Reproduction Number Research Articles

Linking Spontaneous Behavioral Changes to Disease Transmission Dynamics: Behavior Change Includes Periodic Oscillation.

Behavior change significantly influences the transmission of diseases during outbreaks. To incorporate spontaneous preventive measures, we propose a model that integrates behavior change with disease transmission. The model represents behavior change through an imitation process, wherein players exclusively adopt the behavior associated with higher payoff. We find that relying solely on spontaneous behavior change is insufficient for eradicating the disease. The dynamics of behavior change are contingent on the basic reproduction number corresponding to the scenario where all players adopt non-pharmaceutical interventions (NPIs). When , partial adherence to NPIs remains consistently feasible. We can ensure that the disease stays at a low level or maintains minor fluctuations around a lower value by increasing sensitivity to perceived infection. In cases where oscillations occur, a further reduction in the maximum prevalence of infection over a cycle can be achieved by increasing the rate of behavior change. When , almost all players consistently adopt NPIs if they are highly sensitive to perceived infection. Further consideration of saturated recovery leads to saddle-node homoclinic and Bogdanov-Takens bifurcations, emphasizing the adverse impact of limited medical resources on controlling the scale of infection. Finally, we parameterize our model with COVID-19 data and Tokyo subway ridership, enabling us to illustrate the disease spread co-evolving with behavior change dynamics. We further demonstrate that an increase in sensitivity to perceived infection can accelerate the peak time and reduce the peak size of infection prevalence in the initial wave.

Modelling the co-infection of malaria and zika virus disease

In this work, a new model for the co-infection of malaria and zika virus disease incorporating vaccination, treatment and vector control using sterile-insect technology (SIT) is formulated. The importance of this study is to highlight the possibility of the co-infection of humans with malaria and zika virus disease in any environment where both diseases co-circulate. Also, to suggest a new and comprehensive method for controlling the individual diseases and their co-infection. Through stability analysis, we showed that the disease-free equilibrium, (DFE) point of the co-infection model is locally asymptotically stable when the basic reproduction numbers, Rmz is less than one, and unstable otherwise. But, the DFE failed to be globally stable when Rmz < 1 which is an indication of existence of backward bifurcation in the model. This shows that bringing down the reproduction number, Rmz to less than one is not enough to eradicate the co-infection of the two diseases. Furthermore, it is shown that the two diseases have positive impact on the spread of each other, which could be attributed to misdiagnoses of one disease as the other. We also showed that effective treatment of infectious humans, increasing the rate of vaccination and employing sterile-insect technique to control the vectors significantly helped to control the individual diseases as well as the co-infection. From the results obtained in the study, it can be concluded that effective control of malaria and zika virus disease requires measures that will control their spread in both human and mosquito populations.

Research on Risk Propagation in Fresh E-commerce Supply Chain Based on Complex Networks

In recent years, the rapid growth of the fresh e-commerce industry has introduced several potential risk factors to the supply chain that necessitate preventative measures. This paper aims to study the risk propagation within the fresh e-commerce supply chain and propose strategies for risk control. Firstly, a dual local world fitness network model is constructed by combining the fitness model with the local world model. This model is then validated, showing consistency with the actual network. Building upon this, an improved SEIRS risk propagation model is developed, and the basic reproduction number is calculated to simulate the risk propagation within the fresh e-commerce supply chain. The results indicate that the degree of risk propagation is positively correlated with the initial infection rate, risk outbreak rate, and loss of immunization rate, while negatively correlated with the risk recovery rate and risk elimination rate.

Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand

This research introduces a sophisticated mathematical model for understanding the transmission dynamics of COVID-19, incorporating both integer and fractional derivatives. The model undergoes a rigorous analysis, examining equilibrium points, the reproduction number, and feasibility. The application of fixed point theory establishes the existence of a unique solution, demonstrating stability in the model. To derive approximate solutions, the generalized Adams-Bashforth-Moulton method is employed, further enhancing the study's analytical depth. Through a numerical simulation based on Thailand's data, the research delves into the intricacies of COVID-19 transmission, encompassing thorough data analysis and parameter estimation. The study advocates for a holistic approach, recommending a combined strategy of precautionary measures and home remedies, showcasing their substantial impact on pandemic mitigation. This comprehensive investigation significantly contributes to the broader understanding and effective management of the COVID-19 crisis, providing valuable insights for shaping public health strategies and guiding individual actions.

Mathematical modeling of two strains tuberculosis and COVID-19 vaccination model: a co-infection study with cost-effectiveness analysis

Tuberculosis and COVID-19 co-infection is currently the major issue of public health in many nations, including Ghana. Therefore, to explore the effects of the two Tuberculosis strains on COVID-19, we suggest a Tuberculosis and COVID-19 co-infection model. The study also provides the most economical and effective control methods to reduce the co-infection of tuberculosis and COVID-19. Based on the behavioral patterns of the two Tuberculosis strains and COVID-19 reproduction numbers, the stability of the co-infection model is examined. We explore the sensitivity of the parameters to examine the effect of the drug-resistant and drug-sensitive strain of Tuberculosis on the co-infection of COVID-19. We determine the most cost-effective and optimal treatment strategies that aim to maximize outcomes while minimizing tuberculosis and/or COVID-19 incidences, cost-effectiveness, and optimization approaches. The outcomes of this work contribute to a better understanding of Tuberculosis and COVID-19 epidemiology and provide insights into implementing interventions needed to minimize Tuberculosis and COVID-19 burden in similar settings worldwide.

Comprehensive Analysis of Omicron Subvariants: EG.5 Rise, Vaccination Strategies, and Global Impact.

The emergence of new variants of the SARS-CoV-2 virus during the COVID-19 pandemic has prompted significant developments in the understanding, monitoring, and response to these strains. This comprehensive review focuses on two prominent variants of interest (VoI), XBB. 1.5 (Kraken) and XBB.1.16 ("Arcturus"), along with seven variants under observation (VuM), including EG.5. The World Health Organization (WHO) identified these variants in July 2023, highlighting EG.5's noteworthy rise in prevalence. EG.5, also known as "Eris," has exhibited an increased effective reproductive rate, prompting concerns about its contagiousness and immune evasion capabilities. With an altered spike protein in the Receptor-Binding Domain (RBD), EG.5 shares similarities with XBB.1.5 but surpasses it in prevalence, constituting 20% of COVID-19 cases in the United States by late August. EG.5's subvariant, EG.5.1, poses challenges with mutations like Q52H and F456L, contributing to its ability to bypass neutralizing antibodies. The global distribution of SARS-CoV-2 variants presents a dynamic landscape, with XBB.1.16 and other strains gaining prominence. The advent of the BA.2.86 variant further complicates the scenario, with its notable spread in regions lacking robust viral surveillance. A thorough analysis of mutations reveals the evolving nature of the Omicron variant, with distinct amino acid changes characterizing XBB.1.5, XBB.1.16, and EG.5. The WHO designates EG.5 as a "variant of interest" due to its increased contagiousness and potential immune evasion, emphasizing the need for vigilant monitoring. The risk assessment of EG.5 underscores its rapid development and growing prevalence globally. While booster vaccines targeting XBB.1.5 are in development, antiviral medications like nirmatrelvir/ritonavir (Paxlovid) continue to exhibit efficacy. In the context of the evolving variants, the FDA has granted emergency use authorization for updated COVID-19 vaccines targeting circulating strains, reflecting the adaptability of vaccination strategies to address emerging challenges. This comprehensive overview provides a nuanced understanding of the diverse Omicron subvariants, their global impact, and the ongoing efforts to combat their spread through vaccination and therapeutic interventions.

Global stability analysis and modelling onchocerciasis transmission dynamics with control measures

ABSTRACT Background: Onchocerciasis infection is one of the neglected tropical diseases targeted for eradication by 2030. The disease is usually transmitted to humans through the bites of black flies. These black flies mostly breed near well-oxygenated fast-running water bodies. The disease is common in mostly remote agricultural villages near rivers and streams. Objective: In this study, a deterministic model describing the infection dynamics of human onchocerciasis disease with control measures is presented. Methods: We derived the model’s reproductive number and used a stability theorem of a Metzler matrix to show that disease-free equilibrium is both locally and globally asymptotically stable whenever the reproductive number is less than one. Parameter contribution was conducted using sensitivity analysis. The model endemic equation is shown to be a cubic polynomial in the presence of infected immigrants and a quadratic form in their absence. Results: When the inflow of infected immigrants is null, the model endemic equation may admit a unique equilibrium if the reproductive number is greater than one, or admits multiple endemic equilibria if the reproductive number is less than unity. We carried out a sensitivity analysis to identify the significant parameters that contribute to onchocerciasis spread. Conclusion: Onchocerciasis disease can be eradicated if the importation of infected immigrants is properly monitored. The integration of the One Health concept in the public health system is key in tackling the emergence and spread of diseases.

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.

Cost–benefit analysis of the COVID-19 vaccination model incorporating different infectivity reductions

The spread and control of coronavirus disease 2019 (COVID-19) present a worldwide economic and medical burden to public health. It is imperative to probe the effect of vaccination and infectivity reductions in minimizing the impact of COVID-19. Therefore, we analyze a mathematical model incorporating different infectivity reductions. This work provides the most economical and effective control methods for reducing the impact of COVID-19. Using data from Ghana as a sample size, we study the sensitivity of the parameters to estimate the contributions of the transmission routes to the effective reproduction number Re. We also devise optimal interventions with cost–benefit analysis that aim to maximize outcomes while minimizing COVID-19 incidences by deploying cost-effectiveness and optimization techniques. The outcomes of this work contribute to a better understanding of COVID-19 epidemiology and provide insights into implementing interventions needed to minimize the COVID-19 burden in similar settings worldwide.

Mosquitoes harvested from rice fields as alternative protein ingredient in broiler feed: insights from the first pilot study.

Global population continuous growth and increasing consumers' demands for protein-rich diets have posed sustainability challenges for traditional livestock feed sources. Consequently, exploring alternative and sustainable protein sources has become imperative to address the environmental burden and resource limitations associated with conventional ingredients. With respect to food security assurance, insects have emerged as a promising solution due to their exceptional nutritional profile, rapid reproduction rates, and low environmental impact. In the present pilot study, 10% of a soybean meal-based diet was replaced by adult mosquitoes harvested from rice fields. The objective was to assess the effect of this partial substitution on meat quality aspects and consumer acceptance. A total of 40 Cobb hybrid broiler chickens were randomly placed in a control and a mosquito-fed group. The study was conducted for 42 days and carcass physicochemical, nutritional, and microbiological characteristics, as well as sensory attributes were evaluated. Overall, results regarding quality attributes were comparable between the control and the treatment group. The organoleptic evaluation showed that the thighs from the mosquito-fed group had the highest overall consumer acceptance. These outcomes indicate that mosquitoes could be successfully used as a protein source for broiler feed without compromising the quality and acceptability of the meat.

Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination

Measles is a highly contagious disease that mainly affects children worldwide. Even though a reliable and effective vaccination is available, there were 140,000 measles deaths worldwide in 2018, and most of them were children under the age five years. In this paper, we comprehensively investigate a novel fractional SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) model of the measles epidemic powered by nonlinear fractional differential equations to understand the epidemic’s dynamical behaviour. We use a non-singular Atangana-Baleanu fractional derivative to analyze the proposed model, taking advantage of non-locality. The existence, uniqueness, positivity and boundedness of the solutions are shown via concepts of fixed point theory, and we also perform the Ulam-Hyers stability of the considered model. The parameter sensitivity is discussed in the context of the variance with each parameter using 3-D graphics based on the basic reproduction number. Moreover, with the Atangana-Toufik numerical scheme, numerical findings are depicted for different fractional-order values. The presented approach produce results that are efficiently consistent and in excellent agreement with the theoretical results.

Cow age, resilience and productivity of cow–calf systems

Context The energy availability for cow–calf systems is related to climate disturbances, and energy use is influenced by the age of the cows. Both factors determine the productivity and resilience of herds after climate disruption. Aims Identify the time needed for the herds composed of cows of a varying age to achieve resilience after energy restriction in the pre- and postpartum. Methods The resilience of systems was compared by deterministic dynamic simulation and herds were considered initially stable but different in (1) energy availability for all herd in the first year of production, namely at 50% (low, L), 75% (medium, M) of 100% (high, H) of the requirements according to the NRC (2000, 2016), with these energy levels being restricted to 60 days before and 60 days after the birth, and (2) the maximum age of the cull cow (lifetime, LT), namely 4 (LT4L, LT4M, LT4H), 6 (LT6L, LT6M, LT6H) of 11 (LT11L, LT11M, LT11H) years. From the second year, availability returned to meet the energy requirements of all animals. The availability of energy for the herd was simulated in natural and cultivated pasture. The productivity was determined as the relation between the kilograms of animals sold and the area used for production over a productive cycle. The system model was considered resilient when 95% of the standard productivity was reached (prior to energy restriction). Key results The time required to return to stability was 2 years in the LT6 and LT11, whereas LT4 required 3 years. Furthermore, LT6 had a higher productivity than did the other herds. The older the culled cow was, the greater was the change in the composition of the product commercialised. Conclusions Cows with an intermediate culling age allowed a sustainable intensification of the system, because they showed better productivity than did older cull cows. Furthermore, after climate disturbance, they presented more resilience than did younger cull cows. The level of energy restriction did not directly influence the time to resilience within each evaluated discard-age group. Implications Herds that culled females before reaching adult age are less resilient after disturbances, such as changes in climate or changes of any nature that interfere with reproductive rates.

A fractional order Ebola transmission model for dogs and humans

Ebola is a serious disease that affects people; in many cases, it results in death. Ebola outbreaks have also occurred in communities where residents keep pets, particularly dogs. Due to a lack of food, the dogs must hunt for food. Dogs eat the internal organs of wildlife that the locals have killed and eaten, as well as small dead animals that are found within the communities which may contain the Ebola virus. This study introduces a mathematical model based on the Caputo–Fabrizio derivative to describe the Ebola transmission dynamics between dogs and humans. The model’s existence and the uniqueness of its solution were investigated using fixed-point theory. Furthermore, through the Sumudu transform criterion, we established that the Caputo–Fabrizio Ebola model is Picard stable. Some qualitative analysis was also carried out to investigate the Ebola propagation trend in the dog-to-human model. The proposed model is fitted to the reported Ebola incidence in Uganda between October 15, 2022, and November 2, 2022. The Ebola reproduction number obtained using the cumulative data was 2.65. It is noticed that as the fractional order reduces, the Ebola reproduction number also reduces. We derived a numerical scheme for our model using the two-step Lagrange interpolation. It has been discovered that the fractional orders significantly influence the model, indicating that natural occurrences could affect the dynamics of Ebola. It is observed that when the recovery rate is enhanced, such as through the hospitalisation of Ebola-infected individuals, the disease will reduce. Finally, as we ensure a reduction in the contact rate among the dog’s compartments, the disease does not spread adiabatically. Therefore, we urge that quarantine measures be put in place to control interactions among the dogs during the outbreak.

Effects of Beauveria bassiana on the growth and reproductive rates of Nezara viridula

Effects of Beauveria bassiana on the growth and reproductive rates of Nezara viridula

The effect of temperature on the boundary conditions of West Nile virus circulation in Europe.

West Nile virus (WNV) is a vector-borne flavivirus that causes an increasing number of human and equine West Nile fever cases in Europe. While the virus has been present in the Mediterranean basin and the Balkans since the 1960s, recent years have witnessed its northward expansion, with the first human cases reported in Germany in 2018 and the Netherlands in 2020. WNV transmission and amplification within mosquitoes are temperature-dependent. This study applies a mathematical modelling approach to assess the conditions under which WNV circulation occurs based on the proportion of mosquito bites on WNV-competent birds (dilution), vector-host ratios, mosquito season length and the observed daily temperature data. We modelled five distinct European regions where previous WNV circulation has been observed within the Netherlands, Germany, Spain, Italy, and Greece. We observed that the number of days in which the basic reproduction number (R0) is above one, increased over the last 40 years in all five regions. In the Netherlands, the number of days in which the R0 is above one, is 70% lower than in Spain. The temperature in Greece, Spain and Italy allowed for circulation under low vector-host ratios, and at a high dilution. On the other hand in the Netherlands and Germany, given the observed daily temperature, the thresholds for circulation requires a lower dilution and higher vector-host ratios. For the Netherlands, a short window of introductions between late May and mid-June would result in detectable outbreaks. Our findings revealed that the temperate maritime climate of the Netherlands allows WNV circulation primarily during warmer summers, and only under high vector-host ratios. This research contributes valuable insights into the dynamic relationship between temperature, vector properties, and WNV transmission, offering guidance for proactive strategies in addressing this emerging health threat in Europe.

Modelling the impact of precaution on disease dynamics and its evolution.

In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number . For , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics.

Dynamical behavior of fractal-fractional order monkeypox virus model

A virus that infects both humans and animals, monkeypox is common in many West African countries and has sporadically spread to other parts of the world. There are serious public health concerns around the globe as a result of the recent spike in cases of monkeypox among both endemic and non-endemic populations. This paper proposes to use the Caputo sense of fractal fractional-order derivatives to examine the dynamics of monkeypox transmission. The study uses Schauder’s fixed point theorem to evaluate the solutions qualitatively and establish their uniqueness inside the model. The next generation matrix technique is used to compute the essential reproduction number. The stability of equilibrium points is further investigated in the research, and a sensitivity analysis of model parameters is carried out. When the basic reproduction number R0 is less than 1, the equilibrium without infections is locally stable. Also, when R0 exceeds 1, this equilibrium becomes unstable. The proposed model incorporates Ulam–Hyers stability through nonlinear functional analysis. To estimate solutions for the fractal-fractional order monkeypox model, the Lagrange’s interpolation method is utilized. In addition, numerical simulations are carried out to examine the influence of some parameters on the overall dynamics of the model. Numerical simulations are performed using MATLAB software to exemplify the model behavior in the context of the Nigerian case study. The graphical representations suggest that the fractal fractional order affects the dynamics of the monkeypox. The findings indicate that isolation of infected individuals in the human population helps to reduce disease transmission.

Challenges of COVID-19 Case Forecasting in the US, 2020-2021.

During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub (https://covid19forecasthub.org). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1-4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.

Asymptotic profiles of basic reproduction number for a degenerate reaction–diffusion host–pathogen model

In this paper, the basic reproduction number (BRN) is explored in terms of a degenerate reaction–diffusion host–pathogen model. The expressions of BRN and local basic reproduction number (LBRN) for the model are calculated. Some basic properties of with respect to the general diffusion rates and the asymptotic profiles of with respect to large diffusion rates and small diffusion rates are established by introducing two compact operators and . Our results reveal that is the spectral radius of a sum of the product of additive operators and strongly positive compact linear operators with spectral radii one.

Metaflumizone susceptibility baseline, reproduction, locomotion, and respiration responses on the Hypothenemus hampei

Coffee berry borer (CBB) is the world's primary coffee pest. Recently, metaflumizone was registered for the control of CBB. This study investigated the susceptibility baseline, reproduction, locomotion, and respiration responses in the CBB (Hypothenemus hampei) exposed to metaflumizone. Lethal concentration (LC10, LC50, and LC99) values for metaflumizone were determined for seventeen populations from Brazil. Coffea arabica fruits infested with the CBB were collected during 2020–2021 from regions with significant coffee production. Metaflumizone reduced the respiration rate of H. hampei from 0.51 to 0.22 μL CO2 h−1 at LC50 for up to 3 h after insecticide exposure. A low concentration (LC10) of metaflumizone showed a stable respiration rate for H. hampei. The locomotion and reproduction (number of eggs) of H. hampei were affected. The recommended diagnostic concentration for H. hampei was 58.0 mg a.i. L−1. Our findings suggest that metaflumizone-based insecticides can be an effective alternative for use in rotation with insecticides of different chemical groups to control this key pest.