A review of commonly used compartmental models in epidemiology

Mehdaoui, Mohamed

doi:10.48550/arxiv.2110.09642

Cited by 4 publications

(7 citation statements)

References 42 publications

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“…in which a susceptible (S) individual j contracts the pathogen from their infected (I) neighbor i, leading to both i and j becoming infected. The rate of the process in (7), β(j, 0), represents the infection rate of the transmitted strain, i.e. the selected pathogen from Z i , which will now begin to replicate and potentially mutate within j.…”

Section: Resultsmentioning

confidence: 99%

“…In the limit where σ = 0, we have Δψ = 0 in (8) at all times, mutations are suppressed, and Eqs. (7)(8)(9) converge to the classic SIR model, with a stable R 0 . In contrast, as σ is increased, significant ψ-mutations become more frequent and the inter-host fitness rapidly evolves.…”

Section: Evolutionary Dynamicsmentioning

confidence: 87%

“…Then, once reaching a sufficient load, transmission between hosts helps the pathogen penetrate the social network. These two processes, each characterized by its own intrinsic timescales and relevant parameters, are often modeled independently: the in-host dynamics is captured by a random process of mutation and selection [1][2][3][4] ; the inter-host propagation is tracked using compartmental dynamics, such as the susceptibleinfected-recovered (SIR) model 5,6 , or its more elaborate variants 7 . While the former is inherently stochastic, most analytical advances on the latter 5 are achieved via deterministic methods, i.e.…”

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confidence: 99%

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Epidemic spreading under mutually independent intra- and inter-host pathogen evolution

et al. 2022

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The dynamics of epidemic spreading is often reduced to the single control parameter R0 (reproduction-rate), whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, R0 may change over time, potentially leading to a mutation-driven spread, in which an initially sub-pandemic pathogen undergoes a breakthrough mutation. To predict the boundaries of this pandemic phase, we introduce here a modeling framework to couple the inter-host network spreading patterns with the intra-host evolutionary dynamics. We find that even in the extreme case when these two process are driven by mutually independent selection forces, mutations can still fundamentally alter the pandemic phase-diagram. The pandemic transitions, we show, are now shaped, not just by R0, but also by the balance between the epidemic and the evolutionary timescales. If mutations are too slow, the pathogen prevalence decays prior to the appearance of a critical mutation. On the other hand, if mutations are too rapid, the pathogen evolution becomes volatile and, once again, it fails to spread. Between these two extremes, however, we identify a broad range of conditions in which an initially sub-pandemic pathogen can breakthrough to gain widespread prevalence.

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Section: Resultsmentioning

confidence: 99%

Section: Evolutionary Dynamicsmentioning

confidence: 87%

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confidence: 99%

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Epidemic spreading under mutually independent intra- and inter-host pathogen evolution

et al. 2022

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“…For long-lasting epidemics such as HIV, new generations of susceptible individuals influence epidemic dynamics. In this case, time delay corresponds to the maturation period after which young adults become susceptible to infection (see [42][43][44] Here, N(t) = S(t) + I(t), g(N(t − τ)) is the susceptible recruitment function, which incorporates the maturation delay τ and h(S, I) is the disease transmission rate.…”

Section: Discussionmentioning

confidence: 99%

An Epidemic Model with Time Delay Determined by the Disease Duration

2022

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Immuno-epidemiological models with distributed recovery and death rates can describe the epidemic progression more precisely than conventional compartmental models. However, the required immunological data to estimate the distributed recovery and death rates are not easily available. An epidemic model with time delay is derived from the previously developed model with distributed recovery and death rates, which does not require precise immunological data. The resulting generic model describes epidemic progression using two parameters, disease transmission rate and disease duration. The disease duration is incorporated as a delay parameter. Various epidemic characteristics of the delay model, namely the basic reproduction number, the maximal number of infected, and the final size of the epidemic are derived. The estimation of disease duration is studied with the help of real data for COVID-19. The delay model gives a good approximation of the COVID-19 data and of the more detailed model with distributed parameters.

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“…In order to comprehend the dynamics of an epidemic, it is necessary to examine a number of structural factors, including the age of the sick people, the length of the disease, and the hosts' level of immunity [20]. Time plays an important role in this field since it gives a continuous perspective on the numerous systems that might have an impact on the epidemic [21].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling and dynamics of immunological exhaustion caused by measles transmissibility interaction with HIV host

Ozsahin,

Khan,

Aqeel

et al. 2024

PLoS ONE

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This paper mainly addressed the study of the transmission dynamics of infectious diseases and analysed the effect of two different types of viruses simultaneously that cause immunodeficiency in the host. The two infectious diseases that often spread in the populace are HIV and measles. The interaction between measles and HIV can cause severe illness and even fatal patient cases. The effects of the measles virus on the host with HIV infection are studied using a mathematical model and their dynamics. Analysing the dynamics of infectious diseases in communities requires the use of mathematical models. Decisions about public health policy are influenced by mathematical modeling, which sheds light on the efficacy of various control measures, immunization plans, and interventions. We build a mathematical model for disease spread through vertical and horizontal human population transmission, including six coupled nonlinear differential equations with logistic growth. The fundamental reproduction number is examined, which serves as a cutoff point for determining the degree to which a disease will persist or die. We look at the various disease equilibrium points and investigate the regional stability of the disease-free and endemic equilibrium points in the feasible region of the epidemic model. Concurrently, the global stability of the equilibrium points is investigated using the Lyapunov functional approach. Finally, the Runge-Kutta method is utilised for numerical simulation, and graphic illustrations are used to evaluate the impact of different factors on the spread of the illness. Critical factors that effect the dynamics of disease transmission and greatly affect the rate and range of the disease’s spread in the population have been determined through a thorough analysis. These factors are crucial in determining the expansion of the disease.

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A review of commonly used compartmental models in epidemiology

Cited by 4 publications

References 42 publications

Epidemic spreading under mutually independent intra- and inter-host pathogen evolution

Epidemic spreading under mutually independent intra- and inter-host pathogen evolution

An Epidemic Model with Time Delay Determined by the Disease Duration

Mathematical modeling and dynamics of immunological exhaustion caused by measles transmissibility interaction with HIV host

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