Reproduction Ratio Research Articles

Dynamics of HIV-1/HTLV-I Co-Infection Model with Humoral Immunity and Cellular Infection

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses which infect the same target, CD T cells. This type of cell is considered the main component of the immune system. Since both viruses have the same means of transmission between individuals, HIV-1-infected patients are more exposed to the chance of co-infection with HTLV-I, and vice versa, compared to the general population. The mathematical modeling and analysis of within-host HIV-1/HTLV-I co-infection dynamics can be considered a robust tool to support biological and medical research. In this study, we have formulated and analyzed an HIV-1/HTLV-I co-infection model with humoral immunity, taking into account both latent HIV-1-infected cells and HTLV-I-infected cells. The model considers two modes of HIV-1 dissemination, virus-to-cell (V-T-C) and cell-to-cell (C-T-C). We prove the nonnegativity and boundedness of the solutions of the model. We find all steady states of the model and establish their existence conditions. We utilize Lyapunov functions and LaSalle’s invariance principle to investigate the global stability of all the steady states of the model. Numerical simulations were performed to illustrate the corresponding theoretical results. The effects of humoral immunity and C-T-C transmission on the HIV-1/HTLV-I co-infection dynamics are discussed. We have shown that humoral immunity does not play the role of clearing an HIV-1 infection but it can control HIV-1 infection. Furthermore, we note that the omission of C-T-C transmission from the HIV-1/HTLV-I co-infection model leads to an under-evaluation of the basic HIV-1 mono-infection reproductive ratio.

Assessing the Impact of Contact Tracing, Quarantine and Red Zone on the Dynamical Evolution of the Covid-19 Pandemic using the Cellular Automata Approach and the Resulting Mean Field System: A Case study in Mauritius

A cellular automaton (CA) depicting the dynamics of the Covid-19 pandemic, is set up. Unlike the classic CA models, the present CA is an enhanced version, embodied with contact tracing, quarantine and red zones to model the spread of the Covid-19 pandemic. The incubation and illness periods are assimilated in the CA system. An algorithm is provided to showcase the rules governing the CA, with and without the enactment of red zones. By means of mean field approximation, a nonlinear system of delay differential equations (DDE) illustrating the dynamics of the CA is emanated. The concept of red zones is incorporated in the resulting DDE system, forming a DDE model with red zone. The stability analysis of both systems are performed and their respective reproduction numbers are derived. The effect of contact tracing and vaccination on both reproduction numbers is also investigated. Numerical simulations of both systems are conducted and real time Covid-19 data in Mauritius for the period ranged from 5 March 2021 to 2 September 2021, is employed to validate the model. Our findings reveal that a combination of both contact tracing and vaccination is indispensable to attenuate the reproductive ratio to less than 1. Effective contact tracing, quarantine and red zones have been the key strategies to contain the Covid-19 virus in Mauritius. The present study furnishes valuable perspectives to assist the health authorities in addressing the unprecedented rise of Covid-19 cases.

Time-dependent force of infection and effective reproduction ratio in an age-structure dengue transmission model in Bandung City, Indonesia.

Dengue virus infection is a leading health problem in many endemic countries, including Indonesia, characterized by high morbidity and wide spread. It is known that the risk factors that influence the transmission intensity vary among different age groups, which can have implications for dengue control strategies. A time-dependent four − age structure model of dengue transmission was constructed in this study. A vaccination scenario as control strategy was also applied to one of the age groups. Daily incidence data of dengue cases from Santo Borromeus Hospital, Bandung, Indonesia, from 2014 to 2016 was used to estimate the infection rate. We used two indicators to identify the changes in dengue transmission intensity for this period in each age group: the annual force of infection (FoI) and the effective reproduction ratio based on a time-dependent transmission rate. The results showed that the yearly FoI of children (age 0–4 years) increased significantly from 2014 to 2015, at 10.08%. Overall, the highest FoI before and after vaccination occurred in youngsters (age 5–14 years), with a FoI of about 6% per year. In addition, based on the daily effective reproduction ratio, it was found that vaccination of youngsters could reduce the number of dengue cases in Bandung city faster than vaccination of children.

Stationary distribution and long-time behavior of COVID-19 model with stochastic effect

The coronavirus disease (COVID-19) is a dangerous pandemic and it spreads to many people in most of the world. In this paper, we propose a COVID-19 model with the assumption that it is affected by randomness. For positivity, we prove the global existence of positive solution and the system exhibits extinction under certain parametric restrictions. Moreover, we establish the stability region for the stochastic model under the behavior of stationary distribution. The stationary distribution gives the guarantee of the appearance of infection in the population. Besides that, we find the reproduction ratio [Formula: see text] for prevail and disappear of infection within the human population. From the graphical representation, we have validated the threshold conditions that define in our theoretical findings.

Modeling the Importation and Local Transmission of Huanglongbing Disease: Bifurcation and Sensitivity Analysis

Huanglongbing (HLB), primarily transmitted by the citrus psyllid, is the most devastating citrus disease worldwide. Planting disease-free citrus seedlings is one of the significant intervention strategies for HLB. In this paper, a compartment model is used to investigate the importation and local transmission of the disease. Due to the continuous input of the diseased citrus seedlings from outside, the traditional theoretical analysis methods are insufficient to describe and predict its dynamical behaviors based on the analysis determined by the basic reproductive ratio [Formula: see text]. The criteria for the existence and local stability of disease-free and endemic equilibria are deduced. Then a complete theoretical, bifurcation, and sensitivity analyses are carried out on the simplified system. Based on our study, we have the following interesting findings: (a) the importation of diseased citrus seedlings in orchards plays a vital role in the transmission of HLB, and planting disease-free citrus seedlings will effectively inhibit the spread of the disease; (b) the importation of diseased citrus seedlings can affect the stability of the equilibrium of the full system; (c) the simplified system may exhibit some complex dynamic phenomena, such as saddle-node bifurcation, forward bifurcation, backward bifurcation, and bistability; (d) global sensitivity analysis shows that the mortality and biting rate of citrus psyllids have a greater impact on [Formula: see text] than other parameters. These observations provide theoretical guidance for policymakers to determine the long-term viability of implemented HLB intervention strategies.

Informing Surveillance through the Characterization of Outbreak Potential of Chronic Wasting Disease in White-Tailed Deer

Understanding the role that an environmental prion reservoir plays in the outbreak dynamics of chronic wasting disease (CWD) in free ranging white-tailed deer (Odocoileus virginianus) is critical for the allocation of disease surveillance resources by state and provincial wildlife agencies. We hypothesized that demographic, ecological, and epidemiological configurations naturally attenuate epidemic risk despite the introduction of infectious prions into a susceptible population of deer, but the magnitude of infectious prions in the environmental prion reservoir complicate outbreak expectations. We developed a Susceptible-Latent-Exposed-Infective (SLEI) compartment model to represent the dynamics of CWD epidemics in free-ranging white-tailed deer, then used the basic reproductive ratio (R0) to pinpoint counties under which pathogenic introduction (transport of infectious bodily fluids, tissues, and carcasses through natural or anthropogenic means) naturally produced (or failed to produce) an epidemic. We found that the outlook for an epidemic hinged on transmission rates, the magnitude of environmental contamination, and system type (density-, frequency-, or density/frequency-dependent). CWD can persistently infect individuals living in a contaminated environment even if direct transmission is insufficient to sustain circulation. Theoretical results show that transmission of CWD cannot be exclusively density dependent, and must behave as either a mix between frequency and density dependent, or strictly frequency dependent. While the compartment model is a simplistic representation of reality and did not contain many complicating biological considerations, it was immediately useful in hypothesis generation, motivating the collection of additional data for use in more biologically detailed models, and in the allocation of finite surveillance resources to place emphasis on data collection in areas where an introduction of infectious prions is comparatively more likely to result in an epidemic.

A Prospective Method for Generating COVID-19 Dynamics

Generating dynamic operators are constructed here from the cumulative case function to recover all state dynamics of a Susceptible–Exposed–Infectious–Recovered (SEIR) model for COVID-19 transmission. In this study, recorded and unrecorded EIRs and a time-dependent infection rate are taken into account to accommodate immeasurable control and intervention processes. Generating dynamic operators are built and implemented on the cumulative cases. All infection processes, which are hidden in this cumulative function, can be recovered entirely by implementing the generating operators. Direct implementation of the operators on the cumulative function gives all recorded state dynamics. Further, the unrecorded daily infection rate is estimated from the ratio between IFR and CFR. The remaining dynamics of unrecorded states are directly obtained from the generating operators. The simulations are conducted using infection data provided by Worldometers from ten selected countries. It is shown that the higher number of daily PCR tests contributed directly to reducing the effective reproduction ratio. The simulations of all state dynamics, infection rates, and effective reproduction ratios for several countries in the first and second waves of transmissions are presented. This method directly measures daily transmission indicators, which can be effectively used for the day-to-day control of the epidemic.

A fractional–order model with different strains of COVID-19

This study examines the dynamics of COVID-19 variants using a Caputo–Fabrizio fractional order model. The reproduction ratio R0 and equilibrium solutions are determined. The purpose of this article is to use a non-integer order derivative in order to present information about the model solutions, uniqueness, and existence using a fixed point theory. A detailed analysis of the existence and uniqueness of the model solution is conducted using fixed point theory. For the computation of the iterative solution of the model, the fractional Adams–Bashforth method is used. Using the estimated values of the model parameters, numerical results are used to support the significance of the fractional-order derivative. The graphs provide useful information about the complexity of the model, and provide reliable information about the model for any case, integer or non-integer. Also, we demonstrate that any variant with the largest basic reproduction ratio will automatically outperform the other variant.

A novel method for basic reproduction ratio of a diffusive size-structured population model with delay

A novel method for basic reproduction ratio of a diffusive size-structured population model with delay

Transmission dynamics and economic impacts of sheeppox and goatpox disease outbreak in Chifra district of Afar Region Ethiopia

Sheep and goatpox are caused by pox virus and economically very important. The study was conducted to estimate the economic losses due to sheep and goatpox, to estimate the morbidity and mortality as well as the transmission parameters. A cross sectional study was conducted in Chifra districts of Afar region from July 2020 to December 2020 using questioner survey. For the estimation of the economic impacts and the transmission parameters of the outbreak, a data was collected at the end of the outbreak through a direct face to face interview. Transmission parameters were estimated based on a final size approach. Whereas, economic impacts were estimated descriptively using different formulas based on the type of losses. The overall morbidity, mortality and case fatality of sheep and goatpox were 51.6%, 2.0%, and 3.9%, respectively. The average flock level losses due to treatment cost, mortality and abortion were 320.3, 1250 and 1195.6 Ethiopian birr (ETB), respectively. The outbreak caused a total of 63617 ETB losses in the district. The highest loss was due to mortality (28750ETB), whereas the least loss was due to treatment cost (7367ETB). The outbreak had 0.14 and 1.41 transmission rate parameters per day and basic reproduction ratio, respectively. There was a significant difference in the transmission of the infection between individual animals (p < 0.001). To limit the economic losses due to this disease, the farmers should give more attention towards this disease and a systematic control program comprising vaccination and limitation of movement of sheep and goat should be implemented to alleviate the losses due to sheep and goatpox.

Mathematical Analysis of the Causes of Examination Malpractices in Nigeria: An Epidemic Modelling Approach

Examination malpractice is a social disease that derails the entire process, conduct and outcome of examinations. In this study, the entire causes of examination malpractice in Nigeria are categorised into four and a deterministic compartmental mathematical model is built around the four classes in order to identify the factors to be addressed to curb the menace of examination malpractice in the country. The solutions of the model are proved to exist, unique and positive. The equilibrium analysis is conducted and the stability theory of nonlinear differential equations is employed to show that the examination malpractice endemic equilibrium of the model is locally asymptotically stable. The societal disposition reproductive ratio, a quantity that measures the rate at which societal values influence the rate of indulgence in examination malpractices, is also derived following the approach of epidemic modelling and the results obtained from the study reveal that the causes of examination malpractice in Nigeria can be brought under control if there is a radical change in the norms and institutions of the society as well as drastic reduction in the population of examination contractors.

When Is Mass Prophylaxis Cost-Effective for Epidemic Control? A Comparison of Decision Approaches.

For certain communicable disease outbreaks, mass prophylaxis of uninfected individuals can curtail new infections. When an outbreak emerges, decision makers could benefit from methods to quickly determine whether mass prophylaxis is cost-effective. We consider 2 approaches: a simple decision model and machine learning meta-models. The motivating example is plague in Madagascar. We use a susceptible-exposed-infectious-removed (SEIR) epidemic model to derive a decision rule based on the fraction of the population infected, effective reproduction ratio, infection fatality rate, quality-adjusted life-year loss associated with death, prophylaxis effectiveness and cost, time horizon, and willingness-to-pay threshold. We also develop machine learning meta-models of a detailed model of plague in Madagascar using logistic regression, random forest, and neural network models. In numerical experiments, we compare results using the decision rule and the meta-models to results obtained using the simulation model. We vary the initial fraction of the population infected, the effective reproduction ratio, the intervention start date and duration, and the cost of prophylaxis. We assume homogeneous mixing and no negative side effects due to antibiotic prophylaxis. The simple decision rule matched the SEIR model outcome in 85.4% of scenarios. Using data for a 2017 plague outbreak in Madagascar, the decision rule correctly indicated that mass prophylaxis was not cost-effective. The meta-models were significantly more accurate, with an accuracy of 92.8% for logistic regression, 95.8% for the neural network model, and 96.9% for the random forest model. A simple decision rule using minimal information about an outbreak can accurately evaluate the cost-effectiveness of mass prophylaxis for outbreak mitigation. Meta-models of a complex disease simulation can achieve higher accuracy but with greater computational and data requirements and less interpretability. We use a susceptible-exposed-infectious-removed model and net monetary benefit to derive a simple decision rule to evaluate the cost-effectiveness of mass prophylaxis.We use the example of plague in Madagascar to compare the performance of the analytically derived decision rule to that of machine learning meta-models trained on a stochastic dynamic transmission model.We assess the accuracy of each approach for different combinations of disease dynamics and intervention scenarios.The machine learning meta-models are more accurate predictors of mass prophylaxis cost-effectiveness. However, the simple decision rule is also accurate and may be a preferred substitute in low-resource settings.

The impact of travelling on the COVID-19 infection cases in Germany

BackgroundCOVID-19 continues to disrupt social lives and the economy of many countries and challenges their healthcare capacities. Looking back at the situation in Germany in 2020, the number of cases increased exponentially in early March. Social restrictions were imposed by closing e.g. schools, shops, cafés and restaurants, as well as borders for travellers. This reaped success as the infection rate descended significantly in early April. In mid July, however, the numbers started to rise again. Of particular reasons was that from mid June onwards, the travel ban has widely been cancelled or at least loosened. We aim to measure the impact of travellers on the overall infection dynamics for the case of (relatively) few infectives and no vaccinations available. We also want to analyse under which conditions political travelling measures are relevant, in particular in comparison to local measures. By travel restrictions in our model we mean all possible measures that equally reduce the possibility of infected returnees to further spread the disease in Germany, e.g. travel bans, lockdown, post-arrival tests and quarantines.MethodsTo analyse the impact of travellers, we present three variants of an susceptible–exposed–infected–recovered–deceased model to describe disease dynamics in Germany. Epidemiological parameters such as transmission rate, lethality, and detection rate of infected individuals are incorporated. We compare a model without inclusion of travellers and two models with a rate measuring the impact of travellers incorporating incidence data from the Johns Hopkins University. Parameter estimation was performed with the aid of the Monte–Carlo-based Metropolis algorithm. All models are compared in terms of validity and simplicity. Further, we perform sensitivity analyses of the model to observe on which of the model parameters show the largest influence the results. In particular, we compare local and international travelling measures and identify regions in which one of these shows larger relevance than the other.ResultsIn the comparison of the three models, both models with the traveller impact rate yield significantly better results than the model without this rate. The model including a piecewise constant travel impact rate yields the best results in the sense of maximal likelihood and minimal Bayesian Information Criterion. We synthesize from model simulations and analyses that travellers had a strong impact on the overall infection cases in the considered time interval. By a comparison of the reproductive ratios of the models under traveller/no-traveller scenarios, we found that higher traveller numbers likely induce higher transmission rates and infection cases even in the further course, which is one possible explanation to the start of the second wave in Germany as of autumn 2020. The sensitivity analyses show that the travelling parameter, among others, shows a larger impact on the results. We also found that the relevance of travel measures depends on the value of the transmission parameter: In domains with a lower transmission parameter, caused either by the current variant or local measures, it is found that handling the travel parameters is more relevant than those with lower value of the transmission.ConclusionsWe conclude that travellers is an important factor in controlling infection cases during pandemics. Depending on the current situation, travel restrictions can be part of a policy to reduce infection numbers, especially when case numbers and transmission rate are low. The results of the sensitivity analyses also show that travel measures are more effective when the local transmission is already reduced, so a combination of those two appears to be optimal. In any case, supervision of the influence of travellers should always be undertaken, as another pandemic or wave can happen in the upcoming years and vaccinations and basic hygiene rules alone might not be able to prevent further infection waves.

Prediction of COVID-19 Pandemic in Bangladesh: Dual Application of Susceptible-Infective-Recovered (SIR) and Machine Learning Approach.

The outbreak of COVID-19 is a global problem today, and, to reduce infectious cases and increase recovered cases, it is relevant to estimate the future movement and pattern of the disease. To identify the hotspot for COVID-19 in Bangladesh, we performed a cluster analysis based on the hierarchical k-means approach. A well-known epidemiological model named “susceptible-infectious-recovered (SIR)” and an additive regression model named “Facebook PROPHET Procedure” were used to predict the future direction of COVID-19 using data from IEDCR. Here we compare the results of the optimized SIR model and a well-known machine learning algorithm (PROPHET algorithm) for the forecasting trend of the COVID-19 pandemic. The result of the cluster analysis demonstrates that Dhaka city is now a hotspot for the COVID-19 pandemic. The basic reproduction ratio value was 2.1, which indicates that the infection rate would be greater than the recovery rate. In terms of the SIR model, the result showed that the virus might be slightly under control only after August 2022. Furthermore, the PROPHET algorithm observed an altered result from SIR, implying that all confirmed, death, and recovered cases in Bangladesh are increasing on a daily basis. As a result, it appears that the PROPHET algorithm is appropriate for pandemic data with a growing trend. Based on the findings, the study recommended that the pandemic is not under control and ensured that if Bangladesh continues the current pattern of infectious rate, the spread of the pandemic in Bangladesh next year will increase.

Dynamics of an HIV infection model with virus diffusion and latently infected cell activation

Effective combination therapy usually reduces the plasma viral load of HIV to below the detection limit, but it cannot eradicate the virus. The latently infected cell activation is considered to be the main obstacle to completely eradicating HIV infection. In this paper, we consider an HIV infection model with latently infected cell activation, virus diffusion and spatial heterogeneity under Neumann boundary condition. The basic reproduction ratio is characterized by the principal eigenvalue of the related elliptic eigenvalue problem. Besides, by constructing Lyapunov functionals and using Green’s first identity, the global threshold dynamics of the system are completely established. Numerical simulations are carried out to illustrate the theoretical results, in particular, the influence of virus diffusion rate on the basic reproduction ratio is addressed.

Global dynamics of an age–space structured HIV/AIDS model with viral load-dependent infection and conversion rates

Distinguished from the existing HIV/AIDS epidemic models, we formulate a model by considering three-age-structured, spacial diffusion, viral load-dependent infection and conversion rates to study the global dynamical behaviors of HIV/AIDS transmission. The generation operator ℛ and the explicit expression of basic reproduction ratio R0 are introduced. The global stability of steady states and the uniform persistence of the disease are presented. Sensitivity analysis indicates that some parameters impact the value of R0 markedly and the intervening measure plays a crucial role in the intervention of HIV infection at population level. Furthermore, numerical simulations suggest that intervening measure at the individual and population levels is highly effective in controlling the transmission of the disease.

How many cooperators are too many? Foundress number, reproduction and sex ratio in a quasi‐social parasitoid

AbstractIn the parasitoid genusSclerodermus, multiple foundresses produce and care for communal broods on large hosts, which can lead to greater reproductive success for group members than attempting to reproduce alone.We explore the consequences of foundress group size on the benefits of cooperative brooding and on brood sex ratios by providing groups of 10–55 foundresses with a single host and no alternative reproductive options.Within this range, increasing foundress group size leads to increasingly common failure in brood production and diminishedper capitasuccess. Group production of adult offspring declines once foundress number reaches around 25.Brood failure is usually at the early developmental stages, and current evidence suggests that there may be competition among foundresses for oviposition sites, possibly involving reproductive dominance and ovicide, which also delays initial brood production. Once broods become established, their rate of development is enhanced by large foundress numbers.The sex ratios of broods are very strongly female biased, irrespective of the foundress number. As this bias is not easily explained by standard models of local mate competition or by a recent model of local resource enhancement, we suggest an explanation based on control of sex allocation by a minority of dominant foundresses, which monopolise the production of adult males.

The dynamical behaviors of fractional-order SE[formula omitted]E[formula omitted]IQR epidemic model for malware propagation on Wireless Sensor Network

In order to investigate the effectiveness of quarantine strategy and the heterogeneity of scale-free network on epidemic spreading, this paper focuses on the investigation of a new fractional epidemiology model, namely fractional SE1E2IQR epidemic model. Our proposed model introduces an isolation class (Q) and an exposure class with two distinct compartments E1 (Type 1-exposed) and E2 (Type 2-exposed). The dynamics of the network-based fractional-order SE1E2IQR epidemic model are studied from the viewpoint of stability analysis and bifurcation. Firstly, by using the next-generation method, we derive the basic reproductive ratio ℛ0 of the proposed epidemic model, which plays an important role in determining not only the unique existence of epidemic equilibrium point E∗ but also the locally asymptotically stability of malware-free equilibrium point E0. However, the paper points out that the condition ℛ0<1 is not sufficient to eliminate the malware from the network. In addition, the direction of bifurcation at ℛ0=1 is also presented. Furthermore, by graphical simulations and computations, we can evaluate the importance of parameters in the basic reproductive ratio ℛ0 and show that the quarantine treatment plays a key role in controlling the epidemic disease.

DYNAMIC ANALYSIS OF THE COVID-19 MODEL WITH ISOLATION FACTORS

Covid-19 is a type of infectious disease caused by SARS Cov-2. This virus has spread throughout the world to cause a pandemic. This study aimed to model and analyze the spread of Covid-19 with the isolation factor. The spread of Covid-19 can be made into an epidemic model by taking into account the population of susceptible humans (S), infected humans (I), isolated humans (L), and recovered humans (R). The method used in this research was to derive a non-linear system of differential equations model, complete the model qualitatively, find the primary reproduction ratio ( , see the model’s behavior by analyzing the dynamics of the equilibrium point and make model simulations. This model has a disease-free equilibrium point that is asymptotically stable, while at the equilibrium point, the endemic is unstable. The results of the model simulation and analysis of the value indicate that the chance of successful Covid-19 spread and the isolation factor is a significant controlled parameter in reducing the value.

Learning from the initial deployment of digital contact tracing apps

Learning from the initial deployment of digital contact tracing apps