Cost-Effectiveness Analysis of Nonpharmaceutical Interventions Combined with Inactivated Vaccination and Oral Medicine in China

Objectives: Various interventions were used to control the COVID-19 pandemic and protect population health, including vaccination, medication and nonpharmaceutical interventions (NPIs). This study aims to examine the cost-effectiveness of different combinations of NPIs (including social distancing, mask wearing, tracing-testing-isolation, mass testing, and lockdown), oral medicine (Paxlovid), and vaccination (including two-dose and three-dose vaccination) under the Delta and Omicron pandemic in China. Method(s): We constructed a Markov model using a SIRI structure with a one-week cycle length over one-year time horizon to estimate the cost-effectiveness of different combinations in China from societal perspective. Effectiveness of interventions, disease transition probabilities and costs were from published data, quality-adjusted life years (QALYs) gained and incremental cost-effectiveness ratios (ICER) and net monetary benefits were calculated for one-year time horizon. One-way and probabilistic sensitivity analyses were performed to test the robustness of the model. Scenario analysis was developed to examine different situations under the Omicron pandemic. Result(s): Under the Delta pandemic, implementing the combination of social distancing, mask wearing, mass testing and three-dose vaccination was the optimal strategy, with cost at $11165635.33 and utility of 94309.94 QALYs, and had 60% probability of being cost-effective compared with other strategies. Three-dose vaccination combinations were better than two-dose combinations. Under the Omicron pandemic, antigen testing was better than nucleic testing by avoiding cross infections;second, adding Paxlovid or lockdown to the combined intervention strategies could increase limited health outcomes at huge cost and thus were not cost-effective;last, encouraging patients to stay at home can save societal costs compared with concentrated quarantine at hospitals. Conclusion(s): Three-dose vaccination and self-quarantine of asymptomatic and mild cases can save total costs. Under the Omicron pandemic outbreak, antigen testing is a better way to control the pandemic, and adding Paxlovid or lockdown to intervention combinations is not cost-effective.Copyright © 2023

Bayesian Markov Chain Monte Carlo for reparameterized Stochastic volatility models using Asian FX rates during Covid-19.

In this paper, reparameterization and student-t are applied to Stochastic Volatility (SV) model. We aim to reduce the amount of autocorrelation of the SV parameters and to introduce heavy-tailed model via the Bayesian computation of the Markov Chain Monte Carlo (MCMC) samplers. This research paper helps support better MCMC estimation of the SV model for volatile Asian FX series during Covid-19.

Coupling Random Forest, Allometric Scaling, and Cellular Automata to Predict the Evolution of LULC under Various Shared Socioeconomic Pathways

Accurately estimating land-use demand is essential for urban models to predict the evolution of urban spatial morphology. Due to the uncertainties inherent in socioeconomic development, the accurate forecasting of urban land-use demand remains a daunting challenge. The present study proposes a modeling framework to determine the scaling relationship between the population and urban area and simulates the spatiotemporal dynamics of land use and land cover (LULC). An allometric scaling (AS) law and a Markov (MK) chain are used to predict variations in LULC. Random forest (RF) and cellular automata (CA) serve to calibrate the transition rules of change in LULC and realize its micro-spatial allocation (MKCA(RF-AS)). Furthermore, this research uses several shared socioeconomic pathways (SSPs) as scenario storylines. The MKCA(RF-AS) model is used to predict changes in LULC under various SSP scenarios in Jinjiang City, China, from 2020 to 2065. The results show that the figure of merit (FoM) and the urban FoM of the MKCA(RF-AS) model improve by 3.72% and 4.06%, respectively, compared with the MKCA(ANN) model during the 2005-2010 simulation period. For a 6.28% discrepancy between the predicted urban land-use demand and the actual urban land-use demand over the period 2005-2010, the urban FoM degrades by 21.42%. The growth of the permanent urban population and urban area in Jinjiang City follows an allometric scaling law with an exponent of 0.933 for the period 2005-2020, and the relative residual and R-2 are 0.0076 and 0.9994, respectively. From 2020 to 2065, the urban land demand estimated by the Markov model is 19.4% greater than the urban area predicted under scenario SSP5. At the township scale, the different SSP scenarios produce significantly different spatial distributions of urban expansion rates. By coupling random forest and allometric scaling, the MKCA(RF-AS) model substantially improves the simulation of urban land use.

Exploring the role of superspreading events in SARS-CoV-2 outbreaks.

The novel coronavirus SARS-CoV-2 emerged in 2019 and subsequently spread throughout the world, causing over 600 million cases and 6 million deaths as of September 7th, 2022. Superspreading events (SSEs), defined here as public or social events that result in multiple infections over a short time span, have contributed to SARS-CoV-2 spread. In this work, we compare the dynamics of SSE-dominated SARS-CoV-2 outbreaks, defined here as outbreaks with relatively higher SSE rates, to the dynamics of non-SSE-dominated SARS-CoV-2 outbreaks. To accomplish this, we derive a continuous-time Markov chain (CTMC) SARS-CoV-2 model from an ordinary differential equation (ODE) SARS-CoV-2 model and incorporate SSEs using an events-based framework. We simulate our model under multiple scenarios using Gillespie's direct algorithm. The first scenario excludes hospitalization and quarantine; the second scenario includes hospitalization, quarantine, premature hospital discharge, and quarantine violation; and the third scenario includes hospitalization and quarantine but excludes premature hospital discharge and quarantine violation. We also vary quarantine violation rates. Results indicate that, with either no control or imperfect control, SSE-dominated outbreaks are more variable but less severe than non-SSE-dominated outbreaks, though the most severe SSE-dominated outbreaks are more severe than the most severe non-SSE-dominated outbreaks. We measure severity by the time it takes for 50 active infections to be achieved; more severe outbreaks do so more quickly. SSE-dominated outbreaks are also more sensitive to control measures, with premature hospital discharge and quarantine violation substantially reducing control measure effectiveness.

Fixed-length interval estimation of population sizes: sequential adaptive Monte Carlo mark–recapture–mark sampling

Mark–recapture sampling schemes are conventional approaches for population size (N) estimation. In this paper, we mainly focus on providing fixed-length confidence interval estimation methodologies for N under a mark–recapture–mark sampling scheme, where, during the resampling phase, non-marked items are marked before they are released back in the population. Using a Monte Carlo method, the interval estimates for N are obtained through a purely sequential procedure with an adaptive stopping rule. Such an adaptive decision criterion enables the user to "learn” with the subsequent marked and newly tagged items. The method is then compared with a recently developed accelerated sequential procedure in terms of coverage probability and expected number of captured items during the resampling stage. To illustrate, we explain how the proposed procedure could be applied to estimate the number of infected COVID-19 individuals in a near-closed population. In addition, we present a numeric application inspired on the problem of estimating the population size of endangered monkeys of the Atlantic forest in Brazil.

Hierarchical Bayesian hedonic regression analysis of Japanese rice wine: is the price right?

PurposeThis paper aims to formulate a hedonic pricing model for Japanese rice wine, sake, via hierarchical Bayesian modeling estimated using an efficient Markov chain Monte Carlo (MCMC) method. Using the estimated model, the authors examine how producing regions, rice breeds and taste characteristics affect sake prices.Design/methodology/approachThe datasets in the estimation consist of cross-sectional observations of 403 sake brands, which include sake prices, taste indicators, premium categories, rice breeds and regional dummy variables. Data were retrieved from Rakuten, Japan's largest online shopping site. The authors used the Bayesian estimation of the hedonic pricing model and used an ancillarity–sufficiency interweaving strategy to improve the sampling efficiency of MCMC.FindingsThe estimation results indicate that Japanese consumers value sweeter sake more, and the price of sake reflects the cost of rice preprocessing only for the most-expensive category of sake. No distinctive differences were identified among rice breeds or producing regions in the hedonic pricing model.Originality/valueTo the best of the authors' knowledge, this study is the first to estimate a hedonic pricing model of sake, despite the rich literature on alcoholic beverages. The findings may contribute new insights into consumer preference and proper pricing for sake breweries and distributors venturing into the e-commerce market.

Health and Economic Impacts of Lockdown Policies in the Early Stage of COVID-19 in the United States

Lockdown policies, such as stay-at-home orders, are known to be effective in controlling the spread of the novel coronavirus disease 2019. However, concerns over eco-nomic burdens of these policies rapidly propelled U.S. states to move toward reopening in the early stage of the pandemic. Decision making in most states has been challenging, espe-cially because of a dearth of quantitative evidence on health gains versus economic bur-dens of different policies. To assist decision makers, we study the health and economic impacts of various lockdown policies across U.S. states and shed light on policies that are most effective. To this end, we make use of detailed data from 50 U.S. states plus the Dis-trict of Columbia on various factors, including number of tests, positive and negative results, hospitalizations, ICU beds and ventilators used, residents' mobility obtained from cellphone data, and deaths. Our analyses allow quantifying the total cost versus the total quality-adjusted life year (QALY) associated with various lockdown policies. We utilize a compartmental model with Markov chain Monte Carlo simulation to estimate the spread of disease. To calibrate our model separately for each U.S. state, we make use of empirical data on the intensity of intervention policies, age, ratio of Black/Hispanic populations, per capita income, residents' mobility, and number of daily tests and feed them to a longitudi-nal mixed-effect model. Finally, we utilize a microsimulation model to estimate the total cost and total QALY for each state and perform cost-effectiveness analysis to identify poli-cies that would have worked best. Our results show that, compared with no intervention during March-June 2020, the policies undertaken across the United States saved, on aver-age, about 41,284.51 years' worth of QALY (per 100K capita), incurring $164.01 million (per 100K capita). Had the states undertaken more strict policies during the same time frame than those they adopted, these values would be 44,909.41 years and $117.28 million, respec-tively. By quantifying the impact of various lockdown policies separately for each state, our results allow federal and state authorities to avoid following a "one size fits all" strat-egy and instead enact policies that are better suited for each state. Specifically, by studying the trade-offs between health gains and economic impacts, we identify the particular states that would have benefited from implementing more restrictive policies. Finally, in addition to shedding light on the impact of lockdown policies during our study period (March-June 2020), our results have important implications on curbing future fast-spreading variants of the coronavirus or other related potential epidemics.

Probabilistic analysis of COVID-19 transmission in Kenya using Markov chain

Since the outbreak of the COVID-19 pandemic, many countries have continued to suffer economically due to trade losses. COVID-19 has evolved into different forms and hence became a problem to analyze its transmission. As a result of increased COVID-19 infections, there has been a scarcity of resources like hospital facilities, quarantine centers, and personal protective equipment (PPEs) for the medics. Therefore, accurate planning has to be made by the government of Kenya to ensure that resources are made available to combat the rising COVID-19 cases. To ensure effective future planning for the COVID-19 pandemic, proper analysis of the COVID-19 pandemic among the population is key. Therefore, this study will go a long way in providing insights on how to plan for the Kenyan population through probabilistic analysis of the COVID-19 pandemic using the Markov chain. The study used Secondary Cumulative data from the Kenya ministry of health for a period between 1st June 2021 and 1st May 2022. The data was analyzed using a steady-state Markov chain in which the transition probability matrix for the COVID-19 pandemic was computed. The number of individuals infected by the COVID-19 virus and who recovered at the end of the study period was set at zero since COVID-19 disease is not curable. The results were presented in the table and reported at a 95% confidence level. Based on the findings, the study concluded that a steady-state Markov chain is beneficial in simulating the coronavirus infection in numerous stages. Also, it is noted that the use of the steady-state Markov chain model allows for capturing short and long-term memory effects that greatly improve the estimation of the number of new cases of COVID-19 and indicate whether the disease has an upward/downward trend. © 2022 The Authors.

Forecasting of Indonesian Digital Economy based on Available New Start-up

Since the last 5 years, digital economy is growing steadily in Indonesia. Right now, the digital economy faces some potential problems and Covid-19 pandemic. This paper presents current data of the national Gross Domestic Product (GDP) and other GDPs (billion IDR) and the number of start-up, and predicts near some categories of future GDP and numbers of available new start-up for the next few years. The forecast will use Markov chain analysis. The results indicate that, while there are problems faced by the digital economy industry, the GDP and numbers of start-up are significantly increasing.

Does climate change affect the transmission of COVID-19? A Bayesian regression analysis.

Aim: Coronavirus is an airborne and infectious disease and it is crucial to check the impact of climatic risk factors on the transmission of COVID-19. The main objective of this study is to determine the effect of climate risk factors using Bayesian regression analysis. Methods: Coronavirus disease 2019, due to the effect of the SARS-CoV-2 virus, has become a serious global public health issue. This disease was identified in Bangladesh on March 8, 2020, though it was initially identified in Wuhan, China. This disease is rapidly transmitted in Bangladesh due to the high population density and complex health policy setting. To meet our goal, The MCMC with Gibbs sampling is used to draw Bayesian inference, which is implemented in WinBUGS software. Results: The study revealed that high temperatures reduce confirmed cases and deaths from COVID-19, but low temperatures increase confirmed cases and deaths. High temperatures have decreased the proliferation of COVID-19, reducing the virus's survival and transmission. Conclusions: Considering only the existing scientific evidence, warm and wet climates seem to reduce the spread of COVID-19. However, more climate variables could account for explaining most of the variability in infectious disease transmission.

Covid19 Reproduction Number: Credibility Intervals by Blockwise Proximal Monte Carlo Samplers

Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries. IEEE

CAUSES OF DEATH IN TURKEY: HOW THE INCREASE IN THE BURDEN OF COMMUNICABLE DISEASES VARY BY SEX AND AGE?

Causes of death statistics are essential tools for public health, but Turkey lags in the number of studies on causes and trends of death. This study measures causes and trends of death in Turkey for the 2013-2019 period, with special emphasis on the increase in communicable diseases (CDs). This study has a representative research design based on the national population and cause of death registration systems. Causes of death with International Classification of Diseases, Tenth Revision (ICD-10) codes were grouped and garbage codes were determined and redistributed. To understand how the increase in the burden of CDs vary by sex and age, modal age at death, age-specific death rates, probability of eventual death, years of life lost (YLL) due to three main causes of death were calculated by using discrete absorbing Markov chain model. According to results, modal age at death among male population shifted to older ages, the share of respiratory infectious diseases and other infectious and parasitic diseases increased rapidly between 2013 and 2019, just before the onset of COVID-19 pandemic. Overall, our results suggest that burden of CDs increased for both sexes, and elderly male population was among the most effected group. Since non-communicable diseases were still the leading causes of death, increasing rate of CDs may create an extra burden on health system.Alternate abstract: Ölüm nedeni istatistikleri, halk sağlığı için çok önemli araçlardır, ancak Türkiye ölüm nedenleri ve eğilimlerine ilişkin yapılan çalışmalarda geride kalmaktadır. Bu çalışma, bulaşıcı hastalıklardaki (BH'lerdeki) artışa özel bir vurgu yaparak, 2013-2019 döneminde Türkiye'deki ölüm nedenlerini ve eğilimlerini değerlendirmektedir. Çalışma, ulusal nüfus ve ölüm nedeni kayıt sistemlerine dayalı temsili araştırma tasarımına sahiptir. Uluslararası Hastalık Sınıflandırması Onuncu Revizyon (UHS-10) kodlarına sahip tüm ölüm nedenleri gruplandırılmış ve çöp kodlar belirlenerek ölüm nedenleri içinde yeniden dağıtılmıştır. BH yükündeki artışın cinsiyete ve yaşa göre nasıl değiştiğini anlamak için ayrık Markov zinciri modellemesi kullanılmış ve en fazla ölümün meydana geldiği yaş, üç ana ölüm nedenine göre yaşa özel ölüm oranları, ölüm olasılıkları ve kaybedilen yaşam yılları hesaplanmıştır. Çalışmanın sonuçlarına göre, erkek nüfusta en fazla ölümün meydana geldiği yaş daha ileri yaşlara kaymış;her iki cinsiyette de 2013-2019 yılları arasında- COVID-19 pandemisinin başlamasından hemen önce- solunum yolu enfeksiyon hastalıkları ile diğer bulaşıcı ve parazit hastalıkların payı hızla artmıştır. Genel olarak, sonuçlarımız her iki cinsiyet için de BH yükünün arttığını ve yaşlı erkek nüfusunun en çok etkilenen grup arasında olduğunu göstermektedir. Bulaşıcı olmayan hastalıklar hala önde gelen ölüm nedenleri olduğundan, artan BH oranları sağlık sistemi üzerinde fazladan bir yük oluşturabilir.

Trust based COVID-19 vaccine distribution using blockchain technology

The COVID-19 outbreak has impacted huge number of individuals all around the world and has caused a great economic loss all over the world. Vaccination is most effective solution to prevent this disease. It helps in protecting the whole community. It improves the human immune system and fights against corona virus reducing the death rate. This paper deals with the different types of COVID-19 vaccine and their related distribution, it includes measures to ensure safe and secured distribution of the vaccine through block chain technology with the help of supply chain. Any malfunction in the chain is identified by the trust value of the function point method and the value of the Markov Chain. © 2023 - IOS Press. All rights reserved.

Modeling for Implications of COVID-19 Pandemic on Healthcare System in India

The COVID-19 pandemic has affected the global healthcare system in many countries. India has faced complex multidimensional problems concerning the healthcare system during the COVID-19 outbreak. This article explores some of the implications of COVID-19 on the health system. Also, we attempt to study health economics and other related issues. We have developed the susceptible-exposed-infection-recovered model, logistic growth model, time interrupted regression model, and a stochastic approach for these problems. These models focus on the effect of prevention measures and other interventions for a pandemic on the healthcare system. Our study suggests that the above models are appropriate for COVID-19 at break and effective models for the implications of the pandemic on the healthcare system. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Monitoring of SARS-CoV-2 RNA in wastewater: A surveillance tool to foresee infection's evolution in the Mexican Caribbean.

The study aims to determine SARS-CoV-2 RNA in sewage of Cancun wastewater treatment plants, the main touristic destination of Mexico, and to estimate the infected persons during the sampling period. SARS-CoV-2 RNA traces were detected in the inlet of the five plants during almost all the sampling months. However, there is no presence of SARS-CoV-2 RNA traces in the effluent of the five WWTPs during the study period. ANOVA analysis showed differences in the concentrations of RNA traces of SARS-CoV-2 between the sample dates, but no differences were found from one WWTP to another. Estimated infected individuals by Markov chain Monte Carlo simulation are higher (between 77% and 91%) than the cases reported by the health authority. Wastewater monitoring and the estimation of infected individuals are a helpful tool, because estimation provides early warning signs on how broadly SARS-CoV-2 is circulating in the city, and led to the authorities to take measures wisely. PRACTITIONER POINTS: There is no presence of SARS-CoV-2 RNA traces in the effluent of the facilities, suggesting the effectiveness of treatment. Surveillance of viral RNA concentrations at treatment plants revealed presence in the influent of five plants Estimated infected individuals by MCMC simulation are higher than cases reported by health authority Environmental surveillance approach in wastewater influent is helpful to identify the clusters and to take informed decisions.

Impact and mitigation of sampling bias to determine viral spread: Evaluating discrete phylogeography through CTMC modeling and structured coalescent model approximations.

Bayesian phylogeographic inference is a powerful tool in molecular epidemiological studies, which enables reconstruction of the origin and subsequent geographic spread of pathogens. Such inference is, however, potentially affected by geographic sampling bias. Here, we investigated the impact of sampling bias on the spatiotemporal reconstruction of viral epidemics using Bayesian discrete phylogeographic models and explored different operational strategies to mitigate this impact. We considered the continuous-time Markov chain (CTMC) model and two structured coalescent approximations (Bayesian structured coalescent approximation [BASTA] and marginal approximation of the structured coalescent [MASCOT]). For each approach, we compared the estimated and simulated spatiotemporal histories in biased and unbiased conditions based on the simulated epidemics of rabies virus (RABV) in dogs in Morocco. While the reconstructed spatiotemporal histories were impacted by sampling bias for the three approaches, BASTA and MASCOT reconstructions were also biased when employing unbiased samples. Increasing the number of analyzed genomes led to more robust estimates at low sampling bias for the CTMC model. Alternative sampling strategies that maximize the spatiotemporal coverage greatly improved the inference at intermediate sampling bias for the CTMC model, and to a lesser extent, for BASTA and MASCOT. In contrast, allowing for time-varying population sizes in MASCOT resulted in robust inference. We further applied these approaches to two empirical datasets: a RABV dataset from the Philippines and a SARS-CoV-2 dataset describing its early spread across the world. In conclusion, sampling biases are ubiquitous in phylogeographic analyses but may be accommodated by increasing the sample size, balancing spatial and temporal composition in the samples, and informing structured coalescent models with reliable case count data.

The coevolution of the spread of a disease and competing opinions in multiplex networks.

The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion.

Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body's immune system are affected by the disease. In this study, the SVEIHR deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number (R0). Detailed stability analysis of the no-disease equilibrium (E0) of the proposed model to observe the dynamics of the system was carried out and the results showed that E0 is stable if R0<1 and unstable when R0>1. The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of R0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our SVEIHR model, the results showed that R0=0.208, which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, R0=1.7214, which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community. © 2022 The Authors

Pathogen diversity in meta-population networks

The pathogen diversity means that multiple strains coexist, and widely exist in the biology systems. The new mutation of SARS-CoV-2 leading to worldwide pathogen diversity is a typical example. What are the main factors of inducing the pathogen diversity? Previous studies indicated the pathogen mutation is the most important reason for inducing the pathogen diversity. The traffic network and gene network are crucial in shaping the dynamics of pathogen contagion, while their roles for the pathogen diversity still lacking a theoretical study. To this end, we propose a reaction–diffusion process of pathogens with mutations on meta-population networks, which includes population movement and strain mutation. We extend the Microscopic Markov Chain Approach (MMCA) to describe the model. Traffic networks make pathogen diversity more likely to occur in cities with lower infection densities. The likelihood of pathogen diversity is low in cities with short effective distances in the traffic network. Star-type gene network is more likely to lead to pathogen diversity than lattice-type and chain-type gene networks. When pathogen localization is present, infection is localized to strains that are at the endpoints of the gene network. Both the increased probability of movement and mutation promote pathogen diversity. The results also show that the population tends to move to cities with short effective distances, resulting in the infection density is high. © 2022 Elsevier Ltd

Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications. © 2022 Elsevier Ltd