Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

Vandamme, L.K.J.; Rocha, Paulo R. F.

doi:10.3390/app11094159

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…Two basic cases can be considered for an isolated system where a population develops. [27][28][29][30][31][32][33] The first is related to renewable resources and the system's carrying capacity, i.e., they remain constant despite population growth. In the first phase, the population increases according to the Malthus pattern (Eq.…”

Section: Introductionmentioning

confidence: 99%

Global Population: from Super-Malthus behavior to Doomsday Criticality

Drozd-Rzoska,

Sojecka

2024

Preprint

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The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence:$P\left(t\right)={P}_{0}exp{\left[\pm \left(t/\right)\right]}^{}$, and SM-2 is the Malthus-type relation with the time-dependent growth rate $r\left(t\right)$ or relaxation time $\left(t\right)=1/r\left(t\right)$:$P\left(t\right)={P}_{0}exp\left(r\left(t\right)\times t\right)={P}_{0}exp\left[/\left(t\right)\right]$. Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~3 billion): from the compressed exponential behavior ($>1)$ to the stretched exponential one ($<1$). For SM-2 dependence, linear changes of $\left(T\right)$ during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior $P\left(t\right)={P}_{0}exp\left[b{\prime }t/\left({T}_{C}-t\right)\right]$, where ${T}_{C}\approx 2216$ is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

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Section: Introductionmentioning

confidence: 99%

Global Population: from Super-Malthus behavior to Doomsday Criticality

Drozd-Rzoska,

Sojecka

2024

Preprint

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“…Two basic cases can be considered for an isolated system with a developing population 27 – 33 . The first one is related to renewable energy, and the system's carrying capacity remaining constant despite population growth.…”

Section: Introductionmentioning

confidence: 99%

Global population: from Super-Malthus behavior to Doomsday criticality

Sojecka,

Drozd-Rzoska

2024

Sci Rep

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The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: $$P\left(t\right)={P}_{0}exp{\left[\pm \left(t/\tau \right)\right]}^{\beta }$$ P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate $$r(t)$$ r ( t ) or relaxation time τ$$(t)=1/r(t)$$ ( t ) = 1 / r ( t ) : $$P\left(t\right)={P}_{0}exp\left(r\left(t\right)\times t\right)={P}_{0}exp\left[\tau \left(t\right)/t\right]$$ P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ($$\beta >1)$$ β > 1 ) to the stretched exponential one ($$\beta <1$$ β < 1 ). For SM-2 dependence, linear changes of $$\tau \left(T\right)$$ τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior $$P\left(t\right)={P}_{0}exp\left[b{\prime}t/\left({T}_{C}-t\right)\right]$$ P t = P 0 e x p b ′ t / T C - t , where $${T}_{C}\approx 2216$$ T C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

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“…The simulation is based on the Verhulst model with general analytical logistic equations for limited growth. The exponential growth for the first wave is faster than for the next wave [12]. This paper investigates the environmental effect on logistic processes with an external effect, i.e., the slowly varying effect of natural growth.…”

Section: Introductionmentioning

confidence: 99%

An Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Salim¹,

Sulaiman²,

Kenji³

2023

J. Multidiscip. Appl. Nat. Sci.

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The present study aims to obtain an analytic solution for the inhomogeneous Verhults equation using multiple expansion methods. This study identifies the external factors represented by the inhomogeneous term that determine optimal variable conditions for ecosystem population growth. The simulation involves scenarios that utilize constant growth rates, periodic growth rates, constant external factors, and periodic external factors. It is found that external factors increase population growth, whereas constant external factors prevent growth under saturation conditions. Periodic external factors cause fluctuations in the amplitude of growth regions. The present study will highlight and discuss the development and application of the solution.

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Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

Cited by 5 publications

References 13 publications

Global Population: from Super-Malthus behavior to Doomsday Criticality

Global Population: from Super-Malthus behavior to Doomsday Criticality

Global population: from Super-Malthus behavior to Doomsday criticality

An Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

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