On nonlinear dynamics of a fractional order monkeypox virus model

El-Mesady, A.; Elsonbaty, Amr; Adel, Waleed

doi:10.1016/j.chaos.2022.112716

Cited by 48 publications

(20 citation statements)

References 39 publications

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“…No geographic region identified Compartmental (fractional order) [9] disease spread include compartments for those vaccinated [38,37], those clinically ill [32], and compartments to model different stages of mpox where infection can occur (prodromal and rash phases) [39]. Two of the nine compartmental studies considered an extension of the classical model by introducing fractional order time-derivative [9,31] and one considered a stochastic extension with Lévy noise [18]. Furthermore, the non-human population in the compartmental studies included monkeys and/or rodents [4,31,32], squirrels [3], or all of the species that can carry mpox [38].…”

Section: Compartmental Modelsmentioning

confidence: 99%

“…Susceptible (S(t)) , exposed (E(t)), infectious (I(t)), recovered (R(t)). Subindices indicate humans (h) or rodents (r) [9].…”

Section: Compartments Definitionmentioning

confidence: 99%

“…[4,31,3]) as well as a fractional compartmental framework (cf. [32,9]). Both approaches identify a reproduction number in their model and derive the conditions under which the mpox disease is eradicated (reproduction number is smaller than 1) and when it persists (reproduction number is larger than 1).…”

Section: Compartments Definitionmentioning

confidence: 99%

“…Human to humans contact rate 0.00006 year −1 [31], 0.01 § [9], 0.022 per weeks [32] Effective contact rate for mpox infection (0.75, 1.5, 3.0) year −1 [4] Human-to-human transmission rate 32.85 year −1 [3] Progression from exposed to infectious class 0.017 per weeks [32], 13 § [39] Clinically ill rate 0.5 per weeks [32] Proportion of exposed human to infected humans 0.2 year −1 [31,9] Humans recovery rate 0. Recovery rate of clinically ill humans 0.036 per weeks [32] Disease induced death rate for humans 0.025 day −1 [38], 0.15 year −1 [4], 0.2 year −1 [31], 3.12 § [3], 0.2 § [9], 0.004 per weeks [32] Clinically ill human disease-induced death rate 0.055 per weeks [32] Reduction in infection risk due to smallpox vaccine 0.05 § [38] Proportion not detected after diagnosis 2.0 year −1 [31,9] Progression from isolated to recovered class 0.52 year −1 [31,9] mpox induced basic reproduction number (humans) 0.9804 [4], 2.13 [37] § No units reported.…”

Section: Parameter Valuementioning

confidence: 99%

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Mathematical modeling of mpox: a scoping review

Molla

Sekkak

Mundo

et al. 2022

Preprint

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Background: Mpox (monkeypox), a disease historically endemic to Africa, has seen its largest outbreak in 2022 by spreading to many regions of the world and has become a public health threat. Informed policies aimed at controlling and managing the spread of this disease necessitate the use of adequate mathematical modelling strategies. Objective: In this scoping review, we sought to identify the mathematical models that have been used to study mpox transmission in the literature in order to determine what are the model classes most frequently used, their assumptions, and the modelling gaps that need to be addressed in the context of the epidemiological characteristics of the ongoing mpox outbreak. Methods: This study employed the methodology of the PRISMA guidelines for scoping reviews to identify the mathematical models available to study mpox transmission dynamics. Three databases (PubMed, Web of Science and MathSciNet) were systematically searched to identify relevant studies. Results: A total of 5827 papers were screened from the database queries. After screening, 35 studies that met the inclusion criteria were analyzed, and 19 were finally included in the scoping review. Our results show that compartmental, branching process, Monte Carlo (stochastic), agent-based, and network models have been used to study mpox transmission dynamics between humans as well as between humans and animals. Furthermore, compartmental and branching models have been the most commonly used classes. Conclusions: There is a need to develop modelling strategies for mpox transmission that take into account the conditions of the current outbreak, which has been largely driven by human-to-human transmission in urban settings. In the current scenario, the assumptions and parameters used by most of the studies included in this review (which are largely based on a limited number of studies carried in Africa in the early 80s) may not be applicable, and therefore, can complicate any public health policies that are derived from their estimates. The current mpox outbreak is also an example of how more research into neglected zoonoses is needed in an era where new and re-emerging diseases have become global public health threats.

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Section: Compartmental Modelsmentioning

confidence: 99%

“…Susceptible (S(t)) , exposed (E(t)), infectious (I(t)), recovered (R(t)). Subindices indicate humans (h) or rodents (r) [9].…”

Section: Compartments Definitionmentioning

confidence: 99%

Section: Compartments Definitionmentioning

confidence: 99%

Section: Parameter Valuementioning

confidence: 99%

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Mathematical modeling of mpox: a scoping review

Molla

Sekkak

Mundo

et al. 2022

Preprint

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“…The impact of smallpox vaccines on MPX epidemics was investigated in [23]. The fractional order ODE models were developed in [24] and [25]. A model incorporating sexual behavior dynamics and stratifying the population into high-and low-risk groups was developed in [26].…”

Section: Mathematical Models Of Mpxmentioning

confidence: 99%

Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model

et al. 2022

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Monkeypox (MPX) is a viral zoonotic disease that was endemic to Central and West Africa. However, during the first half of 2022, MPX spread to almost 60 countries all over the world. Smallpox vaccines are about 85% effective in preventing MPX infections. Our objective is to determine whether the vaccines should be mandated or whether voluntary use of the vaccine could be enough to stop the MPX outbreak. We incorporate a standard SVEIR compartmental model of MPX transmission into a game-theoretical framework. We study a vaccination game in which individuals decide whether or not to vaccinate by assessing their benefits and costs. We solve the game for Nash equilibria, i.e., the vaccination rates the individuals would likely adopt without any outside intervention. We show that, without vaccination, MPX can become endemic in previously non-endemic regions, including the United States. We also show that to “not vaccinate” is often an optimal solution from the individual’s perspective. Moreover, we demonstrate that, for some parameter values, there are multiple equilibria of the vaccination game, and they exhibit a backward bifurcation. Thus, without centrally mandated minimal vaccination rates, the population could easily revert to no vaccination scenario.

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Mathematical analysis of monkeypox infection with optimal control analysis: A case study with a new outbreak in the United States

Alshehri

Ullah

2023

Math Methods in App Sciences

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Monkeypox infection is a serious illness to human health, and its outbreak has been reported in many non‐endemic regions. Various approaches have been implemented to explore the epidemiology, transmission patterns, and effective control of monkeypox. In this paper, we focus on the implementation of a mathematical modeling approach to study the dynamics of monkeypox infection with a case study of the United States, the most impacted country in 2022. The proposed mathematical model is initially constructed using a nonlinear system of differential equations with constant control measures. The human population is divided into four subgroups while the animal (non‐human) population is divided into three subclasses. An extensive theoretical analysis of the proposed monkeypox model is presented including the stability of equilibria. Further, to make the present study more visible to the literature, a real data set of the cumulative confirmed cases of monkeypox in the United States from May to October 2022 is used to estimate the proposed model parameters. Some of the demographic parameters are estimated from the population of the United States. The most important biological parameter of the problem is investigated theoretically as well as numerically based on the reported cases. The impact of various model parameters on the dynamics of state variables and is shown graphically. Furthermore, we analyzed the impact of various model parameters on the basic reproduction number to explore the most influential intervention strategy to curb the infection. The most crucial components of the proposed system are identified and health officials are advised. Finally, using optimization theory, the most effective optimized preventive strategies are suggested to curtail the infection in a community. We believe that the present investigation will be helpful in understanding the dynamics and prevention of monkeypox infection.

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On nonlinear dynamics of a fractional order monkeypox virus model

Cited by 48 publications

References 39 publications

Mathematical modeling of mpox: a scoping review

Mathematical modeling of mpox: a scoping review

Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model

Mathematical analysis of monkeypox infection with optimal control analysis: A case study with a new outbreak in the United States

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