the incidence of schistosomiasis. A model was developed with attention given to the snail and human populations that are the hosts of the cercariae and miracidia respectively. The existence and stability of disease-free and endemic equilibrium states were established. The disease-free and endemic equilibrium states were shown to be locally asymptotically stable whenever the basic reproduction number was less than unity. Numerical simulations of the model were carried out to evaluate the impact of interventions (public health education and snail control measures) on schistosomiasis transmission. It was observed that the implementation of low coverage snail control with highly efficacious molluscicide and massive public health education will make the basic reproduction number smaller than unity, which implies the eradication of schistosomiasis in the population.

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Stability analysis of a schistosomiasis model with delays

Cited by 11 publications

References 17 publications

The temporal patterns of disease severity and prevalence in schistosomiasis

The temporal patterns of disease severity and prevalence in schistosomiasis

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

The Role of Non-pharmacological Interventions on the Dynamics of Schistosomiasis

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