Simulation Platforms to Support Teaching and Research in Epidemiological Dynamics⋆
Authors: Getz Wayne M , Salter Richard , Vissat Ludovica Luisa 
Published: February 2022

An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP® (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs. In this paper, we take the reader through simulations that are used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that ‘burn’ through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R0, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R0 > 1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, and both recovery and mortality rates; 7) similarly, the impacts of vaccination are equally complicated and, in addition, when a fixed number of vaccination regimens are available, the rate and timing of delivery are crucially important to maximizing there ability to reducing mortality. Our presentation makes transparent the key assumptions underlying SIR epidemic models. The model and simulations tools described in this paper and the four RAMPs that we provide are meant to augment rather than replace classroom material when teaching epidemiological dynamics. Our RAMPs are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

Highlights

Basic concepts used to build epidemiological models and think about epidemics are introduced

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disease class structure and homogeneity

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well-mixed population

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flows of individuals among classes

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rates of change and mathematical representation

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deterministic versus stochastic formulations

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disease reproductive value and R-zero

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cessation of an epidemic versus endemicity

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formulation of transmission

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adaptive contact behavior

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infectious, latent, and immunity waning periods (waiting times)

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competing risks and rates to proportions transformations

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effects of treatment and vaccination measures

Principles of epidemiological dynamics are illustrated through simulation including:

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rise to peak prevalence, subsequent fall to extirpation as herd immunity level is reached, but some individuals remain uninfected

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level of endemicity inversely related to rate at which immunity wanes

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effects of adaptive contact behavior on flattening the prolonging the prevalence peak

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proportion of stuttering transmission chains that lead to an outbreak is related to size of R0 (basic reproductive rate of the disease)

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complexities involved in incorporating treatment effects

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trade-off between early vaccination rollout and availability of vaccination regimens

Four simple-to-use basic and applied deterministic and stochastic runtime alterable model platforms are provided for students to use in replicating illustrative examples, carrying out suggested exercises, and exploring novel idea. These are:

Deterministic SIRS RAMP

Stochastic SIRS RAMP

Deterministic SIRS+DTV RAMP

Stochastic SIRS+DTV RAMP