Effective Reproduction Number Research Articles

Construction of effective reproduction number of infectious disease individuals based on spatiotemporal discriminant search model: take hand-foot-mouth disease as an example

ObjectiveIn order to facilitate the tracing of infectious diseases in a small area and to effectively carry out disease control and epidemiological investigations, this research proposes a novel spatiotemporal model to estimate effective reproduction number(Re)for infectious diseases, based on the fundamental concept of contact tracing.MethodsThis study utilizes the incidence of hand, foot, and mouth disease (HFMD) among children in Bishan District, Chongqing, China from 2015 to 2019. The study incorporates the epidemiological characteristics of HFMD and aims to construct a Spatiotemporal Correlation Discrimination of HFMD. Utilizing ARC ENGINE and C# programming for the creation of a spatio-temporal database dedicated to HFMD to facilitate data collection and analysis. The scientific validity of the proposed method was verified by comparing the effective reproduction number obtained by the traditional SEIR model.ResultsWe have ascertained the optimal search radius for the spatiotemporal search model to be 1.5 km. Upon analyzing the resulting Re values, which range from 1.14 to 4.75, we observe a skewed distribution pattern from 2015 to 2019. The median and quartile Re value recorded is 2.42 (1.98, 2.72). Except for 2018, the similarity coefficient r of the years 2015, 2016, 2017, and 2019 were all close to 1, and p <0.05 in the comparison of the two models, indicating that the Re values obtained by using the search model and the traditional SEIR model are correlated and closely related. The results exhibited similarity between the Re curves of both models and the epidemiological characteristics of HFMD. Finally, we illustrated the regional distribution of Re values obtained by the search model at various time intervals on Geographic Information System (GIS) maps which highlighted variations in the incidence of diseases across different communities, neighborhoods, and even smaller areas.ConclusionThe model comprehensively considers both temporal variation and spatial heterogeneity in disease transmission and accounts for each individual's distinct time of onset and spatial location. This proposed method differs significantly from existing mathematical models used for estimating Re in that it is founded on reasonable scientific assumptions and computer algorithms programming that take into account real-world spatiotemporal factors. It is particularly well-suited for estimating the Re of infectious diseases in relatively stable mobile populations within small geographical areas.

Effect of awareness and saturated treatment on the transmission of infectious diseases

Abstract In this article, we study the role of awareness and its impact on the control of infectious diseases. We analyze a susceptible-infected-recovered model with a media awareness compartment. We find the effective reproduction number R 0 {R}_{0} . We observe that our model exhibits transcritical forward bifurcation at R 0 = 1 {R}_{0}=1 . We also performed the sensitivity analysis to determine the sensitivity of parameters of the effective reproduction number R 0 {R}_{0} . In addition, we study the corresponding optimal control problem by considering control in media awareness and treatment. Our studies conclude that we can reduce the rate of spread of infection in the population by increasing the treatment rate along with media awareness.

Unraveling the importance of early awareness strategy on the dynamics of drug addiction using mathematical modeling approach.

A drug is any substance capable of altering the functioning of a person's body and mind. In this paper, a deterministic nonlinear model was adapted to investigate the behavior of drug abuse and addiction that incorporates intervention in the form of awareness and rehabilitation. In the mathematical analysis part, the positivity and boundedness of the solution and the existence of drug equilibria have been ascertained, which shows that the model consists of two equilibria: a drug-free equilibrium and a drug endemic equilibrium point. The drug-free equilibrium was found to be both globally and locally asymptotically stable if the effective reproduction number is less than or equal to one (Rc≤1). Furthermore, we were able to show the existence of a unique drug endemic equilibrium whenever Rc>1. Global asymptotic stability of a drug endemic equilibrium point has been ascertained using a nonlinear Lyapunov function of Go-Volterra type, which reveals that the drug endemic equilibrium point is globally asymptotically stable if an effective reproduction number is greater than unity and if there is an absence of a reversion rate of mended individuals (i.e., ω=0). In addition, an optimal control problem was formulated to investigate the optimal strategy for curtailing the spread of the behavior using control variables. The control variables are massive awareness and rehabilitation intervention of both public and secret addicted individuals. The optimal control simulation shows that massive awareness control is the best to control drug addiction in a society. In sensitivity analysis section, the proportion of those who are exposed publicly shows to be a must sensitive parameter that can reduce the reproduction number, and the effective contact rate shows to be a must sensitive parameter to increase the reproduction number. Numerical simulations reveal that the awareness rate of exposed publicly and the rehabilitation rate of addicted publicly are very important parameters to control drug addiction in a society.

Effective Reproduction Number of Smear-Positive Pulmonary Tuberculosis in Iran: A Registry-Based Study (2011-2021).

Tuberculosis (TB) remains a major public health issue in Iran, especially smear-positive pulmonary tuberculosis (SPPTB), due to its high transmission rate. Examining the effective reproduction number(Rt ) of SPPTB and patient characteristics is crucial for crafting targeted TB control measures. This study aimed to assess the Rt of SPPTB in Iran from 2011 to 2021 and profile SPPTB patient demographics, initial smear bacilli density, diagnosis delays, and spatial distribution. Study Design: This is a historical cohort study. A time-dependent method was used to estimate Rt , and monthly data from the national TB registry were scrutinized from 2011 to 2021. A decline was observed in SPPTB incidence rates of 50909 SPPTB cases in Iran from 2011 to 2021. Approximately 29.1% of the cases were diagnosed within a month, while 44.5% experienced a one to three-month delay in diagnosis. The analysis revealed substantial heterogeneity in TB transmission dynamics across various provinces of Iran. Provinces such as Sistan and Baluchestan, Golestan, Guilan, Khuzestan, Tehran, and Khorasan Razavi exhibited the highest effective reproduction numbers. Additionally, there was a decreasing trend in the effective reproduction numbers across all provinces from 2011 to 2020. Effective reproduction numbers declined in most provinces from 2011 to 2020 but increased moderately after the COVID-19 pandemic, highlighting the need for targeted public health interventions. Although SPPTB incidence rates are declining nationally, elevated incidence rates and effective reproduction numbers in regions such as Sistan and Baluchestan, Golestan, Guilan, Khuzestan, Tehran, and Khorasan Razavi signify the need for persistent TB management efforts in Iran.

Using the near real-time effective reproduction number rt as an early-warning tool for seasonal bronchiolitis and influenza-like illness epidemics.

Yearly bronchiolitis and influenza-like illness epidemics in France often involve high morbidity and mortality, which severely impacts healthcare. Epidemics are declared by the French National Institute of Public Health based on syndromic surveillance of primary care and emergency departments (ED), using statistics-based alarms. Although the effective reproduction number (Rt) is used to monitor the dynamics of epidemics, it has never been used as an early warning tool for bronchiolitis or influenza-like illness epidemics in France.We assessed whether Rt is useful for detecting seasonal epidemics by comparing it to the tool currently used (MASS) by epidemiologists to declare epidemic phases. We used anonymized ED syndromic data from the Île-de-France region in France from 2010 to 2022. We estimated Rt and compared the indication of accelerated transmission (Rt >1) to the MASS epidemic alarm time points. We computed the difference between those two time points, time to epidemic peak, and the daily cases documented at first indication and peak. Rt provided alarms for influenza-like illness and bronchiolitis epidemics that were, respectively, 6 days (IQR[4;8]) and 64 days (IQR[52;80]) - in median - earlier than the alarms provided by MASS. Rt detected earlier signals of bronchiolitis and influenza-like illness epidemics. Using this early-warning indicator in combination with others to declare an annual epidemic could provide opportunities to improve healthcare system readiness.

Jointly estimating epidemiological dynamics of Covid-19 from case and wastewater data in Aotearoa New Zealand

BackgroundTimely and informed public health responses to infectious diseases such as COVID-19 necessitate reliable information about infection dynamics. The case ascertainment rate (CAR), the proportion of infections that are reported as cases, is typically much less than one and varies with testing practices and behaviours, making reported cases unreliable as the sole source of data. The concentration of viral RNA in wastewater samples provides an alternate measure of infection prevalence that is not affected by clinical testing, healthcare-seeking behaviour or access to care.MethodsWe construct a state-space model with observed data of levels of SARS-CoV-2 in wastewater and reported case incidence and estimate the hidden states of the effective reproduction number, R, and CAR using sequential Monte Carlo methods.ResultsWe analyse data from 1 January 2022 to 31 March 2023 from Aotearoa New Zealand. Our model estimates that R peaks at 2.76 (95% CrI 2.20, 3.83) around 18 February 2022 and the CAR peaks around 12 March 2022. We calculate that New Zealand’s second Omicron wave in July 2022 is similar in size to the first, despite fewer reported cases. We estimate that the CAR in the BA.5 Omicron wave in July 2022 is approximately 50% lower than in the BA.1/BA.2 Omicron wave in March 2022.ConclusionsEstimating R, CAR, and cumulative number of infections provides useful information for planning public health responses and understanding the state of immunity in the population. This model is a useful disease surveillance tool, improving situational awareness of infectious disease dynamics in real-time.

A mean field analysis of the role of indirect transmission in emergent infection events

We developed a mathematical model to investigate the role of indirect transmission in the spread of infectious diseases, using the illustrative example of sarcoptic mange as a case study. This disease can be transmitted through direct contact between an infected host and a susceptible one, or indirectly when potential hosts encounter infectious mites and larvae deposited in the environment, commonly referred to as fomites. Our focus is on exploring the potential of these infectious reservoirs as triggers for emerging infection events and as stable reservoirs of the disease. To achieve this, our mean field compartmental model incorporates the epidemiological dynamics driven by indirect transmission via fomites. We identify different types of dynamics that the system can go into, controlled by different levels of direct and indirect transmission. Among these, we find a new regime where the disease can emerge and persist over time solely through fomites, without the necessity for direct transmission. This possibility of the system reveals an evolutionary pathway that could enable the parasite to enhance its fitness beyond host co-evolution. We also define a new threshold based on an effective reproductive number, that enables us to predict the conditions for disease persistence. Our model allows us to assess the potential effectiveness of various disease intervention measures by incorporating a feature observed in real systems. We hope this contributes to a better understanding of infectious disease outbreaks.

Prevention and control of Ebola virus transmission: mathematical modelling and data fitting.

The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.

Modelling the Impact of Relapse and Weaning Off Immunity on Hepatitis B Virus Transmission Dynamics

In this study, we present a numerical simulation of the impact of relapse in patients with chronic HBV infection and weaning off immunity on vaccinated individuals within the transmission dynamics of Hepatitis B. The sensitivity analysis result establishes that relapse rate and weaning off immunity increase the value of the effective reproduction number when it is increased. Similarly, the result of the numerical simulation reveals that the combined effect of relapse and weaning off immunity increases the number of infected persons and thus, increases the spread of the Hepatitis B Virus. Also, relapse delays the quick response to the treatment regimen which consequently slows down the potential of recovery from the infection, whereas, weaning off immunity reduces the number of vaccinated individuals.

Semiparametric inference of effective reproduction number dynamics from wastewater pathogen surveillance data.

Concentrations of pathogen genomes measured in wastewater have recently become available as a new data source to use when modeling the spread of infectious diseases. One promising use for this data source is inference of the effective reproduction number, the average number of individuals a newly infected person will infect. We propose a model where new infections arrive according to a time-varying immigration rate which can be interpreted as an average number of secondary infections produced by one infectious individual per unit time. This model allows us to estimate the effective reproduction number from concentrations of pathogen genomes, while avoiding difficulty to verify assumptions about the dynamics of the susceptible population. As a byproduct of our primary goal, we also produce a new model for estimating the effective reproduction number from case data using the same framework. We test this modeling framework in an agent-based simulation study with a realistic data generating mechanism which accounts for the time-varying dynamics of pathogen shedding. Finally, we apply our new model to estimating the effective reproduction number of SARS-CoV-2, the causative agent of COVID-19, in Los Angeles, CA, using pathogen RNA concentrations collected from a large wastewater treatment facility.

The role of digital tools and emerging devices in COVID-19 contact tracing during the first 18 months of the pandemic: a systematic review.

Contact tracing is a public health intervention implemented in synergy with other preventive measures to curb epidemics, like the coronavirus pandemic. The development and use of digital devices have increased worldwide to enhance the contact tracing process. The aim of the study was to evaluate the effectiveness and impact of tracking coronavirus disease 2019 (COVID-19) patients using digital solutions. Observational studies on digital contact tracing (DCT), published 2020-21, in English were identified through a systematic literature review performed on nine online databases. An ad hoc form was used for data extraction of relevant information. Quality assessment of the included studies was performed with validated tools. A qualitative synthesis of the findings is reported. Over 8000 records were identified and 37 were included in the study: 24 modelling and 13 population-based studies. DCT improved the identification of close contacts of COVID-19 cases and reduced the effective reproduction number of COVID-19-related infections and deaths by over 60%. It impacted positively on societal and economic costs, in terms of lockdowns and use of resources, including staffing. Privacy and security issues were reported in 27 studies. DCT contributed to curbing the COVID-19 pandemic, especially with the high uptake rate of the devices and in combination with other public health measures, especially conventional contact tracing. The main barriers to the implementation of the devices are uptake rate, security and privacy issues. Public health digitalization and contact tracing are the keys to countries' emergency preparedness for future health crises.

Cost-effectiveness analysis of optimal control strategies on the transmission dynamics of HIV and Varicella-Zoster co-infection

HIV and Varicella-Zoster co-infection has been threatens the lives and livelihood of millions of individuals all over the world. In various nations of the world the co-infection disease is presently a major health problem. Although, various researchers carried out studies related with HIV and Zoster single infections, no one has carried out a study on the co-infection disease. Therefore, investigating the HIV and Varicella-Zoster co-infection transmission dynamics using mathematical modeling approach is relatively necessary. The main objective of this study is to investigate the cost-effective analysis of the proposed optimal control strategies on the transmission dynamics of HIV and Varicella-Zoster co-infection in the community using compartmental modeling approach. Qualitatively, we have computed the model equilibrium points and analyze their local stabilities using Routh-Hurwitz stability criteria, the effective reproduction numbers by using the next generator matrix operator method, we re-formulated the optimal control problem of the complete co-infection model by implementing five time dependent optimal control strategies, analyzed the optimal control problem by applying the Pontryagin's Maximum/Minimum principle. Sensitivity analysis and numerical simulations have been carried out using the forward sensitivity index formula and the fourth order Runge-Kutta numerical methods respectively and verified the analytic results. Finally, we have performed the cost effective analysis for the proposed controlling strategies and from the result we have observed that implementing strategy four (treatment of Varicella-Zoster infected individuals to increase their recovery rate and recovery period) is the most cost effective-strategy as compared with other alternatives.

Analyzing evolutionary game theory in epidemic management: A study on social distancing and mask-wearing strategies.

When combating a respiratory disease outbreak, the effectiveness of protective measures hinges on spontaneous shifts in human behavior driven by risk perception and careful cost-benefit analysis. In this study, a novel concept has been introduced, integrating social distancing and mask-wearing strategies into a unified framework that combines evolutionary game theory with an extended classical epidemic model. To yield deeper insights into human decision-making during COVID-19, we integrate both the prevalent dilemma faced at the epidemic's onset regarding mask-wearing and social distancing practices, along with a comprehensive cost-benefit analysis. We explore the often-overlooked aspect of effective mask adoption among undetected infectious individuals to evaluate the significance of source control. Both undetected and detected infectious individuals can significantly reduce the risk of infection for non-masked individuals by wearing effective facemasks. When the economical burden of mask usage becomes unsustainable in the community, promoting affordable and safe social distancing becomes vital in slowing the epidemic's progress, allowing crucial time for public health preparedness. In contrast, as the indirect expenses associated with safe social distancing escalate, affordable and effective facemask usage could be a feasible option. In our analysis, it was observed that during periods of heightened infection risk, there is a noticeable surge in public interest and dedication to complying with social distancing measures. However, its impact diminishes beyond a certain disease transmission threshold, as this strategy cannot completely eliminate the disease burden in the community. Maximum public compliance with social distancing and mask-wearing strategies can be achieved when they are affordable for the community. While implementing both strategies together could ultimately reduce the epidemic's effective reproduction number ([Formula: see text]) to below one, countries still have the flexibility to prioritize either of them, easing strictness on the other based on their socio-economic conditions.

Optimal Control Strategies on Mobility for Preventing COVID-19 Transmission: A study with A Three-Patch Compartmental Model

Human mobility can be identified as one of the main factors that directly affect the spread of COVID-19. Accordingly, human mobility must be controlled in a proper way to deficit the spread of COVID-19 as the economy of a country depends on human mobility. Nevertheless, due to the lack of proper management of the lockdown restrictions, the economy of many countries has already suffered a severe decline. In this research, a compartmental model (SIR) has been presented using optimal control theory to deficit the spread of COVID-19. Thus, the districts of Sri Lanka were divided into three regions (three-patch), and two control variables, were used to control the normal human mobility within the region and between the region. Also, when designing the cost function, two competing factors which deficit the spread of COVID-19 and save the country's economy were considered. Furthermore, optimal solutions were obtained using the Pontryagin's maximum principle and the data related to the spread of COVID-19 in Sri Lanka from April 15 to May 15, 2021, have been used here. In this research, a lockdown policy has been mainly focused on formally imposing and removing lockdown restrictions to compromise both the competing factors of economic security and control the spread of disease. Based on the results, a clear idea could be obtained about the time limits that should be imposed lockdown restrictions within the region and between the regions. Consequently, it was apparent that starting the systematic removal of the lockdown limits within the regions and between the regions are approximately equal. Furthermore, effective reproductive number are used to check the spread of COVID-19. Hence, it can be assumed that the spread of disease is less when mobility controls are activated. The results which were obtained here can be used not only for COVID-19 but for any pandemic and endemic.

Theoretical and numerical study of case reporting rate with application to epidemiology

A clear understanding of actual infection rate is imperative for control and prevention of diseases. In particular, it helps in formulating effective vaccination strategies and in assessing the level of herd immunity required to contain the virus. In this paper, we conduct theoretical and numerical study of a novel optimization procedure aimed at stable estimation of incidence reporting rate and time-dependent effective reproduction number from real data on new incidence cases, daily new deaths, and vaccination percentages. The iteratively regularized optimization algorithm can be applied to a broad class of data fitting problems constrained by various biological models, where one has to account for under-reporting of cases. To that end, general nonlinear observation operators in real Hilbert spaces are considered in the proposed convergence analysis. To illustrate theoretical findings, numerical simulations with SVIsIvRD compartmental model and real data for Delta variant of COVID-19 pandemic in different states of the US are conducted.

A Mathematical Model to Investigate How Vaccination Affect the Reproduction Number for COVID-19

In this paper a mathematical model that investigates how vaccination affects the dynamics of COVID-19 was considered. More particularly the model takes into account the waning rate of immunity after vaccination as well as administration of booster vaccine. Posititivity and boundedness of solutions of the model were proved. The disease free equilibrium of the model was determined and by using the next generation matrix method both the basic and effective reproduction numbers of the model were determined. Further, from the effective reproduction number, the minimum critical value of individuals to be vaccinated for containment of the diseases was determined. It was found that the value is less for a perfect vaccine compared to an imperfect vaccine. Numerical simulation of the model was done to determine how the parameters of interest in the study (waning rate of immunity, vaccination rate, administration of booster vaccine and efficacy of the vaccine) affect the effective reproduction number. The results show that increasing the rates of vaccination, administering booster vaccine will decrease the effective reproduction number while an increase in waning rate of immunity increases the effective reproduction number. The disease persist in the population due to the declining of immunity after vaccination which increases the effective reproduction number.

The emerging challenge of FLiRT variants: KP.1.1 and KP.2 in the global pandemic landscape.

The SARS-CoV-2 virus has undergone substantial evolution, leading to emergence of new FLiRT variants characterized by specific spike mutations-F to L at position 456 and R to T at position 346-enhancing their transmissibility and immune evasion capabilities. Particularly, KP.2 shows a significant increase in cases in the USA, indicating a potential shift in the pandemic landscape due to its greater ability to evade vaccine-induced immunity and its higher effective reproduction number compared to JN.1. This evolving scenario underscores the need for continuous monitoring and adaptive response strategies to address the challenges posed by these new variants. This abstract examines the emergence of FLiRT variants KP.2 and KP1.1, descendants of the Omicron JN.1 variant, as they draw global attention amidst the ongoing coronavirus disease-2019 pandemic.

Estimation of SARS-CoV-2 fitness gains from genomic surveillance data without prior lineage classification

The emergence of SARS-CoV-2 variants with increased fitness has had a strong impact on the epidemiology of COVID-19, with the higher effective reproduction number of the viral variants leading to new epidemic waves. Tracking such variants and their genetic signatures, using data collected through genomic surveillance, is therefore crucial for forecasting likely surges in incidence. Current methods of estimating fitness advantages of variants rely on tracking the changing proportion of a particular lineage over time, but describing successful lineages in a rapidly evolving viral population is a difficult task. We propose a method of estimating fitness gains directly from nucleotide information generated by genomic surveillance, without a priori assigning isolates to lineages from phylogenies, based solely on the abundance of single nucleotide polymorphisms (SNPs). The method is based on mapping changes in the genetic population structure over time. Changes in the abundance of SNPs associated with periods of increasing fitness allow for the unbiased discovery of new variants, thereby obviating a deliberate lineage assignment and phylogenetic inference. We conclude that the method provides a fast and reliable way to estimate fitness advantages of variants without the need for a priori assigning isolates to lineages.

Influence of the Effective Reproduction Number on the SIR Model with a Dynamic Transmission Rate

In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate B. We define this dynamic law by the differential equation B′/B=F⊕−F⊖, where F⊖ represents a reaction factor reflecting the stress proportional to the active group’s percentage variation. Conversely, F⊕ is a factor proportional to the deviation of B from its intrinsic value. We introduce the notion of contagion impulse f and explore its role within the model. Specifically, for the case where F⊕=0, we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model’s behavior and its implications for understanding disease transmission.

A mathematical analysis of the effects of control strategies on the transmission dynamics of Chlamydiosis

Chlamydiosis remains a major public health concern in both developed and developing countries due to its effects on the human reproductive system. While limited modeling studies have been conducted on the transmission dynamics of the disease, none of them have examined the impacts of the combination of environmental hygiene and other control strategies. In this paper, we present a mathematical model to investigate the impacts of public health education, vaccination of susceptible individuals, treatment of symptomatic infected individuals, and environmental hygiene. The basic reproduction number is computed using the next-generation operator and is employed in the stability analysis of equilibrium points. We also perform a sensitivity analysis of the model using a normalized forward sensitivity index to identify the parameters significantly affecting the effective reproduction number. Findings from analytical solutions and numerical simulations demonstrate that, public health education, vaccination, treatment, and environmental hygiene significantly reduce chlamydiosis incidence and prevalence in the population. Consequently, the study recommends implementing these control measures, particularly in regions where the disease is endemic. Thus, findings from this study could be utilized to support decision-making in Chlamydiosis control strategies.