Reproduction Number Of Disease Research Articles

Modeling the Inflow of Exposed and Infected Migrants on the Dynamics of Malaria

Malaria is currently a life-threatening vector borne disease which is endemic in most of the developing and underdeveloped countries associated with poor health care systems. In this study, a host-vector mathematical model that takes into account the inflow of human migrants who have been exposed or infected with malaria is formulated and analysed. The reproduction number of the mosquito vector population is derived and used as a threshold quantity for determining the existence of the model trivial and realistic steady states. The Routh-Hurwitz criterion and some stability theorems of Metzler matrices are used to show that the realistic disease free equilibrium is both locally and globally asymptotically stable whenever the disease reproductive number is less than one. We derived an equation for the model endemic condition and used Descartes Rule of Sign Change to established the conditions for the model to admit one or three endemic equilibrium state(s). It is further shown that in the absence of inflow of exposed or infected migrants, the model admits a globally asymptotically unique endemic equilibrium when R0>1 and two endemic equilibria when R0<1. Our local sensitivity analysis revealed that the adults mosquito removal and biting rates were respectively the most significant contributing parameters to the spread of malaria. The numerical simulations results suggested that the exposed and infected immigrants have no significant impact on the dynamical behaviour of the model population sub-classes.

Analysis of a mathematical model with hybrid fractional derivatives under different kernel for hearing loss due to mumps virus

ABSTRACT Genetics, birth defects, some viral diseases, persistent ear infections, medications, loud noises, and age can all cause hearing loss, a global health issue. The mumps are typically the cause of unilaterally acquired sensorineural hearing loss in children. A hybrid fractional operator model employing Constant Proportional Caputo (CPC), Constant Proportional Caputo Fabrizio (CPCF), and Constant Proportional Atangana-Baleanu Caputo (CPABC) in the Caputo sense is developed to investigate mumps induced hearing loss in children. We focused on the region that is positively invariant and well-posed in the suggested model. We assessed the endemic and disease free equilibrium, reproductive number, strength number, and parameter sensitivity, and examined the global stability of the proposed system. The existence, uniqueness, and Hilfer generalized proportional operators for the constant of proportionality of the system’s solutions are demonstrated using fixed-point theorems. We simulated a system of fractional differential equations analytically using the Laplace Adomian Decomposition Method (LADM). This study is important since it is the first to model mumps related hearing loss using a fractional order model based on hybrid fractional operators without a singular kernel. The fractional-order derivative retains the system memory effect, is nonlocal, and outperforms the integer-order derivative in this regard. This sort of study aids medical professionals in diagnosis, treatment planning, and decision-making for mumps induced hearing loss.

Bayesian monitoring of COVID-19 in Sweden

In an effort to provide regional decision support for the public healthcare, we design a data-driven compartment-based model of COVID-19 in Sweden. From national hospital statistics we derive parameter priors, and we develop linear filtering techniques to drive the simulations given data in the form of daily healthcare demands. We additionally propose a posterior marginal estimator which provides for an improved temporal resolution of the reproduction number estimate as well as supports robustness checks via a parametric bootstrap procedure.From our computational approach we obtain a Bayesian model of predictive value which provides important insight into the progression of the disease, including estimates of the effective reproduction number, the infection fatality rate, and the regional-level immunity. We successfully validate our posterior model against several different sources, including outputs from extensive screening programs. Since our required data in comparison is easy and non-sensitive to collect, we argue that our approach is particularly promising as a tool to support monitoring and decisions within public health.Significance: Using public data from Swedish patient registries we develop a national-scale computational model of COVID-19. The parametrized model produces valuable weekly predictions of healthcare demands at the regional level and validates well against several different sources. We also obtain critical epidemiological insights into the disease progression, including, e.g., reproduction number, immunity and disease fatality estimates. The success of the model hinges on our novel use of filtering techniques which allows us to design an accurate data-driven procedure using data exclusively from healthcare demands, i.e., our approach does not rely on public testing and is therefore very cost-effective.

Epidemic spread on patch networks with community structure

Predicting and preparing for the trajectory of disease epidemics relies on a knowledge of environmental and socioeconomic factors that affect transmission rates on local and global spatial scales. This article discusses the simulation of epidemic outbreaks on human metapopulation networks with community structure, such as cities within national boundaries, for which infection rates vary both within and between communities. We demonstrate mathematically, through next-generation matrices, that the structures of these communities, setting aside all other considerations such as disease virulence and human decision-making, have a profound effect on the reproduction rate of the disease throughout the network. In high modularity networks, with high levels of separation between neighboring communities, disease epidemics tend to spread rapidly in high-risk communities and very slowly in others, whereas in low modularity networks, the epidemic spreads throughout the entire network as a steady pace, with little regard for variations in infection rate. The correlation between network modularity and effective reproduction number is stronger in population with high rates of human movement. This implies that the community structure, human diffusion rate, and disease reproduction number are all intertwined, and the relationships between them can be affected by mitigation strategies such as restricting movement between and within high-risk communities. We then test through numerical simulation the effectiveness of movement restriction and vaccination strategies in reducing the peak prevalence and spread area of outbreaks. Our results show that the effectiveness of these strategies depends on the structure of the network and the properties of the disease. For example, vaccination strategies are most effective in networks with high rates of diffusion, whereas movement restriction strategies are most effective in networks with high modularity and high infection rates. Finally, we offer guidance to epidemic modelers as to the ideal spatial resolution to balance accuracy and data collection costs.

Transmission parameters of coronavirus disease 2019 in South Asian countries.

ObjectivesThis study aimed to estimate the transmission parameters, effective reproduction number, epidemic peak, and future exposure of coronavirus disease 2019 (COVID-19) in South Asian countries.Methods A susceptible-exposed-infected-recovered-death (SEIRD) model programmed with MATLAB was developed for this purpose. Data were collected (till June 28, 2021) from the official webpage of World Health Organization, along with the Center for Systems Science and Engineering at Johns Hopkins University. The model was simulated to measure the primary transmission parameters. The reproduction number was measured using the next-generating matrix method.Results The primary transmission rate followed an exponential Gaussian process regression. India showed the highest transmission rate (0.037) and Bhutan the lowest (0.023). The simulated epidemic peaks matched the reported peaks, thereby validating the SEIRD model. The simulation was carried out up to December 31, 2020 using the reported data till June 9, 2020. Conclusion The information gathered in this research will be helpful for authorities to prevent the transmission of COVID-19 in the subsequent wave or in the future.

Inter-Country COVID-19 Contagiousness Variation in Eight African Countries.

The estimates of contiguousness parameters of an epidemic have been used for health-related policy and control measures such as non-pharmaceutical control interventions (NPIs). The estimates have varied by demographics, epidemic phase, and geographical region. Our aim was to estimate four contagiousness parameters: basic reproduction number (R0), contact rate, removal rate, and infectious period of coronavirus disease 2019 (COVID-19) among eight African countries, namely Angola, Botswana, Egypt, Ethiopia, Malawi, Nigeria, South Africa, and Tunisia using Susceptible, Infectious, or Recovered (SIR) epidemic models for the period 1 January 2020 to 31 December 2021. For reference, we also estimated these parameters for three of COVID-19's most severely affected countries: Brazil, India, and the USA. The basic reproduction number, contact and remove rates, and infectious period ranged from 1.11 to 1.59, 0.53 to 1.0, 0.39 to 0.81; and 1.23 to 2.59 for the eight African countries. For the USA, Brazil, and India these were 1.94, 0.66, 0.34, and 2.94; 1.62, 0.62, 0.38, and 2.62, and 1.55, 0.61, 0.39, and 2.55, respectively. The average COVID-19 related case fatality rate for 8 African countries in this study was estimated to be 2.86%. Contact and removal rates among an affected African population were positively and significantly associated with COVID-19 related deaths (p-value < 0.003). The larger than one estimates of the basic reproductive number in the studies of African countries indicate that COVID-19 was still being transmitted exponentially by the 31 December 2021, though at different rates. The spread was even higher for the three countries with substantial COVID-19 outbreaks. The lower removal rates in the USA, Brazil, and India could be indicative of lower death rates (a proxy for good health systems). Our findings of variation in the estimate of COVID-19 contagiousness parameters imply that countries in the region may implement differential COVID-19 containment measures.

A periodic Chikungunya model with virus mutation and transovarial transmission

In this paper, a Chikungunya dynamical model with virus mutation and transovarial transmission is developed, which incorporates the effect of seasonal temperature changes on disease transmission through time-dependent parameters. Firstly, the threshold parameter R0m that determines the persistence and extinction of mosquito populations is given, and then the disease reproduction number R0 is defined. Secondly, it is proved that if R0m > 1 and R0 < 1, the disease disappears; if R0m > 1 and R0 > 1, then Chikungunya with mutants and non-mutants will persist simultaneously. Finally, a case study is carried out with the data in Kerala, India, where the virus mutation causes the outbreak of Chikungunya. Data on newly confirmed human cases in the state between 2007 and 2010 is fitted and the theoretical results obtained in the previous section are validated. In addition, the effects of seasonal temperature change, virus mutation and transovarial transmission on the prevalence of the disease are studied by numerical simulations from different aspects.2020 MSC: 34K13; 37N25; 92D30.

Investigations on the Control of COVID-19 and Suggestions for Re-Open Based on Model Study

Data-based analysis gives out an estimation of the incubation period. A dynamic model is established and discussed. Disease reproduction number reveals the high probability of COVID-19 pandemic, but strengthening the exposure of asymptomatic people will help to curb the transmission, and measures of contact-tracking and stay-at-home play a replaceable role. Discussions point out that social disruption can be avoided if the contact tracking rate can be more than 0.5. Investigations for re-opening show that a city of the same size as Wuhan can be reopened if new cases are continuously below 1000 for a few days and when they are less than 500, with the assurance of contact tracking associated with extensive testing. In short, tracking and testing are the prioritized strategies, while maintaining awareness can shorten the epidemic period and mobility restrictions can be avoided.

COVID-19 infection control parameters in Iran: an epidemiological modeling :

Abstract Background: We aimed to evaluate Iran's current COVID-19 infection, emphasizing the number of infection detection and the disease's reproductive number in its high peak in November and after the lockdown in December. Materials and Methods: Using the Johns Hopkins Bloomberg School of Public Health Contact Tracing Evaluation and Strategic Support Application, we used the average weekly new cases and average case mortality in November and December 2020. The average case isolation and identification time (25%, Four days) and the average case contact within the household and community were entered into the application. We examined Two modeling systems with 50% and 70% case isolation for the November period as alternative scenarios for the current infection control rate. Results: Our modeling showed only 11% and 30% of the infections were detected in November and December. The disease's reproductive number is similar to the natural reproductive number of the disease (2-3) in November. The two models used to increase the rate of case isolation to 50% and 70% did not significantly change the reproductive number. Conclusion: The priority in Iran for COVID-19 infection control should be a dramatic increase in the number of testing to achieve the correct number of case detection and fulfill the contact tracing criteria to reduce the disease spread.

The impact of phased university reopenings on mitigating the spread of COVID-19: a modeling study

BackgroundSeveral American universities have experienced COVID-19 outbreaks, risking the health of their students, employees, and local communities. Such large outbreaks have drained university resources and forced several institutions to shift to remote learning and send students home, further contributing to community disease spread. Many of these outbreaks can be attributed to the large numbers of active infections returning to campus, alongside high-density social events that typically take place at the semester start. In the absence of effective mitigation measures (e.g., high-frequency testing), a phased return of students to campus is a practical intervention to minimize the student population size and density early in the semester, reduce outbreaks, preserve institutional resources, and ultimately help mitigate disease spread in communities.MethodsWe develop dynamic compartmental SARS-CoV-2 transmission models to assess the impact of a phased reopening, in conjunction with pre-arrival testing, on minimizing on-campus outbreaks and preserving university resources (measured by isolation bed capacity). We assumed an on-campus population of N = 7500, 40% of infected students require isolation, 10 day isolation period, pre-arrival testing removes 90% of incoming infections, and that phased reopening returns one-third of the student population to campus each month. We vary the disease reproductive number (Rt) between 1.5 and 3.5 to represent the effectiveness of alternative mitigation strategies throughout the semester.ResultsCompared to pre-arrival testing only or neither intervention, phased reopening with pre-arrival testing reduced peak active infections by 3 and 22% (Rt = 1.5), 22 and 29% (Rt = 2.5), 41 and 45% (Rt = 3.5), and 54 and 58% (improving Rt), respectively. Required isolation bed capacity decreased between 20 and 57% for values of Rt ≥ 2.5.ConclusionUnless highly effective mitigation measures are in place, a reopening with pre-arrival testing substantially reduces peak number of active infections throughout the semester and preserves university resources compared to the simultaneous return of all students to campus. Phased reopenings allow institutions to ensure sufficient resources are in place, improve disease mitigation strategies, or if needed, preemptively move online before the return of additional students to campus, thus preventing unnecessary harm to students, institutional faculty and staff, and local communities.

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies.

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, to a target value but in distinct ways, which we implement in our model equations. We find that for the same TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

Optimal control of the spread of meningitis: in the presence of behaviour change of the society and information dependent vaccination

A mathematical model of meningococcal meningitis with incidence dependent self-protection measure and vaccination is formulated and analysed. The vaccination considered is assumed to be given to everyone and is information dependent. It is shown that the disease free equilibrium is globally asymptotically stable, which implies that if the disease reproduction number R 0 can be reduced to a value less than unity then it is possible to eradicate the meningococcal meningitis. In addition, the behaviour modification parameters are found to have significant impact on the dynamics of the disease. Moreover, an optimal control theory is applied to propose the optimal combination of efforts in controlling the disease. It is shown that the optimal use of controls, such as preventive education, vaccination and treatment reduces the incidence of the disease. It is also indicated that, incidence dependent self-protection measure and vaccination are important in controlling meningitis, and the costeffectiveness analysis reveals that combining education with vaccination is the most cost-effective strategy in the setting of the model.

Clinical Characteristics and Reproduction Number of Coronavirus Disease (COVID-19) Cases in Markazi Province in Iran.

ABSTRACTBackground: The first case of Coronavirus Disease (COVID-19) was reported in Iran on February 19, 2020. This study aimed to assess the characteristics and reproduction number (R) of COVID-19 in Markazi province in Iran. Methods: This is a cross-sectional study. Confirmed cases (N=2430) in the regions covered by Arak University of Medical Sciences from Feb 20 to Aug 26, 2020 were enrolled in the study. The included variables were clinical and demographic characteristics of COVID-19 patients. The case fatality rate (CFR), incidence rates, and R were estimated based on the daily reported data. For estimating R, generation time was assumed on multi scenarios. R was estimated by R0-package. Moreover, Chi square test was applied. All the analyses were performed in STATA, Excel, ArcMap and R. A p-value less than 0.05 was considered as statistically significant.Results:Conclusion: As R is slightly high, the risk of epidemic has reduced gradually. However, observing social distance and related guidelines are still recommended.

Re-estimation of basic reproduction number of COVID-19 based on the epidemic curve by symptom onset date.

Previous studies have reported the basic reproduction number (R0) of coronavirus disease from publicly reported data that lack information such as onset of symptoms, presence of importations or known super-spreading events. Using data from the Republic of Korea, we illustrated how estimates of R0 can be biased and provided improved estimates with more detailed data. We used COVID-19 contact trace system in Korea, which can provide symptom onset date and also serial intervals between contacted people. The total R0 was estimated as 2.10 (95% confidence interval (CI) 1.84-2.42). Also, early transmission of COVID-19 differed by regional or social behaviours of the population. Regions affected by a specific church cluster, which showed a rapid and silent transmission under non-official religious meetings, had a higher R0 of 2.40 (95% CI 2.08-2.77).

Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model

In the work, author’s presents a very significant and important issues related to the health of mankind’s. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam’s type stability for proposed system by using the tools of non-linear analysis. The author’s thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author’s interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.

Dynamics and spreading speed of a reaction-diffusion system with advection modeling West Nile virus

This paper aims to explore the temporal-spatial spreading and asymptotic behaviors of West Nile virus (WNv) by a reaction-advection-diffusion system with free boundaries, especially considering the impact of advection term on the extinction and persistence of West Nile virus. We define the spatial-temporal risk index R0F(t) with the advection rate (μ) and the general basic disease reproduction number R0D to get the vanishing-spreading dichotomy regimes of West Nile virus. We show that there exists a threshold value μ⁎ of the advection rate, and obtain the threshold results of μ⁎. When the spreading occurs, we investigate the asymptotic dynamical behaviors of the solution in the long run and first give an estimate that the asymptotic spreading speed of the leftward front is less than or equal to the rightward front in the case of 0<μ<μ⁎. At last, we give some numerical simulations to identify the significant effects of the advection.

Estimation of time-varying reproduction numbers underlying epidemiological processes: A new statistical tool for the COVID-19 pandemic.

The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical models may not capture the dynamic transmission and removal processes, governed by virus containment strategies taken at various phases of the epidemic. Moreover, few models account for possible inaccuracies of the reported cases. We propose a Poisson model with time-dependent transmission and removal rates to account for possible random errors in reporting and estimate a time-dependent disease reproduction number, which may reflect the effectiveness of virus control strategies. We apply our method to study the pandemic in several severely impacted countries, and analyze and forecast the evolving spread of the coronavirus. We have developed an interactive web application to facilitate readers’ use of our method.

Real-time estimation of the reproduction number of the novel coronavirus disease (COVID-19) in China in 2020 based on incidence data.

BackgroundSince the first appearance in Wuhan, China in December 2019, the novel coronavirus disease (COVID-19) has posed serious threats to the public health in many Chinese places and overseas. It is essential to quantify the transmissibility on real-time basis for designing public health responses.MethodsWe estimated the time-varying reproduction numbers in China, Hubei province and Wuhan city by using the renewable equation determined by the serial interval (SI) of COVID-19. We compare the average reproduction numbers in different periods of time to explore the effectiveness of the public health control measures against the COVID-19 epidemic.ResultsWe estimated the reproduction numbers at 2.61 (95% CI: 2.47–2.75), 2.76 (95% CI: 2.54–2.95) and 2.71 (95% CI: 2.43–3.01) for China, Hubei province and Wuhan respectively. We found that the reproduction number largely dropped after the city lockdown. As of February 16, the three reproduction numbers further reduced to 0.98, 1.14 and 1.41 respectively.ConclusionsThe control of COVID-19 epidemic was effective in substantially reducing the disease transmissibility in terms of the reproduction number in China reduced to 0.98 as of February 16. At the same time, the reproduction number in Wuhan was probably still larger than 1, and thus the enhancement in the public health control was recommended to maintain.

Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach

This work contains a mathematical model able to portray the transmission of Nipah virus within a targeted population. We argued that, the model with classical differential provide a description based on the Markovian process where the evolution equation is memory-less which of course is not in line with the real world situation. In order to include introduce into mathematical model the effect of waiting distribution able to capture the exponential and power which are natural law follow by several physical problem, we replaced the local time differential operator with a differential operator with the Mittag-Leffler function. We presented in detail the study disease free equilibrium and reproduction number. Some interesting theorems were suggested and proven. The model was solved numerical via a newly established numerical method.

Large-scale Lassa fever outbreaks in Nigeria: quantifying the association between disease reproduction number and local rainfall.

Lassa fever (LF) is increasingly recognised as an important rodent-borne viral haemorrhagic fever presenting a severe public health threat to sub-Saharan West Africa. In 2017-18, LF caused an unprecedented epidemic in Nigeria and the situation was worsening in 2018-19. This work aims to study the epidemiological features of epidemics in different Nigerian regions and quantify the association between reproduction number (R) and state rainfall. We quantify the infectivity of LF by the reproduction numbers estimated from four different growth models: the Richards, three-parameter logistic, Gompertz and Weibull growth models. LF surveillance data are used to fit the growth models and estimate the Rs and epidemic turning points (τ) in different regions at different time periods. Cochran's Q test is further applied to test the spatial heterogeneity of the LF epidemics. A linear random-effect regression model is adopted to quantify the association between R and state rainfall with various lag terms. Our estimated Rs for 2017-18 (1.33 with 95% CI 1.29-1.37) was significantly higher than those for 2016-17 (1.23 with 95% CI: (1.22, 1.24)) and 2018-19 (ranged from 1.08 to 1.36). We report spatial heterogeneity in the Rs for epidemics in different Nigerian regions. We find that a one-unit (mm) increase in average monthly rainfall over the past 7 months could cause a 0.62% (95% CI 0.20%-1.05%)) rise in R. There is significant spatial heterogeneity in the LF epidemics in different Nigerian regions. We report clear evidence of rainfall impacts on LF epidemics in Nigeria and quantify the impact.