On the Number of Periodic Inspections During Outbreaks of Discrete-Time Stochastic SIS Epidemic Models

Gamboa, María; Lopez-Herrero, M. J.

doi:10.3390/math6080128

Cited by 3 publications

(1 citation statement)

References 29 publications

(43 reference statements)

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“…The SIR model, and a number of different variations, has been widely analysed both for homogeneous [6,7] and heterogeneous populations [8]. In these systems, of particular interest can be specific summary statistics that characterize an outbreak, such as the size of the outbreak [9], its length [10,11] or the reproduction number [12].…”

Section: Introductionmentioning

confidence: 99%

A Stochastic SVIR Model with Imperfect Vaccine and External Source of Infection

Gamboa

López‐García

Lopez-Herrero

2021

Lecture Notes in Computer Science

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A stochastic SIR (Susceptible -Infected -Recovered) type model, with external source of infection, is considered for the spread of a disease in a finite population of constant size. Our interest is in studying this process in the situation where some individuals have been vaccinated prior to the start of the epidemic, but where the efficacy of the vaccine to prevent infection is not perfect. The evolution of the epidemic is represented by an absorbing three-dimensional continuous-time Markov chain. We focus on analysing the time for a threshold number of individuals to become infected, and carry out a global sensitivity analysis for the impact of varying model parameters on this summary statistic of interest.

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Section: Introductionmentioning

confidence: 99%

A Stochastic SVIR Model with Imperfect Vaccine and External Source of Infection

Gamboa

López‐García

Lopez-Herrero

2021

Lecture Notes in Computer Science

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Estimating the prevalence of terrorism under control policies. A statistical modelling approach

Papageorgiou

2025

Applied Mathematical Modelling

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Deterministic and Stochastic Model for the Transmission of Lassa Fever

Ogwuche,

Emonyi

2024

FJS

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Many models on the transmission dynamics of Lasser fever were based on purely deterministic approach. This approach does not put into cognizance randomness which is inherent in disease transmission resulting from differences in immunity levels, contact patterns, hygienic practices and mutation rates among so many other possibilities. In this work, we attempt to demonstrate the impact of uncertainties in the mode of transmission of Lassa fever by subjecting the dynamics to some white noise modeled by the Brownian motion as a Wiener process. An existing deterministic model involving the Susceptible, Exposed, Infected and Recovered (SEIR) individuals was transformed into a stochastic differential equation model by applying the procedure proposed by Allen et al (2008). The resulting system of Stochastic Differential Equations (SDE) was solved numerically using the Milstein scheme for SDEs. An algorithm for the method was developed and implemented in Python programming language. Numerical simulations of the model was done using four sets of parameters; , representing the natural birth rate, the natural death rate , the recovering rate from infected to recovered, transmission rate from exposed to infected ,transmission rate from susceptible to exposed are carried out to investigate the transmission dynamic of Lassa fever. The results of the simulations indicate that randomness does affect transmission of Lassa fever. We therefore recommend that factors such as social behavior, hygienic practices, contact patters, mutation rate should be considered while formulating mathematics models of disease transmission.

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On the Number of Periodic Inspections During Outbreaks of Discrete-Time Stochastic SIS Epidemic Models

Cited by 3 publications

References 29 publications

A Stochastic SVIR Model with Imperfect Vaccine and External Source of Infection

A Stochastic SVIR Model with Imperfect Vaccine and External Source of Infection

Estimating the prevalence of terrorism under control policies. A statistical modelling approach

Deterministic and Stochastic Model for the Transmission of Lassa Fever

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