Mathematical Models in Epidemiology

Brauer, Fred; Castillo‐Chavez, Carlos; Feng, Zhilan

doi:10.1007/978-1-4939-9828-9

Cited by 451 publications

(463 citation statements)

References 13 publications

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“…Well it depends on levels of protection, cross-immunity, that may protect against future strains. Some relevant references include [8,10,52].…”

Section: Generating Possible Research Questionsmentioning

confidence: 99%

A Tour of the Basic Reproductive Number and the Next Generation of Researchers

Castillo-Garsow

Castillo‐Chavez

2020

Foundations for Undergraduate Research in Mathematics

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The Mathematical and Theoretical Biology Institute (MTBI) is a national award winning Research Experience for Undergraduates (REU) that has been running every summer since 1996. Since 1997, students have developed and proposed their own research questions and derived their research projects from them as the keystone of the program. Because MTBI's mentors have no control over what students are interested in, we need to introduce a suite of flexible techniques that can be applied to a broad variety of interests. In this paper, we walk through examples of some of the most popular techniques at MTBI: epidemiological or contagion modeling and reproductive number analysis. We include an overview of the next generation matrix method of finding the basic reproductive number, sensitivity analysis as a technique for investigating the effect of parameters on the reproductive number, and recommendations for interpreting the results. Lastly, we provide some advice to mentors who are looking to advise student-led research projects. All examples are taken from actual student projects that are generally available through the MTBI website. Suggested Prerequisites Ordinary differential equations, mass action, SIR model, flow diagrams, equilibria, stability, Jacobian matrix, and eigenvalue.

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“…Well it depends on levels of protection, cross-immunity, that may protect against future strains. Some relevant references include [8,10,52].…”

Section: Generating Possible Research Questionsmentioning

confidence: 99%

A Tour of the Basic Reproductive Number and the Next Generation of Researchers

Castillo-Garsow

Castillo‐Chavez

2020

Foundations for Undergraduate Research in Mathematics

Self Cite

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“…The constant c, and the exponents γ and κ are obtained from a least-squares method applied to linear relation between respective logarithms 1 , log(∆I(t)) = log(c) + γ log(I(t)) + κ log(S(t)). 1 The zero entries for ∆I(t), I(t), S(t) are ignored.…”

Section: A Two-dimensional Grid-graphmentioning

confidence: 99%

“…where α is the recovery rate (with time constant of recovery τ := 1/α) and η a parameter regulating the rate at which immunity is lost over time. See [1], [11] for all the details about the SIR model together with an extensive list of references. Multi-compartmental models that include infected but asymptomatic individuals, deceased, etc.…”

Section: Introductionmentioning

confidence: 99%

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Fractional SIR Epidemiological Models

Taghvaei

Georgiou

Norton

et al. 2020

Preprint

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The purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the transmission rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the transmission rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread contact between members of the groups. We content, that contact between infected and susceptible individuals, especially during the early phases of an epidemic, takes place over a (possibly diffused) boundary between the respective subpopulations. As a result, the rate of transmission depends on the product of fractional powers instead. The intuition relies on the fact that infection grows in geographically concentrated cells, in contrast to the standard product model that relies on complete mixing of the susceptible to infected sub-populations. We validate the hypothesis of fractional exponents i) by numerical simulation for disease propagation in graphs imposing a local structure to allowed disease transmissions and ii) by fitting the model to a

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“…Even the simplest models contain several variables, which are hard to determine from the available data. The minimal SIR model describes the behavior of the susceptible S(t), the infected I(t), and the removed (recovered or deceased) R(t) populations [7,8]. Numerous models have been published on COVID-19 [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Transmission Potential and Severity of COVID–19 in Romania and Pakistan

Ozair

Hussain

Hussain³

et al. 2020

Preprint

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During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of Coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time-to-reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed.

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Mathematical Models in Epidemiology

Cited by 451 publications

References 13 publications

A Tour of the Basic Reproductive Number and the Next Generation of Researchers

A Tour of the Basic Reproductive Number and the Next Generation of Researchers

Fractional SIR Epidemiological Models

Estimation of Transmission Potential and Severity of COVID–19 in Romania and Pakistan

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