Reproduction Number Research Articles

Particulate matter hinders the development and reproduction of predatory mites of Euseius finlandicus (Acariformes: Phytoseiidae)

The foliage of the small-leaved lime (Tilia cordata) is characterised by the nerve axils being grown by non-glandular trichomes, which trait contributes to the enhanced retention of the particulate matter (PM). This fact may disturb the ecological service of T. cordata related to the structure of its leaves, which is to provide acarodomatia (micro-shelters) for the predatory mites of the Phytoseiidae family. Phytoseiids are natural enemies of a variety of plant pests, widely applied in integrated pest management (IPM). Their occurrence is largely related to acarodomatia in which these mites hide, feed, reproduce, and develop. For the first time, the influence of PM deposition within spaces typically occupied by phytoseiids is investigated. Experimental populations of Euseius finlandicus were reared on T. cordata leaves in the progressive PM-pollution. The results showed that the values of life table parameters of the predator depended significantly on the level of PM deposition on leaves. Contrary to clean leaves from the control, the medium and high contamination intensities significantly reduced the daily (by 47% and 70%, respectively) and the total fecundity (by 62% and 77%, respectively) of females which, in turn, resulted in a decreased net reproductive rate (by 67% and 81%, respectively), intrinsic rate of increase (by 40% and 55%, respectively) and finite rate of increase (by 8% and 10%, respectively) of E. finlandicus. The pre-ovipositional period was prolonged, while the oviposition duration was shortened and the mites matured longer. In high pollution level the mortality of phytoseiids was boosted by 19% and some females were observed with pollutant lumps adhered to the idiosoma. Also, significant shares of juvenile forms (13%) and adult females (25%) made attempts to escape from highly contaminated experimental arenas. The implications of PM retention on the shelter vegetation are discussed in the context of IPM and ecological services.

Hormetic dose response induced by sublethal-dose sulfoxaflor leads to reproductive stimulation of Aphis gossypii

Aphis gossypii Glover is one of the most agriculturally important phloem-feeding economic pests, causing tremendous loss in crop yield annually. The hormesis is an important cause of A. gossypii resistance formation, population resurgence, and re-outbreak. However, whether the hormesises induced by different insecticides interact mutually remain largely unclear. In the study, four-generation A. gossypii experiment found that the 24-h sublethal-dose (LC20) sulfoxaflor treatment on G0 significantly increased the net reproductive rate (R0) and fecundity of G1 and G2 generation A. gossypii, but it did not significantly affect the fecundity of G3 and G4 individuals. Transcriptomic analyses revealed that the insecticide-induced significant up-regulation of pathways ribosome, energy metabolism, and the DNA replication and reparation might be responsible for the enhancement of fecundity in G1 and G2 A. gossypii. Notably, G0 exposure to LC20 sulfoxaflor followed by G1 exposure to LC30 deltamethrin resulted in a stronger reproductive stimulation than sulfoxaflor or deltamethrin exposure alone. Our findings provide valuable reference for optimizing sulfoxaflor application in integrated pest management strategies.

Modelling the Influence of Climate and Vector Control Interventions on Arbovirus Transmission

Most mathematical models that assess the vectorial capacity of disease-transmitting insects typically focus on the influence of climatic factors to predict variations across different times and locations, or examine the impact of vector control interventions to forecast their potential effectiveness. We combine features of existing models to develop a novel model for vectorial capacity that considers both climate and vector control. This model considers how vector control tools affect vectors at each stage of their feeding cycle, and incorporates host availability and preference. Applying this model to arboviruses of veterinary importance in Europe, we show that African horse sickness virus (AHSV) has a higher peak predicted vectorial capacity than bluetongue virus (BTV), Schmallenberg virus (SBV), and epizootic haemorrhagic disease virus (EHDV). However, AHSV has a shorter average infectious period due to high mortality; therefore, the overall basic reproduction number of AHSV is similar to BTV. A comparable relationship exists between SBV and EHDV, with both viruses showing similar basic reproduction numbers. Focusing on AHSV transmission in the UK, insecticide-treated stable netting is shown to significantly reduce vectorial capacity of Culicoides, even at low coverage levels. However, untreated stable netting is likely to have limited impact. Overall, this model can be used to consider both climate and vector control interventions either currently utilised or for potential use in an outbreak, and could help guide policy makers seeking to mitigate the impact of climate change on disease control.

A Compartmental Approach to Modeling the Measles Disease: A Fractional Order Optimal Control Model

Measles is the most infectious disease with a high basic reproduction number (R0). For measles, it is reported that R0 lies between 12 and 18 in an endemic situation. In this paper, a fractional order mathematical model for measles disease is proposed to identify the dynamics of disease transmission following a declining memory process. In the proposed model, a fractional order differential operator is used to justify the effect and success rate of vaccination. The total population of the model is subdivided into five sub-compartments: susceptible (S), exposed (E), infected (I), vaccinated (V), and recovered (R). Here, we consider the first dose of measles vaccination and convert the model to a controlled system. Finally, we transform the control-induced model to an optimal control model using control theory. Both models are analyzed to find the stability of the system, the basic reproduction number, the optimal control input, and the adjoint equations with the boundary conditions. Also, the numerical simulation of the model is presented along with using the analytical findings. We also verify the effective role of the fractional order parameter alpha on the model dynamics and changes in the dynamical behavior of the model with R0=1.

Exposure to sublethal levels of insecticide-fungicide mixtures affect reproductive success and population growth rates in the solitary bee Osmia cornuta

In agricultural environments, bees are routinely exposed to combinations of pesticides. For the most part, exposure to these pesticide mixtures does not result in acute lethal effects, but we know very little about potential sublethal effects and their consequences on reproductive success and population dynamics. In this study, we orally exposed newly emerged females of the solitary bee Osmia cornuta to environmentally-relevant levels of acetamiprid (a cyano-substituted neonicotinoid insecticide) singly and in combination with tebuconazole (a sterol-biosynthesis inhibitor (SBI) fungicide). The amount of feeding solution consumed during the exposure phase was lowest in bees exposed to the pesticide mixture. Following exposure, females were individually marked and released into oilseed rape field cages to monitor their nesting performance and assess their reproductive success. The nesting performance and reproductive success of bees exposed to the fungicide or the insecticide alone were similar to those of control bees and resulted in a 1.3–1.7 net population increases. By contrast, bees exposed to the pesticide mixture showed lower establishment, shortened nesting period, and reduced fecundity. Together, these effects led to a 0.5–0.6 population decrease. Female establishment and shortened nesting period were the main population bottlenecks. We found no effects of the pesticide mixture on nest provisioning rate, offspring body weight or sex ratio. Our study shows how sublethal pesticide exposure may affect several components of bee reproductive success and, ultimately, population growth. Our results calls for a rethinking of pollinator risk assessment schemes, which should target not only single compounds but also combinations of compounds likely to co-occur in agricultural environments.

A Networked Meta-Population Epidemic Model with Population Flow and Its Application to the Prediction of the COVID-19 Pandemic

This article addresses the crucial issues of how asymptomatic individuals and population movements influence the spread of epidemics. Specifically, a discrete-time networked Susceptible-Asymptomatic-Infected-Recovered (SAIR) model that integrates population flow is introduced to investigate the dynamics of epidemic transmission among individuals. In contrast to existing data-driven system identification approaches that identify the network structure or system parameters separately, a joint estimation framework is developed in this study. The joint framework incorporates historical measurements and enables the simultaneous estimation of transmission topology and epidemic factors. The use of the joint estimation scheme reduces the estimation error. The stability of equilibria and convergence behaviors of proposed dynamics are then analyzed. Furthermore, the sensitivity of the proposed model to population movements is evaluated in terms of the basic reproduction number. This article also rigorously investigates the effectiveness of non-pharmaceutical interventions via distributively controlling population flow in curbing virus transmission. It is found that the population flow control strategy reduces the number of infections during the epidemic.

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.

Developing an SEIHR epidemiological model featuring saturated incidence rate and investigating its stability

Each and every person will inevitably come into contact with infectious diseases over their lifetime. This unavoidable phenomena is a characteristic of all people. Ideally, the effects of such diseases are still controllable, but under unfavourable circumstances, they may worsen and become full-fledged outbreaks. As a result, this article tries to offer an SEIHR model whose main goal is to reduce and stop the transmission of infectious diseases. Notably, infectious diseases continue to plague many countries, represented by the global threat of Covid-19, underlining the urgent need for efficient control methods. This model stands out because it carefully takes into account the saturated incidence rate of infectivity. The concept also divides the infected population into two different groups, enabling more focused and customized medical interventions. The article begins by closely examining the positivity and boundedness of the model, then conducts a thorough analysis of the fundamental reproductive number. The model's stability is then categorically proven at both equilibrium points. In summary, the article concludes with convincing numerical simulations that validate the suggested model, providing convincing evidence of its effectiveness as a whole. In conclusion, the suggested SEIHR model, which is supported by a wealth of empirical evidence confirming its efficacy and optimality, represents a significant advancement in the management and containment of infectious diseases. It offers a promising route for addressing the enduring threat of infectious diseases on a global scale, and its unique form and extensive analysis highlight its potential to alter our approach to infectious disease control.

Stability analysis of a nonlinear malaria transmission epidemic model using an effective numerical scheme

Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(o\\right)$$\\end{document} was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge–Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh–Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R0≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{0}\\le 1$$\\end{document}. The endemic equilibrium is investigated for stability when R0≥1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{0}\\ge 1$$\\end{document}. All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.

Mathematical Model of Community Participation Levels in Elections in Medan City

Political participation is one of the benchmarks of a country's democracy. This can be seen from their involvement in elections. Every general election must have a white group called abstainers who usually consciously do not using their voting rights which may influence individuals not to use their voting rights in general elections. Medan City is the city with the second highest number of abstainers in North Sumatra Province at 33.33%. This study will model the level of public participation in elections in Medan City by comparing the level of public participation in the 2019 and 2024 presidential elections. From the model, two equilibrium points are obtained, namely abstainer and abstainer-free equilibrium points, basic reproduction number and stability analysis of the equilibrium point. The simulation results for 2019 and 2024 showed that for , the abstainer population increases so that the abstainer equilibrium point is asymptotically stable. Then for , the abstainer population will gradually disappear

Cholera disease dynamics with vaccination control using delay differential equation

The COVID-19 pandemic came with many setbacks, be it to a country’s economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination. A novel delay differential model of fractional order was recommended, with two different delays, one representing the latent period of the disease and the other being the delay in adding a disinfectant to the aquatic environment. This model also takes into account the population that will receive a vaccination. This study utilized sensitivity analysis of reproduction number to analytically prove the effectiveness of control measures in preventing the spread of the disease. This analysis provided the mathematical evidence for adding disinfectants in water bodies and inoculating susceptible individuals. The stability of the equilibrium points has been discussed. The existence of stability switching curves is determined. Numerical simulation showed the effect of delay, resulting in fluctuations in some compartments. It also depicted the impact of the order of derivative on the oscillations.

A reaction–diffusion model of major emerging infectious diseases in a spatially heterogeneous environment and case study

During the outbreak of major emerging infectious diseases, virus droplets can survive in the environment as aerosols for hours to days, and their impact on human infectious diseases is often overlooked. In addition, the speed of transmission of infectious diseases is often closely related to transportation. Therefore, studying the impact of environmental viruses and transportation on disease development is significant for effective infectious disease prevention and control. We proposed a degenerate reaction–diffusion infectious disease model ([Formula: see text]) considering environmental virus interference and established a well-posedness and threshold system for this model. We have obtained the system solution approaches the disease-free equilibrium ([Formula: see text]) when the basic reproduction number [Formula: see text]. The system has at least one positive steady state solution (PSS) when [Formula: see text]. This paper used a non-standard finite difference method discretization model while data fitting and parameter estimation were performed based on data provided by the Health Commission. Further sensitivity analysis was conducted on [Formula: see text]. At the same time, we also discussed the impact of various parameters in the early stages of the outbreak of major emerging infectious diseases on the development of the disease. Research found that even if the contact rate between people is controlled at a shallow level, the disease may persist. In the early stages of major emerging outbreak of infectious diseases, immediately reducing the use of transportation can effectively reduce the speed of disease spread.

Time periodic traveling wave solutions of a time-periodic reaction–diffusion SEIR epidemic model with periodic recruitment

This paper focuses on the existence and nonexistence of a time periodic traveling wave solution of a time-periodic reaction–diffusion SEIR epidemic model. The main feature of the model is the possible deficiency of the classical comparison principle such that many known results do not directly work. If the basic reproduction number of the model, denoted by R0, is larger than one, there exists a minimal wave speed c∗>0 satisfying for each c>c∗, the system admits a nontrivial time periodic traveling wave solution with wave speed c and for c<c∗, there exists no nontrivial time periodic traveling waves such that the system; if R0<1, the system admits no nontrivial time periodic traveling waves.

Aporrectodea caliginosa life history traits are improved by positive earthworm interaction and organic matter addition

Earthworm species interact with each other in soils, but these interactions are poorly understood. Moreover, these key soil organisms are influenced by abiotic soil components such as organic matter. Here, we investigated the influence of Allolobophora chlorotica and Aporrectodea nocturna, two earthworm species from different ecological categories, on the incorporation of organic matter, reproduction and weight change of the endogeic Aporrectodea caliginosa. Two different types of organic matter i) a compost and ii) a fresh refined organic material, both from green waste, were used. Earthworm parameters were monitored during an 8-weeks laboratory experiment using a vineyard soil in order to identify positive and negative interactions between species. Irrespective of species, earthworms interacted preferentially with smaller particles, more decomposed and with a lower C/N ratio. For an equivalent earthworm biomass, similar amount of green compost was incorporated by A. caliginosa and A. nocturna. However, A. chlorotica did not bury this material. The green compost increased the reproduction rate of A. caliginosa when associated to A. chlorotica. Moreover, the association with the epi-anecic A. nocturna increased the reproduction rate of A. caliginosa with the addition of refined organic matter (fresh material). Furthermore, in both earthworm associations, the weight loss of A. caliginosa was reduced by the addition of green compost to the soil surface. These results highlight the importance of earthworm interactions in maintaining populations, and emphasized the need of field studies to confirm these interactions, particularly in the context of soil fertility where organic amendments are often applied.

Analysis of COVID-19 epidemic with intervention impacts by a fractional operator

This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.

Classification of spatial dynamics of a vector–host epidemic model in advective heterogeneous environment

AbstractIn this paper, we propose and analyze a reaction–diffusion vector–host disease model with advection effect in an one‐dimensional domain. We introduce the basic reproduction number (BRN) and establish the threshold dynamics of the model in terms of . When there are no advection terms, we revisit the asymptotic behavior of w.r.t. diffusion rate and the monotonicity of under certain conditions. Furthermore, we obtain the asymptotic behavior of under the influence of advection effects. Our results indicate that when the advection rate is large enough relative to the diffusion rate, tends to be the value of local basic reproduction number (LBRN) at the downstream end, which enriches the asymptotic behavior results of the BRN in nonadvection heterogeneous environments. In addition, we explore the level set classification of , that is, there exists a unique critical surface indicating that the disease‐free equilibrium is globally asymptotically stable on one side of the surface, while it is unstable on the other side. Our results also reveal that the aggregation phenomenon will occur, namely, when the ratio of advection rate to diffusion rate is large enough, infected individuals will gather at the downstream end.

Dynamics of a spatiotemporal SIS epidemic model with distinct mobility range

In this study, we consider an epidemic model for susceptible-infected-susceptible populations with nonlocal dffusion, described by convolution operators. Our main objective is to model different diffusion strategies for the susceptible and infected populations by using distinct kernel functions in the convolution operator to model the different movements of individuals for each class. This approach eliminates the simplification of reducing the stationary problem to a single equation, which makes the analysis more challenging. However, we have shown the existence of at least one positive endemic steady state when the basic reproduction number is greater than one, using the index degree theory of Leray-Schauder. Additionally, we investigated the asymptotic profile of the endemic equilibrium state for both, large and small diffusion rates, to demonstrate the persistence or extinction of the disease. Overall, our study indicates that restricting individual movements only partially cannot eliminate the disease unless the total population size is small.

Fractional Order and Numerical Solution Application of Modeling in the Management of Examination Misconducts

The fractional order model that represents the spread of Examination misconduct using compartments of the population of honest students (susceptible), those lightly involved in misconduct (exposed), seriously involved ones (infected), and quitters (removed) is provided. The fractional order derivative is considered in the Caputo sense. To determine the epidemic forecast and persistence, we calculate the reproduction number. Analyzing the stability of this scheme ensures a non-negative and unique solution within the defined domain (0,1). Employing the Laplace-Adomian Decomposition Method aids in estimating the solution for the nonlinear fractional differential equations. Utilizing infinite series helps derive solutions for these equations, ensuring convergence to their precise values. The results obtained align with outcomes from the traditional Differential Transformed Method. Finally, numerical results and an outstanding graphic simulation are presented.

Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay

In this paper, a fractional order HIV model with saturated incidence rate and time delay is proposed and analyzed. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the stability of two equilibriums are obtained. Thirdly, by using time delay as the bifurcation parameter, it is found that Hopf bifurcation may occur when the time delay passes through a sequence of critical values. After that, some numerical simulations are performed to verify the theoretical results. Finally, some discussions and conclusions are listed.

Allometric comparison of viral dynamics in the nasal cavity-nasopharyngeal mucus layer of human and rhesus monkey by CFD-HCD approach

Background and objectiveViral respiratory infections stand as a considerable global health concern, presenting significant risks to the health of both humans and animals. This study aims to conduct a preliminary analysis of the time series of viral load in the nasal cavity-nasopharynx (NC-NP) of the human and rhesus macaque (RM). MethodsTaking into account the random uniform distribution of virus-laden droplets with a diameter of 10 μm in the mucus layer, this study applies the computational fluid dynamics-host cell dynamics (CFD-HCD) method to 3D-shell NC-NP models of human and RM, analyzing the impact of initial distribution of droplets on the viral dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), estimating parameters in the HCD model based on experimental data, integrating them into simulations to predict the time series of viral load and cell counts, and being visualized. The reproductive number (R0) are calculated to determine the occurrence of infection. The study also considers cross-parameter combinations and cross-experimental datasets to explore potential correlations between the human and RM. ResultsThe research findings indicate that the uniform distribution of virus-laden droplets throughout the whole NC-NP models of human and RM is reasonable for simulating and predicting viral dynamics. The visualization results offer dynamic insights into virus infection over a period of 20 days. Studies involving parameter and dataset exchanges between the two species underscore certain similarities in predicting virus infections between the human and RM. ConclusionsThis study lays the groundwork for further exploration into the parallels and distinctions in respiratory virus dynamics between humans and RMs, thus aiding in making more informed decisions in research and experimentation.