Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle

Mpeshe, Saul C.

doi:10.1155/2021/2941961

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…In terms of transmission routes, Cavalerie et al (2015), Durand et al (2020) and Nicolas et al (2014) [41,59,61] included the possibility of direct transmission between vertebrate hosts. Among 11 models including a human compartment (Table 1), three [42,64,73] considered human-to-mosquito transmission, for a total of 10 models considering mosquito-to-human transmission, and one model [67] only considering livestock-to-human transmission. It would seem relevant for future models to evaluate the likelihood of humans being dead-end hosts, considering the difficulty to obtain direct observations on that matter.…”

Section: Resultsmentioning

confidence: 99%

Mechanistic models of Rift Valley fever virus transmission dynamics: A systematic review

Cecilia

Drouin

Métras

et al. 2022

Preprint

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Rift Valley fever (RVF) is a zoonotic arbovirosis which has been reported across Africa including the northernmost edge, South West Indian Ocean islands, and the Arabian Peninsula. The virus is responsible for high abortion rates and mortality in young ruminants, with economic impacts in affected countries. To this day, RVF epidemiological mechanisms are not fully understood, due to the multiplicity of implicated vertebrate hosts, vectors and ecosystems. In this context, mathematical models are useful tools to develop our understanding of complex systems, and mechanistic models are particularly suited to data-scarce settings. In this work, we performed a systematic review of mechanistic models studying RVF, to explore their diversity and their contribution to the understanding of this disease epidemiology. Researching Pubmed and Scopus databases (October 2021), we eventually selected 48 papers, which needed to provide a clear description of a mechanistic model with numerical application to RVF. We categorized models as theoretical, applied or grey, according to their will to represent a specific geographical context and their use of data to fulfill this intention. We discussed their contributions to the understanding of RVF epidemiology, and highlighted that theoretical and applied models can use different tools to meet common objectives. Through the examination of model features, we identified research questions left unexplored across scales, along with a substantial lack of justification when choosing a functional form for the force of infection. Overall, we showed a great diversity in RVF models, leading to substantial progress in our comprehension of epidemiological mechanisms. To go further, data gaps must be fulfilled, and modelers need to go the extra mile regarding transparency.

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Section: Resultsmentioning

confidence: 99%

Mechanistic models of Rift Valley fever virus transmission dynamics: A systematic review

Cecilia

Drouin

Métras

et al. 2022

Preprint

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“…x * i where x * is the equilibrium point of the model system (11). Then, we have the following corollary: Corollary 5 ( [21]). Let x(t) ∈ R + be a continuous differentiable function .…”

Section: Stability Of the Endemic Equilibriummentioning

confidence: 90%

“…The local stability of the disease-free equilibrium implies that the endemic equilibrium is also locally stable [20][21][22]. Therefore, in this section, we only establish the global stability of the endemic equilibrium.…”

Section: Stability Of the Endemic Equilibriummentioning

confidence: 99%

Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

2023

Eur. J. Math. Appl.

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Hepatitis B virus infection shall remain a public health concern in many developed and developing countries. In this paper, we formulate and analyse a simple fuzzy fractional model of HBV infection to assess the dynamics of the disease using fractional-order differential equations. To analyse the effect of the initial transmission of the disease, we computed the basic reproduction number R 0 , and used it to perform stability analysis. The results show that the disease-free and the endemic equilibrium are globally stable with respect to the value of R 0 . Numerical simulations were performed to study the variations of each sub-population with respect to time at different order (α). In general, results for the fractional model show that as the order (α) increases, the population of the susceptible and exposed individuals decreases. In contrast, the other sub-populations increase with an increase in α. Further results from the numerical analysis show that increase in α, decreases the diameter of the fuzzy triangular solutions for the susceptible and exposed individuals in the fuzzy fractional model.

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Optimal control assessment of Rift Valley fever model with vaccination and environmental sanitation in the presence of treatment delay

Falowo

Olaniyi

Oladipo

2022

Model. Earth Syst. Environ.

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Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle

Cited by 6 publications

References 21 publications

Mechanistic models of Rift Valley fever virus transmission dynamics: A systematic review

Mechanistic models of Rift Valley fever virus transmission dynamics: A systematic review

Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

Optimal control assessment of Rift Valley fever model with vaccination and environmental sanitation in the presence of treatment delay

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