MODEL MATEMATIKA PENYEBARAN PENYAKIT PULMONARY TUBERCULOSIS DENGAN PENGGUNAAN MASKER MEDIS

This research developed a model of tuberculosis disease spread using the SIR model with addition of the medical mask usage factor. First, we create a diagram of the tuberculosis disease spread compartment through contact between individuals with medical mask usage. After that, we construct a system of nonlinear differential equations  based on the compartment diagram and then find the disease-free equilibrium point, the endemic equilibrium point, and the initial reproduction number . We use linearization to analyze of the disease-free equilibrium point. The disease-free equilibrium point obtained is asymptotically stable at .  The simulation result shows that the value of  . It means that tuberculosis disease in the future will disappear. But if we reduce the value of medical mask usage and increase the value of tuberculosis disease spread, the value . It means that tuberculosis diseases can become an outbreak

Continuous Time Individual-Level Models of Infectious Disease: a Package EpiILMCT

This paper describes the R package EpiILMCT, which allows users to study the spread of infectious disease using continuous time individual level models (ILMs). The package provides tools for simulation from continuous time ILMs that are based on either spatial demographic, contact network, or a combination of both of them, and for the graphical summarization of epidemics. Model fitting is carried out within a Bayesian Markov Chain Monte Carlo (MCMC) framework. The continuous time ILMs can be implemented within either susceptible-infected-removed (SIR) or susceptible-infected-notified-removed (SINR) compartmental frameworks. As infectious disease data is often partially observed, data uncertainties in the form of missing infection times - and in some situations missing removal times - are accounted for using data augmentation techniques. The package is illustrated using both simulated and an experimental data set on the spread of the tomato spotted wilt virus (TSWV) disease

Exploring the role of spatial configuration and behavior on the spread of the epidemic: A study of factors that affect Covid-19 spreading in the city

This research explores how exterior public space - defined through the configuration of the city - and human behavior affect the spread of disease. In order to understand the virus spreading mechanism and influencing factors of the epidemic which accompany residents' movement, this study attempts to reproduce the process of virus spreading in city areas through computer simulation. The simulation can be divided into residents' movement simulation and the virus spreading simulation. First, the Agent-based model (ABM) can effectively simulate the behavior of the individual and crowd;real location data - uploaded by residents via mobile phone applications - is used as a behavioral driving force for the agent's movement. Second, a mathematical model of infectious diseases is constructed based on SIR (SEIR) Compartmental models in epidemiology. Finally, by analyzing the simulation results of the agent's movement in the city and the virus spreading under different conditions, the influence of multiple factors of city configuration and human behavior on the virus spreading process is explored, and the effectiveness of countermeasures such as social distancing and lockdown are further demonstrated

Simulating the Spread of Peste des Petits Ruminants in Kazakhstan Using the North American Animal Disease Spread Model

In this study, we simulated the potential spread of Peste des Petits Ruminants (PPR) between small ruminant (SR) farms in the Republic of Kazakhstan (RK) in case of the disease’s introduction into the country. The simulation was based on actual data on the location and population of SR farms in the RK using the North American Animal Disease Spread Model (NAADSM). The NAADSM employs the stochastic simulations of the between-farm disease spread predicated on the SIR compartmental epidemic model. The most important epidemiological indicators of PPR, demography of SR farms, and livestock management characteristics in the RK were used for model parameterization. This article considers several scenarios for the initial introduction of PPR into the territory of Kazakhstan, based on previously identified high-risk regions and varying sizes of initially infected farms. It is demonstrated that the duration and size of the outbreak do not depend on the size of initially infected farms but rather depend on the livestock concentration and number of farms in the affected area. This implies that the outbreak may affect the largest number of farms in the case of introduction of the disease into farms in southern Kazakhstan. However, even in the most unfavorable scenario, the total number of affected farms does not exceed 2.4% of all SR farms in the RK. The size of the affected area is, in most cases, no larger than an averaged 2-level administrative division’s size, which suggests the scale of a local epidemic. The chosen model provides ample opportunity to study the impact of different control and prevention measures on the spread of PPR as well as to assess the potential economic damage

Simulation Based Inference in Epidemic Models

From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, we consider stochastic versions of these models, and use two types of stochastic simulation algorithms to solve the models. The Gillespie algorithm is used for internal noise while the stochastic Euler algorithm is used for external noise. To improve our understanding of the dynamics, we employ statistical methods on the simulated data and compare with actual data. Treating the epidemic models as a partially observed Markov process (POMP) or hidden Markov model, we use inferential methods via particle filtering and iterated particle filtering to estimate the disease parameters. This simulation-based inference method is demonstrated using an example of influenza data obtained from an infection at an English boarding school

Individual Variation Affects Outbreak Magnitude and Predictability in an Extended Multi-Pathogen SIR Model of Pigeons Vising Dairy Farms

Zoonotic disease transmission between animals and humans is a growing risk and the agricultural context acts as a likely point of transition, with individual heterogeneity acting as an important contributor. Thus, understanding the dynamics of disease spread in the wildlife-livestock interface is crucial for mitigating these risks of transmission. Specifically, the interactions between pigeons and in-door cows at dairy farms can lead to significant disease transmission and economic losses for farmers; putting livestock, adjacent human populations, and other wildlife species at risk. In this paper, we propose a novel spatio-temporal multi-pathogen model with continuous spatial movement. The model expands on the Susceptible-Exposed-Infected-Recovered-Dead (SEIRD) framework and accounts for both within-species and cross-species transmission of pathogens, as well as the exploration-exploitation movement dynamics of pigeons, which play a critical role in the spread of infection agents. In addition to model formulation, we also implement it as an agent-based simulation approach and use empirical field data to investigate different biologically realistic scenarios, evaluating the effect of various parameters on the epidemic spread. Namely, in agreement with theoretical expectations, the model predicts that the heterogeneity of the pigeons' movement dynamics can drastically affect both the magnitude and stability of outbreaks. In addition, joint infection by multiple pathogens can have an interactive effect unobservable in single-pathogen SIR models, reflecting a non-intuitive inhibition of the outbreak. Our findings highlight the impact of heterogeneity in host behavior on their pathogens and allow realistic predictions of outbreak dynamics in the multi-pathogen wildlife-livestock interface with consequences to zoonotic diseases in various systems

No place like home: cross-national data analysis of the efficacy of social distancing during the COVID-19 pandemic

Background: In the absence of a cure in the time of a pandemic, social distancing measures seem to be the most effective intervention to slow the spread of disease. Various simulation-based studies have been conducted to investigate the effectiveness of these measures. While those studies unanimously confirm the mitigating effect of social distancing on disease spread, the reported effectiveness varies from 10% to more than 90% reduction in the number of infections. This level of uncertainty is mostly due to the complex dynamics of epidemics and their time-variant parameters. However, real transactional data can reduce uncertainty and provide a less noisy picture of the effectiveness of social distancing. Objective: The aim of this paper was to integrate multiple transactional data sets (GPS mobility data from Google and Apple as well as disease statistics from the European Centre for Disease Prevention and Control) to study the role of social distancing policies in 26 countries and analyze the transmission rate of the coronavirus disease (COVID-19) pandemic over the course of 5 weeks. Methods: Relying on the susceptible-infected-recovered (SIR) model and official COVID-19 reports, we first calculated the weekly transmission rate (β) of COVID-19 in 26 countries for 5 consecutive weeks. Then, we integrated these data with the Google and Apple mobility data sets for the same time frame and used a machine learning approach to investigate the relationship between the mobility factors and β values. Results: Gradient boosted trees regression analysis showed that changes in mobility patterns resulting from social distancing policies explain approximately 47% of the variation in the disease transmission rates. Conclusions: Consistent with simulation-based studies, real cross-national transactional data confirms the effectiveness of social distancing interventions in slowing the spread of COVID-19. In addition to providing less noisy and more generalizable support for the idea of social distancing, we provide specific insights for public health policy makers regarding locations that should be given higher priority for enforcing social distancing measures

Mathematical Modeling of Trending Topics on Twitter

Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses information spread, presents case studies pertaining to the prevalence of several “trending” topics on Twitter over time. The study introduces a framework to compare information dynamics on Twitter based on the topical area as well as a framework for the prediction of topic prevalence. Additionally, methodological and results-based comparisons are drawn between the spread of information and the spread of infectious disease

A class of pairwise models for epidemic dynamics on weighted networks

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both models start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with network simulation to evaluate the impact of different weight distributions on epidemic threshold and dynamics in general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is computed, and we show that (i) for both network models $R_{0}$ is maximised if all weights are equal, and (ii) when the two models are equally matched, the networks with a random weight distribution give rise to a higher $R_0$ value. The models are also used to explore the agreement between the pairwise and simulation models for different parameter combinations