scholarly journals Inferring epidemic containment probability from non-pharmaceutical interventions using a Gillespie-based epidemic model

2021 ◽  
Author(s):  
Yasuhiko Kawato ◽  
Masatoshi Yamasaki ◽  
Tomomasa Matsuyama ◽  
Tohru Mekata ◽  
Takafumi Ito ◽  
...  
Keyword(s):  
Stochastic Simulation ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Model Parameters ◽  
Gillespie Algorithm ◽  
Susceptible Population ◽  
Markovian Processes ◽  
Pharmaceutical Interventions

The Gillespie algorithm, which is a stochastic numerical simulation of continuous-time Markovian processes, has been proposed for simulating epidemic dynamics. In the present study, using the Gillespie-based epidemic model, we focused on each single trajectory by the stochastic simulation to infer the probability of controlling an epidemic by non-pharmaceutical interventions (NPIs). The single trajectory analysis by the stochastic simulation suggested that a few infected people sometimes dissipated spontaneously without spreading of infection. The outbreak probability was affected by basic reproductive number but not by infectious duration and susceptible population size.　A comparative analysis suggested that the mean trajectory by the stochastic simulation has equivalent dynamics to a conventional deterministic model in terms of epidemic forecasting. The probability of outbreak containment by NPIs was inferred by trajectories derived from 1000 Monte Carlo simulation trials using model parameters assuming COVID-19 epidemic. The model-based analysis indicated that complete containment of the disease could be achieved by short-duration NPIs if performed early after the import of infected individuals. Under the correctness of the model assumptions, analysis of each trajectory by Gillespie-based stochastic model would provide a unique and valuable output such as the probabilities of outbreak containment by NPIs.

scholarly journals Transmission dynamics and control strategies of COVID-19: a modelling study

2021 ◽  
Vol 102 (2) ◽  
pp. 92-105
Author(s):  
U.T. Mustapha ◽  
◽  
E. Hincal ◽  
A. Yusuf ◽  
S. Qureshi ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Recovery Rate ◽  
Transmission Rate ◽  
Face Mask ◽  
Basic Reproductive Number ◽  
Effective Control ◽  
Reproductive Number ◽  
Model Parameters ◽  
Susceptible Population ◽  
Social Distancing

In this paper a mathematical model is proposed, which incorporates quarantine and hospitalization to assess the community impact of social distancing and face mask among the susceptible population. The model parameters are estimated and fitted to the model with the use of laboratory confirmed COVID-19 cases in Turkey from March 11 to October 10, 2020. The partial rank correlation coefficient is employed to perform sensitivity analysis of the model, with basic reproduction number and infection attack rate as response functions. Results from the sensitivity analysis reveal that the most essential parameters for effective control of COVID-19 infection are recovery rate from quarantine individuals (δ1), recovery rate from hospitalized individuals (δ4), and transmission rate (β). Some simulation results are obtained with the aid of mesh plots with respect to the basic reproductive number as a function of two different biological parameters randomly chosen from the model. Finally, numerical simulations on the dynamics of the model highlighted that infections from the compartments of each state variables decreases with time which causes an increase in susceptible individuals. This implies that avoiding contact with infected individuals by means of adequate awareness of social distancing and wearing face mask are vital to prevent or reduce the spread of COVID-19 infection.

A reliable numerical analysis for stochastic gonorrhea epidemic model with treatment effect

2019 ◽  
Vol 12 (06) ◽  
pp. 1950072 ◽  
Author(s):  
Ali Raza ◽  
Muhammad Shoaib Arif ◽  
Muhammad Rafiq
Keyword(s):  
Treatment Effect ◽  
Epidemic Model ◽  
Numerical Scheme ◽  
Deterministic Model ◽  
Basic Reproductive Number ◽  
Disease Spread ◽  
Reproductive Number ◽  
Step Size ◽  
Realistic Approach ◽  
Stochastic Setting

The phenomena of disease spread are unpredictable in nature due to random mixing of individuals in a population. It is of more significance to include this randomness while modeling infectious diseases. Modeling epidemics including their stochastic behavior could be a more realistic approach in many situations. In this paper, a stochastic gonorrhea epidemic model with treatment effect has been analyzed numerically. Numerical solution of stochastic model is presented in comparison with its deterministic part. The dynamics of the gonorrhea disease is governed by a threshold quantity [Formula: see text] called basic reproductive number. If [Formula: see text], then disease eventually dies out while [Formula: see text] shows the persistence of disease in population. The standard numerical schemes like Euler Maruyama, stochastic Euler and stochastic Runge–Kutta are highly dependent on step size and do not behave well in certain scenarios. A competitive non-standard finite difference numerical scheme in stochastic setting is proposed, which is independent of step size and remains consistent with the corresponding deterministic model.

scholarly journals Dynamics of Tuberculosis (TB) with Drug Resistance to First-Line Treatment and Leaky Vaccination: A Deterministic Modelling Perspective

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dominic Otoo ◽  
Shaibu Osman ◽  
Stephen Atta Poku ◽  
Elvis Kobina Donkoh
Keyword(s):  
Drug Resistance ◽  
Deterministic Model ◽  
Control Measure ◽  
Equilibrium Points ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
First Line ◽  
Susceptible Population ◽  
Deterministic Modelling

A deterministic model was formulated and employed in the analysis of the dynamics of tuberculosis with a keen emphasis on vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, part of the infected individual after treatment grows resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the next-generation matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity R 0 < 1 , then the disease free equilibrium is stable and unstable if R 0 > 1 . Furthermore, we investigated the optimal prevention, treatment, and vaccination as control measures for the disease. As the objective functional was optimised, there have been a significant reduction in the number of infections and an increase in the number of recovery. The best control measure in combating tuberculosis infections is prevention and vaccination of the susceptible population.

scholarly journals Effect of specific non-pharmaceutical intervention policies on SARS-CoV-2 transmission in the counties of the United States

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bingyi Yang ◽  
Angkana T. Huang ◽  
Bernardo Garcia-Carreras ◽  
William E. Hart ◽  
Andrea Staid ◽  
...  
Keyword(s):  
United States ◽  
Home Visiting ◽  
Leisure Activities ◽  
The United States ◽  
Causal Effects ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
County Level ◽  
Metapopulation Model ◽  
Pharmaceutical Interventions

AbstractNon-pharmaceutical interventions (NPIs) remain the only widely available tool for controlling the ongoing SARS-CoV-2 pandemic. We estimated weekly values of the effective basic reproductive number (Reff) using a mechanistic metapopulation model and associated these with county-level characteristics and NPIs in the United States (US). Interventions that included school and leisure activities closure and nursing home visiting bans were all associated with a median Reff below 1 when combined with either stay at home orders (median Reff 0.97, 95% confidence interval (CI) 0.58–1.39) or face masks (median Reff 0.97, 95% CI 0.58–1.39). While direct causal effects of interventions remain unclear, our results suggest that relaxation of some NPIs will need to be counterbalanced by continuation and/or implementation of others.

scholarly journals Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

scholarly journals Global Stability of an SEIS Epidemic Model with General Saturation Incidence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hui Zhang ◽  
Li Yingqi ◽  
Wenxiong Xu
Keyword(s):  
Latent Period ◽  
Epidemic Model ◽  
Convergence Theorem ◽  
Incidence Rates ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable in T by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in T0, and the disease spreads to be endemic.

THE DYNAMICS OF THE CONSTANT AND PULSE BIRTH IN AN SIR EPIDEMIC MODEL WITH CONSTANT RECRUITMENT

2007 ◽  
Vol 15 (02) ◽  
pp. 203-218 ◽  
Author(s):  
WENJUN CAO ◽  
ZHEN JIN
Keyword(s):  
Epidemic Model ◽  
Disease Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Free Solution ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stable Period ◽  
Number Formula ◽  
Globally Stable

In this paper, an SIR epidemic model with constant recruitment is considered. The dynamic behavior of this disease model with constant and pulse birth are analyzed. With constant birth, the infection-free equilibrium is locally and globally stable when the basic reproductive number R0 < 1. However, with pulse birth the system converges to a stable period solution with the number of infectious individuals equal to zero. Furthermore, the local and global stability of the periodic infection-free solution is obtained if the basic reproductive number [Formula: see text]. Numerical simulation shows that the periodic infection-free solution is unstable and the disease will persist when [Formula: see text]. The effectiveness of the constant and pulse birth to eliminating the disease are compared.

COMPLEXITY AND ASYMPTOTICAL BEHAVIOR OF A SIRS EPIDEMIC MODEL WITH PROPORTIONAL IMPULSIVE VACCINATION

2005 ◽  
Vol 08 (04) ◽  
pp. 419-431 ◽  
Author(s):  
GUANG-ZHAO ZENG ◽  
LAN-SUN CHEN
Keyword(s):  
Epidemic Model ◽  
Impulsive Control ◽  
Periodic Oscillation ◽  
The Other ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sirs Epidemic Model ◽  
Other Hand ◽  
Ratio Dependent ◽  
Impulsive Vaccination

This paper considers an SIRS epidemic model with proportional impulsive vaccination, which may inherently oscillate. We study the ratio-dependent impulsive control and obtain the conditions about the basic reproductive number for which the epidemic-elimination solution is globally asymptotic. On the other hand, if the epidemic turns out to be endemic, we study numerically the influences of impulsive vaccination on the periodic oscillation of a system without impulsion and find sophisticated phenomena such as chaos in this case.

scholarly journals Significant Relaxation of SARS-CoV-2-Targeted Non-Pharmaceutical Interventions Will Result in Profound Mortality: A New York State Modelling Study

2020 ◽  
Author(s):  
Benjamin U. Hoffman
Keyword(s):  
New York ◽  
Severe Acute Respiratory Syndrome ◽  
Global Health ◽  
New York State ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Effective Vaccine ◽  
Health Crisis ◽  
York State ◽  
Pharmaceutical Interventions

AbstractSevere acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) is the most significant global health crisis of the 21st century. The aim of this study was to develop a model to estimate the effect of undocumented infections, seasonal infectivity, immunity, and non-pharmaceutical interventions (NPIs), such as social distancing, on the transmission, morbidity, and mortality of SARS-CoV-2 in New York State (NYS). Simulations revealed dramatic infectivity driven by undocumented infections, and a peak basic reproductive number in NYS of 5.7. NPIs have been effective, and relaxation >50% will result in tens-of-thousands more deaths. Endemic infection is likely to occur in the absence of profound sustained immunity. As a result, until an effective vaccine or other effective pharmaceutical intervention is developed, it will be critical to not reduce NPIs >50% below current levels. This study establishes fundamental characteristics of SARS-CoV-2 transmission, which can help policymakers navigate combating this virus in the coming years.

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