Reproduction Number Research Articles

Juvenile and total reproductive values for sexual reproduction under any genetic system

Abstract Reproductive value (RV) is the expected contribution of genes by an individual or class of individuals to the gene pool in the distant future, and it plays a crucial role in understanding adaptation in long-term evolution. Class RVs are linked to the genetic system and to life history: for diploid genetics, Grafen derived expressions for relative RVs of female and male juveniles, and for the absolute RVs of all females and of all males. Subsequently, Gardner presented a derivation for relative RVs of juvenile females and males under haplodiploidy. Here we generalise these results to any genetic system for biparental sexual reproduction, such that RV is explicitly linked to parameters of the genetic system and life history. The earlier results by Grafen and Gardner arise as special cases. Finally, we derive expressions for absolute juvenile and total reproductive values of both sexes under any genetic system.

Analysis of an epidemiology model with a removal-rate parameter

Abstract An epidemiology model is presented that interpolates between the classical SIS and SIR models. In contrast to those models, in the SI $$-\varepsilon \,\hbox {R}-(1-\varepsilon $$ - ε R - ( 1 - ε )S model individuals may become infected a finite number of times that is greater than one. Extensions of the model in which one or both of the S and I compartments is divided into sub-compartments allow the computation of the proportion of susceptibles who never get infected or who become infected exactly once. In the singular limit $$\varepsilon \rightarrow 0$$ ε → 0 in which the SI $$-\varepsilon \, \hbox {R}-(1-\varepsilon $$ - ε R - ( 1 - ε )S model approaches the SIS model, the number of susceptibles converges uniformly in time but the number of infectives does not converge to the number of infectives in the SIS model. However, appropriately renormalized solutions of the SI $$-\varepsilon $$ - ε R $$-(1-\varepsilon $$ - ( 1 - ε )S model differ for all time by at most $$O(\varepsilon )$$ O ( ε ) from the corresponding solutions to a modified SIS model in which the basic reproduction number decays over time.

Metabolic scaling, energy allocation tradeoffs, and the evolution of humans’ unique metabolism

All organisms use limited energy to grow, survive, and reproduce, necessitating energy allocation tradeoffs, but there is debate over how selection impacted metabolic budgets and tradeoffs in primates, including humans. Here, we develop a method to compare metabolic rates as quotients of observed relative to expected values for mammals corrected for size, body composition, environmental temperature, and phylogenetic relatedness. Contrary to previous analyses, these quotients reveal that nonhuman primates have total metabolic rates expected for similar-sized mammals in similar environments. In addition, data from several small-scale societies show that humans evolved exceptionally high resting, activity, and total metabolic rates apparently by overcoming tradeoffs between resting and active energy expenditures that constrain other primates. Enhanced metabolic rates help humans fuel expanded brains, faster reproductive rates, extended longevity, and high percentage of body fat.

Mathematical Model of Counteract Bandits Terrorism in Nigeria

This paper explores a mathematical model for analyzing the dynamics of banditry and terrorism, focusing on equilibrium states and stability conditions. Key concepts include the reproduction number Rb, which serves as a threshold parameter indicating the potential for spread or decline of these activities. The study finds that a banditry-free equilibrium is locally asymptotically stable when Rb < 1, suggesting that the activities will decline over time. In contrast, Rb>0 indicates the possibility of globally stable coexistence equilibrium, where banditry and terrorism persist at endemic levels. The model also identifies invariant regions, ensuring that the system's trajectories remain within certain bounds, and guarantees unique and positive solutions, essential for real-world applicability. These findings provide critical insights for developing comprehensive strategies to mitigate banditry and terrorism, highlighting the importance of addressing both root causes and immediate symptoms

Analysis of a fractional order epidemiological model for tuberculosis transmission with vaccination and reinfection.

This study has been carried out using a novel mathematical model on the dynamics of tuberculosis (TB) transmission considering vaccination, endogenous re-activation of the dormant infection, and exogenous re-infection. We can comprehend the behavior of TB under the influence of vaccination from this article. We compute the basic reproduction number ( ) as well as the vaccination reproduction number ( ) using the next-generation matrix (NGM) approach. The theoretical analysis demonstrates that the disease-free equilibrium point is locally asymptotically stable, and the fractional order system is Ulam-Hyers type stable. We perform numerical simulation of our model using the Adams-Bashforth 3-step method to verify the theoretical results and to show the model outputs graphically. By performing data fitting, we observe that our formulated model produces results that closely match real-world data. Our findings indicate that vaccinating a limited segment of the population can effectively eradicate the disease. The numerical simulations also show that vaccination can reduce the number of susceptible and infectious individuals in the population. Moreover, the graphical representations illustrate that the number of infected individuals rises due to both exogenous reinfection and endogenous reactivation.

Improved estimation of the effective reproduction number with heterogeneous transmission rates and reporting delays.

In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective reproduction number, denoted as , is widely used to assess the transmissibility of the disease at a given time t. Real-time estimating this metric is vital for understanding and managing disease outbreaks. Traditional statistical inference often relies on two assumptions. One is that samples are assumed to be drawn from a homogeneous population distribution, neglecting significant variations in individual transmission rates. The other is the ideal case reporting assumption, disregarding time delays between infection and reporting. In this paper, we thoroughly investigate these critical factors and assess their impact on estimating . We first introduce negative binomial and Weibull distributions to characterize transmission rates and reporting delays, respectively, based on which observation and state equations are formulated. Then, we employ a Bayesian filtering for estimating . Finally, validation using synthetic and empirical data demonstrates a significant improvement in estimation accuracy compared to conventional methods that ignore these factors.

Spatiotemporal analysis of Zika virus transmission dynamics incorporating human mobility and seasonal variations using modified homotopy perturbation method

AbstractThis study employed a mathematical model to evaluate how seasonal variations, vector dispersal, and mobility of people affect the spread of the Zika virus. The model's positive solutions, invariant zones, and solution existence and uniqueness were validated through proved theorems. The equilibria points were identified, and the basic reproduction number was calculated. The model was semi-analytically solved using a modified homotopy perturbation approach, and an applied convergence test proved that the solution converges. The simulation results indicated that under optimal breeding conditions, the density of healthy mosquitoes peaked in the fourth month. Two months later, increased mosquito dispersal and human carriers facilitated by favorable weather led to a rise in mosquito infectiousness, peaking between the fourth and eighth months due to significant seasonal effects, resulting in high Zika transmission. To effectively control mosquito populations and reduce Zika transmission, it is recommended that public health interventions focus on the critical periods spanning the third to eighth months.

SDIR Mathematical Approach with Time Delay Factor to Reveal Indonesian Students' Interest in Government Organizations and Internships: A Case in FMIPA UNM

This study is to build a time-delay SDIR model on the case of student interest in Organizations and Government Internship Programs, analyze the model and conduct a model simulation to predict the level of student interest cases in Organizations. This study is a theoretical and applied study. Analysis of the time-delay SDIR model of the case of student interest in Organizations, while the model simulation uses Maple Software. The population of the study was active students of FMIPA UNM, with a sample size of 1029 students obtained using the Sloving technique. The results of this study are a mathematical model of SDIR on the case of student interest in Organizations which is a system of differential equations. The model analysis provides a value of the free equilibrium point of the case of student interest in Organizations and a stable endemic equilibrium point. The results also found that the basic reproduction number value for cases without a solution would produce R0n = 9.912507841, which means that in social cases where one individual can influence 9-10 people in their environment to hesitate to participate in organizational activities or internship programs, but on the other hand if the case is given a solution, it will produce R0s = 0.2737372211, which means that there is no psychological spread, where each individual does not influence other individuals.

Assessing yellow fever outbreak potential and implications for vaccine strategy.

Yellow fever (YF), a vector-borne viral hemorrhagic fever, is endemic in tropical regions of Africa and South America, with large vaccination programmes being used for control. However, significant outbreaks have occurred in recent years. Data on infection rates and seroprevalence is often sparse, requiring robust mathematical models to estimate the burden of yellow fever. In particular, modelling is required to estimate the risk of outbreaks and inform policy decisions regarding the targeting of vaccination. We present a dynamic, stochastic model of YF transmission which uses environmental covariates to estimate the force of infection due to spillover from the sylvatic (non-human primate) reservoir and the basic reproduction number for human-to-human transmission. We examine the potential for targets identified by the World Health Organization EYE Strategy (50%, 60% or 80% vaccination coverage in 1-60 year olds) to achieve different threshold values for the effective reproduction number. Threshold values are chosen to reflect the potential for seasonal and/or climatic variation in YF transmission even in a scenario where vaccination lowers the median reproduction number below 1. Based on parameter estimates derived from epidemiological data, it is found that the 2022 EYE Strategy target coverage is sufficient to reduce the static averaged annual effective reproduction number R below 1 across most or all regions in Africa depending on the effectiveness of reported vaccinations, but insufficient to reduce it below 0.5 and thereby eliminate outbreaks in areas with high seasonal range. Coverage levels aligned with the 2026 targets are found to significantly decrease the proportion of regions where R is greater than 0.5.

An ODEs multiscale model with cell proliferation for hepatitis C virus infection treated with direct acting antiviral agents

In a recent study, a mathematically identical ODE model is derived from a multiscale PDE model of hepatitis C virus infection, which helps to overcome the limitations of the PDE model in the analysis. Here, an extended proposed model is formulated for this transformed ODE model by including the hepatocyte proliferation of both uninfected and infected cells. Unlike the transformed model, the proposed model can predict the triphasic viral decline and the virus level after therapy cessation without oscillations. Numerical simulations are performed to investigate the effect of hepatocyte proliferation and therapy with direct-acting antivirals agents (DAAs). The basic reproduction number is obtained, the equilibrium points are specified, and their stability is analysed. A bifurcation analysis is performed to specify the bifurcation points and to study the effect of varying system parameters. Various viral load profiles generated by the model are confirmed to fit with reported data in the literature.

Why there are more species in several small patches versus few large patches: A multispecies modelling approach

Abstract As global biodiversity is rapidly declining due to habitat loss, it is important to determine how to protect it. The policies of many conservation agencies are still prioritizing the preservation of a single large habitat area (SL) versus several small areas of the same size (SS), despite empirical support favouring SS. However, to date, while many studies have explored this issue using model communities, the results are mixed. In competitive community models, fragmentation has a negative effect at low habitat amounts, whereas neutral community models suggest positive effects. This work aims to explore spatial multispecies models to verify the SS > SL pattern and determine its causes. We used three types of models: a classical neutral, neutral with habitat selection and a competitive hierarchical model. All models have three parameters, namely extinction, reproduction and dispersal distance. In the classical neutral model, species are equivalent and have the same parameters; when there is a reproduction event, they send the propagule to a surrounding patch blindly, and if the patch is already occupied, the propagule dies. In the neutral with habitat selection model, the propagules select an empty patch, so their survival is ensured. In the hierarchical model, species have competitive dominance and more dominant ones can replace the less dominant with a replacement rate parameter. We use 100 species and start simulating the colonization of an empty area; then, we destroy a fixed amount of habitat using different regular patch sizes. The results for all models are almost always that SS retains more species than SL. The extinction of species in patches depends on the quotient between reproduction and extinction rates in relation to patch size. The only case when SL > SS is when dispersal is insufficient to connect patches, and patch size is smaller than the minimum to prevent extinction. If patch size is above the critical size to maintain local populations, the SS > SL pattern is due to the sampling effect of aggregated species distribution combined with the reduction of dispersal ability of species. High‐dispersal rates produce the homogenization of species distribution and a reduction of species richness and this is why habitat fragmentation by habitat loss retains more species when patches are smaller. The model predicts that if a set of species have more dispersal capabilities, the SS effect would be lower than for species with less dispersal. Read the free Plain Language Summary for this article on the Journal blog.

Filtering coupled Wright-Fisher diffusions.

Coupled Wright-Fisher diffusions have been recently introduced to model the temporal evolution of finitely-many allele frequencies at several loci. These are vectors of multidimensional diffusions whose dynamics are weakly coupled among loci through interaction coefficients, which make the reproductive rates for each allele depend on its frequencies at several loci. Here we consider the problem of filtering a coupled Wright-Fisher diffusion with parent-independent mutation, when this is seen as an unobserved signal in a hidden Markov model. We assume individuals are sampled multinomially at discrete times from the underlying population, whose type configuration at the loci is described by the diffusion states, and adapt recently introduced duality methods to derive the filtering and smoothing distributions. These respectively provide the conditional distribution of the diffusion states given past data, and that conditional on the entire dataset, and are key to be able to perform parameter inference on models of this type. We show that for this model these distributions are countable mixtures of tilted products of Dirichlet kernels, and describe their mixing weights and how these can be updated sequentially. The evaluation of the weights involves the transition probabilities of the dual process, which are not available in closed form. We lay out pseudo codes for the implementation of the algorithms, discuss how to handle the unavailable quantities, and briefly illustrate the procedure with synthetic data.

Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

This paper examines a stochastic SEIS epidemic model motivated by Black–Karasinski process. First, it is shown that Black–Karasinski process is a both biologically and mathematically reasonable assumption compared with existing stochastic modeling methods. By analyzing the diffusion structure of the model and solving the relevant Kolmogorov–Fokker–Planck equation, a complete characterization for explicitly approximating the stationary density function near some quasi-positive equilibria is provided. Then for the deterministic model, the basic reproduction number and related asymptotic stability are studied. Finally, several numerical examples are given to substantiate our theoretical findings.

Modeling Zika Virus Disease Dynamics with Control Strategies

In this research, we formulated a fractional-order model for the transmission dynamics of Zika virus, incorporating three control strategies: health education campaigns, the use of insecticides, and preventive measures. We conducted a theoretical analysis of the model, obtaining the disease-free equilibrium and the basic reproduction number, and analyzing the existence and uniqueness of the model. Additionally, we performed model parameter estimation using real data on Zika virus cases reported in Colombia. We found that the fractional-order model provided a better fit to the real data compared to the classical integer-order model. A sensitivity analysis of the basic reproduction number was conducted using computed partial rank correlation coefficients to assess the impact of each parameter on Zika virus transmission. Furthermore, we performed numerical simulations to determine the effect of memory on the spread of Zika virus. The simulation results showed that the order of derivatives significantly impacts the dynamics of the disease. We also assessed the effect of the control strategies through simulations, concluding that the proposed interventions have the potential to significantly reduce the spread of Zika virus in the population.

Evaluating the risk of malaria transmission within the Central African Republic with the goal of stabilising and eliminating the infection

In this paper, we formulate a multi-compartmental mathematical model for humans and mosquitoes. We construct the system of differential equations for an SEITVR for the human compartment and an SEI for the mosquito compartment. We investigate the outbreak of malaria and its effect on the Central African Republic. The analysis of the compartmental model is carried out using stability analysis and Routh Hurwitz Criterion technique is used to indicate the major impact of the model and to improve the model through minor modifications in the transformation of disease in the population. Our model exhibits two equilibrium points, disease free equilibrium points and endemic equilibrium points. The next generation matrix is used to determine the basic reproduction number R 0. A new compartmental model was framed and estimated the malaria spread after 2023 in the Central African Republic, which is the novelty of this research. Our main motivation is to make the Central African Republic a malaria free country. A Numerical example are provided to validate our results for both the disease free state and endemic state of each model. We believe that this investigation will be more effective in reducing malaria infection and stop spreading.

Mathematical Model on The Control of Intestinal Torsion in Pigs

An institutional based research at Federal College of Education (Technical) Ekiadolor, Benin City, Edo State, Nigeria, examined a pig farm in the Ovia North East Local Government Area, investigating a mathematical model on the control of intestinal torsion in pigs through vaccination and fibre-rich nutritional feeds. It results in the application of a four-compartment mathematical model for pig intestinal torsion, which is made up of the classes S, I, V, and R for the Susceptible, Infected, Vaccinated and Recovered classes. This model is used to solve for the reproduction number (R0) using the Next Generation Matrix (NGM), to solve the positivity model, to solve for the existence and uniqueness of the model, and to plot the model graphs using Maple.

EpiFusion: Joint inference of the effective reproduction number by integrating phylodynamic and epidemiological modelling with particle filtering.

Accurately estimating the effective reproduction number (Rt) of a circulating pathogen is a fundamental challenge in the study of infectious disease. The fields of epidemiology and pathogen phylodynamics both share this goal, but to date, methodologies and data employed by each remain largely distinct. Here we present EpiFusion: a joint approach that can be used to harness the complementary strengths of each field to improve estimation of outbreak dynamics for large and poorly sampled epidemics, such as arboviral or respiratory virus outbreaks, and validate it for retrospective analysis. We propose a model of Rt that estimates outbreak trajectories conditional upon both phylodynamic (time-scaled trees estimated from genetic sequences) and epidemiological (case incidence) data. We simulate stochastic outbreak trajectories that are weighted according to epidemiological and phylodynamic observation models and fit using particle Markov Chain Monte Carlo. To assess performance, we test EpiFusion on simulated outbreaks in which transmission and/or surveillance rapidly changes and find that using EpiFusion to combine epidemiological and phylodynamic data maintains accuracy and increases certainty in trajectory and Rt estimates, compared to when each data type is used alone. We benchmark EpiFusion's performance against existing methods to estimate Rt and demonstrate advances in speed and accuracy. Importantly, our approach scales efficiently with dataset size. Finally, we apply our model to estimate Rt during the 2014 Ebola outbreak in Sierra Leone. EpiFusion is designed to accommodate future extensions that will improve its utility, such as explicitly modelling population structure, accommodations for phylogenetic uncertainty, and the ability to weight the contributions of genomic or case incidence to the inference.

Two-Sex Life Table Analysis of Phenacoccus solenopsis (Hemiptera: Pseudococcidae) on Lettuce, Parsley, and Rocket

Phenacoccus solenopsis Tinsley (Hemiptera: Pseudococcidae), commonly known as the cotton mealybug, is a polyphagous pest causes significant economic losses worldwide. This study aimed to determine two-sex life table analysis of P. solenopsis on lettuce (Lactuca sativa), parsley (Petroselinum crispum), and rocket (Eruca sativa). Experiments were conducted under controlled conditions 26°C, 65 ± 10% relative humidity, and a 16:8 light-dark cycle. The results indicated that lettuce was more suitable for P. solenopsis development comparted to parsley and rocket. Total fecundity of P. solenopsis was recorded as 221.45, 158.00, and 121.64, on lettuce, parsley, and rocket respectively. In addition, ovipositon period of P. solenopsis was 14.00, 9.73, and 8.45 days on lettuce, parsley, and rocket respectively. The highest values of net reproductive rate (R0), intrinsic rate of increase (r), and finite rate of increase (λ) were obtained as 97.44 offspring female-1, 0.14 day-1, 1.16 day-1, respectively from lettuce in this present research. The results showed that lettuce was the better host plant for P. soleneopsis than parsley and rocket. However, further studies should be done about host plant pest interactions to provide successful control measures against P. solenopsis.

Women’s Dilemma and Social Reflection in Film Narrative: A Case Study of Kim Ji-young, Born 1982

Kim Ji-young, Born 1982 portrays the life experiences of an ordinary woman navigating family, work, and society, exposing the patriarchal structures, female discipline, and reproductive oppression in South Korean society. Adapted from Cho Nam-joo’s novel, the film recounts Ji-young’s struggles in childhood and marriage, along with the mental distress caused by the pressures of balancing career and family. It powerfully illustrates how societal expectations lead women to lose their sense of self, highlighting the exploitation of emotional labor and unpaid housework. Ji-young’s story transcends individual experience, reflecting the broader structural gender inequality embedded in society. Upon release, the film sparked intense social debate, particularly from South Korean men, some of whom petitioned the Blue House to block the screening, accusing it of fueling gender conflict. This opposition reveals the patriarchal structure’s defensive response to challenges and men’s anxiety over losing status and privilege. This paper explores how government pro-natalist policies, under the guise of preserving family structures, further entrench the oppression of women’s reproductive and labor value.

Mathematical analysis of the effects of precarious health system on COVID-19 transmission dynamics: case of Burkina Faso

n the early moments of the pandemic of coronavirus disease 2019 (COVID-19), the level of effectiveness in treatment and management of patients was limited due to the lack of effective medications and adapted infrastructures in several countries especially in most developing countries. In this study, we propose an SIR-pattern model to investigate the epidemiological effect of delay in hospitalization and case managements. After computing the basic reproduction number thanks to the Next Generation Matrix method, we proved that the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is less than one, and condition which ensure the appearance of two endemic equilibria indicating the possibility of having backward bifurcation is determined. When the basic reproduction number exceeds one, Lyapunov functional technique is used to establish the global stability of the unique endemic equilibrium point. Also, we presented a local sensitivity analysis that gives better understanding of the role of each model parameter appearing in the basic reproduction number. Numerical simulation of the model is also performed to corroborate the analytical results. Finally, we fitted our model by using reported data for Burkina Faso, and the results showed that it can be used for predicting the disease outcomes.