Reproduction Number Research Articles

Assessment of bidirectional impact of stigmatization induced self-medication on COVID-19 and malaria transmissions using mathematical modeling: Nigeria as a case study

The continual social and economic impact of infectious diseases on nations has maintained sustained attention on their control and treatment, of which self-medication has been one of the means employed by some individuals. Self-medication complicates the attempt of their control and treatment as it conflicts with some of the measures implemented by health authorities. Added to these complications is the stigmatization of individuals with some diseases in some jurisdictions. This study investigates the co-infection of COVID-19 and malaria and its related deaths and further highlights how self-medication and stigmatization add to the complexities of the fight against these two diseases using Nigeria as a study case. Using a mathematical model on COVID-19 and malaria co-infection, we address the question: to what degree does the impact of the interaction between COVID-19 and malaria amplify infections and deaths induced by both diseases via self-medication and stigmatization? We demonstrate that COVID-19 related self-medication due to misdiagnoses contributes substantially to the prevalence of disease. The control reproduction numbers for these diseases and quantification of model parameters uncertainties and sensitivities 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.

Pathogenicity of Root-knot Nematode, Meloidogyne incognita on Tuberose (Polianthes tuberosa L.)

A pot experiment was carried out in the net house of Department of Nematology, Assam Agricultural University, Jorhat, to study the pathogenicity of root-knot nematode, Meloidogyne incognita, on tuberose. The study found that as the inoculum level of M. incognita increased from 10 to 10,000 second-stage juveniles (J2) per pot (containing 1 kg of sterilized soil), all plant growth parameters of tuberose decreased progressively. At the highest inoculum level, the plants became severely stunted, chlorotic, and produced very few bulblets. It was noted that at the highest inoculum level, the root systems were significantly reduced, with larger and mostly coalescent galls. The treatments with no nematode (check and associated check) were free from galls and eggmasses. An initial inoculum level of 100 J2 of M.incognita per kg of soil caused significant reduction in all growth parameters and proved to be pathogenic to the tuberose plants. The number of galls and eggmasses increased gradually in the plants with an initial inoculum level of 10 to 1000 J2 of M.incognita per kg of soil, but it declined at highest inoculum level of 10,000 J2 per kg of soil. The experiment also recorded the variation in nematode population in the soil as well as their reproductive rates. These findings can be used to develop effective, targeted methods for minimizing the damage caused by root-knot nematode in tuberose crops.

The influence of prevention and isolation measures to control the infections of the fractional Chickenpox disease model

In this paper, we propose a mathematical model using the Caputo fractional derivative (CFD) and two control signals to study the transmission dynamics and control of Chickenpox (Varicella) outbreak. The model consists of six compartments representing susceptible, vaccinated, exposed, infected with complications, infected without complications, and recovered individuals. We analyze the theoretical properties of the model, including existence, uniqueness, and boundedness of solutions, and calculate the basic reproduction number (R0). We identify equilibrium points and establish conditions for their stability. Sensitivity analysis helps identify the most influential parameters on R0. We formulate a fractional optimal control problem (FOCP) by incorporating time-dependent prevention and isolation measures. The necessary optimality conditions are derived using Pontryagin’s maximum principle. Numerical simulations based on the Adams–Bashforth–Moulton (ABM) method illustrate the impact of control measures and fractional order on disease propagation. The results highlight the effectiveness of optimal controls and fractional order in understanding and managing epidemics, enhancing stability conditions. The study contributes to a better understanding of Chickenpox transmission dynamics and provides insights for disease control and management, aiding decision-makers and governments in taking preventive measures.

Dynamical and numerical analysis of the hepatitis B virus treatment model through fractal–fractional derivative

Infection with the hepatitis B virus (HBV) is a global health problem and may be controlled via appropriate treatment. We use fractional models to understand infectious diseases because fractional models help us understand treatments' effects on hepatitis B better than integer‐order models. In this article, we introduce a new mathematical model for HBV based on the fractal–fractional derivative with a generalized Mittag–Leffler kernel. Firstly, we discuss the fundamental properties, like the equilibria of the model and the primary reproduction number. Then, we investigate the existence of a unique solution to our model. We use an iterative method to solve the proposed model. Further, we discuss the stability of the model through stability theory. Finally, we offer some graphical illustrations for various values of the parameters.

Surgical outcomes and complications associated with ovariectomy in the southern stingray Hypanus americanus.

Southern stingrays (Hypanus americanus) are relatively large rays that are common and popular in public aquariums because of their size and gentle nature. In aquariums, as well as in the wild, female southern stingrays are fecund. They have a short gestation cycle and can sustain multiple pregnancies each year, each culminating with 2-10 young. This reproductive rate could quickly outpace capacity in managed care and result in a ray surplus. To prevent overpopulation, many aquaria have resorted to single sex groups with a preference for female-only populations. This is an effective way to control population growth, but forces the maintenance of two separated populations of rays; for females this interrupts normal reproductive cycling and replaces it with a protracted non-pregnant condition. An additional consideration is development of reproductive disease in females which is recognized by an enlarged, misshapen, and congested ovary with an abundance of cystic structures and an enlarged uterus with a thickened wall that is often filled with histotroph despite a non-pregnant status. There are no effective long-lasting medical treatments for this type of reproductive disease and mortality is often the result. This report describes a surgical technique for ovariectomy in southern stingrays including outcomes and complications. Ovariectomy as a surgical method prevents unwanted reproduction and has the benefit of reducing reproductive pathologies commonly observed in southern stingrays as they age. Seven stingrays 1-5.2 years old and 42-83.5 cm disc width underwent ovariectomy. After anesthesia, the ovary and a small amount of epigonal was excised via a left para-lumbar incision. Four of the seven rays survived five or more years post-procedure. Two rays died acutely of coelomitis and one ray died of complications unrelated to the procedure. This report details a surgical procedure for ovariectomy in southern stingrays including outcomes, complications, and recommendations.

Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established.

Analytical analysis and bifurcation of pine wilt dynamical transmission with host vector and nonlinear incidence using sustainable fractional approach

To study the dynamical system, it is necessary to formulate a mathematical model to comprehend the dynamics of the diseases that are prevalent around the world by using fractional calculus. A mathematical model is developed with the hypothesis created by adding control and asymptomatic variables to observe the rate of change of pine wilt and the ABC operator is used to turn the model into a fractional ordered model for continuous monitoring. The Boundedness and uniqueness of the developed model are investigated for bounded findings by using Banach space, which are the key properties of such an epidemic model. A newly developed system is examined both qualitatively and quantitatively to determine its stable position, and the verification of flip bifurcation has been made for developed systems. Derived reproductive numbers using the next-generation technique as well as the sensitivity of each involved parameter are verified. The Atangana–Toufik scheme is employed to find the solution for the developed system using different fractional values, which are advanced tools for reliable bounded solutions. Simulations have been made to see the real behavior and effects of pine wilt disease with control and asymptomatic battels in the community. Also, identify the real situation of the spread as well as the control of pine wilt after employing control and asymptomatic battels due to treatment. Such a type of investigation will be useful in investigating the spread of disease as well as helpful in developing control strategies based on our justified outcomes.

Global behavior and optimal control of a dengue transmission model with standard incidence rates and self‐protection

It takes into account that conscious, susceptible individuals with self‐protection cannot be infected by mosquito bites, a seven‐dimensional dengue transmission model with self‐protection, and two different standard incidence rates are proposed. Our focus is on discussing the global behavior and the optimal control of the model. We first calculate the control reproduction number and determine that if , the model has a unique dengue equilibrium . Furthermore, we obtain the local stability of dengue‐free equilibrium and the dengue equilibrium by using the method of proof by contradiction. By utilizing the limit system of the model and the Lyapunov direct method, we acquire that is globally stable if ; is globally attractive if , and if , the model is weakly persistent with a thorough analysis, and then is globally stable. Finally, in order to minimize investment in dengue transmission, an optimal control strategy with four control variables is presented using Pontryagin's minimum principle.

EFFECTS OF SYMBIOTIC BACTERIA IN PATHOGENIC INTERACTIONS: THE CASE OF BATRACHOCHYTRIUM DENDROBATIDIS AND PSEUDOMONAS SP. IN AMPHIBIAN POPULATIONS

The decline in amphibian populations in recent decades may be linked to the occurrence of infectious diseases such as chytridiomycosis, which is caused by the chytrid fungus Batrachochytrium dendrobatidis (Bd). It is known that symbiotic bacteria protect the host due to their inhibitory nature. However, how the population dynamics of amphibians is affected by additional effects provided by symbiotic bacteria has not been analyzed in depth. In this paper, a model is proposed to describe the interaction among susceptible amphibians, susceptible amphibians with symbiotic bacteria and amphibians with chytrid fungus. When the modeling takes into account the additional reproductive benefits that the symbiont Pseudomonas sp. grants to the host, multiple endemic equilibrium points can exist if [Formula: see text] ([Formula: see text] is the basic reproduction number for Bd). In this scenario, the existence of a subcritical bifurcation at [Formula: see text], which can occur in two different disease-free equilibrium points, gives rise to complex dynamics and stability scenarios. Particularly, the analysis of the model shows that a sudden increase of fungus-infected amphibians can occur even when [Formula: see text] due to bistability phenomena. In this scenario, the existence of a subcritical bifurcation, which translates for the fungus into colonization even for values of [Formula: see text] less than one, represents an advantage for the chytrid fungus Batrachochytrium dendrobatidis since the pathogen should benefit from remaining as close as possible to an endemic equilibrium. To control the fungal infection, [Formula: see text] must be reduced to a value below one until the endemic equilibrium points disappear. Finally, we show that the amphibian population can reach a critical population level close to an extinction scenario when [Formula: see text] increases.

DYNAMICAL BEHAVIOR OF AN SIR EPIDEMIC MODEL WITH RATIO-DEPENDENT IMPULSIVE CONTROL AND BEDDINGTON–DEANGELIS INCIDENCE

In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number [Formula: see text] and the relation of the endemic equilibrium [Formula: see text] and the ratio threshold [Formula: see text], dynamical analysis of the controlled system is conducted. Under the control strategy, if [Formula: see text], the solutions converge to the disease-free equilibrium. If [Formula: see text] and [Formula: see text], the impulsive system has periodic solution that is orbitally asymptotically stable, and order-[Formula: see text] periodic solution does not exist. Furthermore, if [Formula: see text] and [Formula: see text], the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results.

A Systematic Review on the Distribution of Invasive Plant Species Across Asia: Assessing the Rates of Invasion Success and Management

The advancement of invasive plant species in a particular environment is threatening across Asia. When they are introduced, they could have a variety of different negative effects, either as minor inconveniences or a severe problem. The aim of this review is to compile a list of invasive plant species across Asia and organize a set of data according to their reproduction rates, growth rates, dispersal rates, and characterize the allelochemicals they produce and allelopathic effects they have on their environment. The target is to know the extent of their spread ability in the area that they inhibit and know what control measures can be done with that specific species. The data has been gathered by compiling research articles and obtaining pertinent data relating to the objective. This review also utilized the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) checklist to confirm the credibility of the collected references. To achieve the needed references, keywords such as "distribution", "invasive", and "Asia" have been used to search for these on search engines and research journals such as Google Scholar, ScienceDirect, ResearchGate, and Directory for Open Access Journals, to be then compiled in spreadsheets and document files. The results show that the growth rate of these species varies from 7.5-60 cm per year, where Ipomoea eberhardtii has the highest growth rate of 60 cm per year. The dispersal rates of the species ranges from 0.002-2592 km from the parent plant, where animal mediated, water, and wind dispersal methods are the primary vector to spread. Allelopathic effects produced by the allelochemicals present mostly inhibit growth and seed germination. There are already implemented approaches to control these species, where biological control, physical means, and the use of chemicals are the most used strategies. In different dynamic processes, physical and chemical control measures are most utilized in this case.

Biocontrol performance and mass production potential of the larval endoparasitoid Campoletis chlorideae Uchida (Hymenoptera: Ichneumonidae) against the fall armyworm, Spodoptera frugiperda (J. E. Smith) (Lepidoptera: Noctuidae)

BackgroundThe fall armyworm (FAW), Spodoptera frugiperda (J. E. Smith) (Lepidoptera: Noctuidae), is an aggressive pest species that causes severe economic losses in outbreak regions. Use of FAW natural enemies, particularly native parasitoids, has been suggested as a promising control strategy. Campoletis chlorideae Uchida (Hymenoptera: Ichneumonidae) is a solitary ichneumonid larval endoparasitoid with a broad host range that includes S. frugiperda. However, its parasitism rate, developmental stages, and population dynamics during parasitization of S. frugiperda remain unclear. A field survey was conducted to determine the emergence rate and sex ratio of C. chlorideae, evaluated the biological control performance, and investigated the production potential of it on the individually reared and group-reared S. frugiperda through age-stage, two-sex life tables, respectively.ResultsThe results showed that C. chlorideae parasitizing individually reared FAW resulted for the parasitoid in a lifetime total fecundity (F) of 301.5 ± 16.4 eggs/female, a net reproduction rate (R0) of 62.03 ± 9.07 adult females/female, an overall life span of females of 28.3 ± 0.52 days, and an intrinsic rate of increase (r) of 0.1946 ± 0.0076 day−1. In contrast, the parameters of F, R0, overall life span of females, and r were 87.71 ± 6.32 pupae/female, 6.02 ± 1.61 adult females/female, 25.21 ± 0.79 days, and 0.0918 ± 0.0148 day−1 in group-reared S. frugiperda.ConclusionsThis study suggests that C. chlorideae has a promising biological control potential against S. frugiperda. Future research should focus on developing methods to increase the production of C. chlorideae.

Stratified epidemic model using a latent marked Hawkes process

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. (2023) to a finite population stratified by age bands. We model the actual unobserved infections using a latent marked Hawkes process and the reported aggregated infections as random quantities driven by the underlying Hawkes process. We apply a Kernel Density Particle Filter (KDPF) to infer the marked counting process, the instantaneous reproduction number for each age group and forecast the epidemic’s trajectory in the near future. Taking into account the individual inhomogeneity in age does not increase significantly the computational cost of the proposed inference algorithm compared to the cost of the proposed algorithm for the homogeneously unstructured epidemic model. We demonstrate that considering the individual heterogeneity in age, we can derive the instantaneous reproduction numbers per age group that provide a real-time measurement of interventions and behavioural changes of the associated groups. We illustrate the performance of the proposed inference algorithm on synthetic data sets and COVID-19-reported cases in various local authorities in the UK, and benchmark our model to the unstructured homogeneously mixing epidemic model. Our paper is a “demonstration” of a methodology that might be applied to factors other than age for stratification.

Ecotoxicity of thallium to two soil animal species with different niches and modification by organic materials

Soil thallium (Tl) contamination is of major public concern but little is known about soil Tl ecological toxicity or potential ecological remediation strategies. Here, two soil animal species with different ecological niches, Folsomia candida and Enchytraeus crypticus, were used to test Tl toxicity and modification by exogenous organic materials (i.e. maize straw and biochar). The endpoints of Tl ecotoxicity to F. candida and E. crypticus were studied at two biological levels, i.e., the individual (body Tl concentrations) and the population (survival, reproduction, and growth). Thallium concentrations in F. candida and E. crypticus increased with increasing soil Tl concentration, and their survival and reproduction rates decreased with increasing soil Tl concentration. The LC50 value of Tl effects on F. candida mortality (28 d) was 24.0 mg kg−1 and the EC50 value of reproduction inhibition was 6.51 mg kg−1. The corresponding values were 4.15 mg kg−1 and 2.31 mg kg−1 respectively for E. crypticus showing higher sensitivity to soil Tl than F. candida. These effective values are comparable to or much lower than the environmental Tl concentrations in field soils, suggesting high potential ecological risk. Both biochar and straw can decrease animal body Tl concentrations in different ways, i.e. reducing Tl availability or offering clean food sources, and addition of exogenous organic materials clearly mitigated Tl ecotoxicity in highly polluted soil. The results highlight the potential Tl ecological risk to soil animals and the potential use of organic materials to control the toxicity.

Fixation times on directed graphs.

Computing the rate of evolution in spatially structured populations is difficult. A key quantity is the fixation time of a single mutant with relative reproduction rate r which invades a population of residents. We say that the fixation time is "fast" if it is at most a polynomial function in terms of the population size N. Here we study fixation times of advantageous mutants (r > 1) and neutral mutants (r = 1) on directed graphs, which are those graphs that have at least some one-way connections. We obtain three main results. First, we prove that for any directed graph the fixation time is fast, provided that r is sufficiently large. Second, we construct an efficient algorithm that gives an upper bound for the fixation time for any graph and any r ≥ 1. Third, we identify a broad class of directed graphs with fast fixation times for any r ≥ 1. This class includes previously studied amplifiers of selection, such as Superstars and Metafunnels. We also show that on some graphs the fixation time is not a monotonically declining function of r; in particular, neutral fixation can occur faster than fixation for small selective advantages.

Nonlinear SIRS Fractional-Order Model: Analysing the Impact of Public Attitudes towards Vaccination, Government Actions, and Social Behavior on Disease Spread

This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the equilibrium points is analyzed. Sensitivity analysis is conducted to calculate and discuss the sensitivity index of various parameters. It has been established that the illness would spread across this system when the basic reproduction number is larger than 1, the system becomes infection-free when the reproduction number lies below its threshold value of 1. Numerical figures depict the effects of positive and negative attitudes towards vaccination to make the system disease-free sooner. A comprehensive study regarding various values of the order of fractional derivatives together with integer-order derivatives has been discussed in the numerical section to obtain some useful insights into the intricate dynamics of the proposed system. The Pontryagin principle is used in the formulation and subsequent discussion of an optimum control issue. The study also reveals the significant role of government actions in controlling the epidemic. A numerical analysis has been conducted to compare the system’s behavior under optimal control and without optimal control, aiming to discern their differences. The policies implemented by the government are regarded as the most adequate control strategy, and it is determined that the execution of control mechanisms considerably diminishes the ailment burden.

Bovine leukemia virus transmission rates in persistent lymphocytotic infected dairy cows.

Bovine leukemia virus (BLV) establishes a lifelong persistent infection in dairy cattle. White blood cell count (WBC) is correlated with proviral load in the blood and milk of BLV-infected cattle, and testing WBC can be used to assess both BLV infectiousness levels and risk of BLV transmission from different types of infected animals. The objective of the study was to compare effective transmission rates (β) and the basic reproduction ratio (R o) among two types of BLV-infected dairy cows in Chile: those affected with persistent lymphocytosis (PL) vs. aleukemic (AL).The estimated (β) coefficient was higher in PL cattle [1.1; 95% Confidence interval (CI) (-1.6, 3.8)], compared to AL cattle (-3.1; 95% CI = -3.7, -2.5). In addition, the R o was higher in PL cattle (60.4; 95% CI = 3.5; 820.6), compared to AL cattle (1.5; 95% CI = 0.7, 3.1). The ratio between PL/AL expected rate of cases was 73.9. The estimated effective transmission rate and the Ro were higher in PL cattle compared to AL cattle. The WBC test is a convenient alternative that can be considered for risk identification and risk management of BLV infection in dairy herds; particularly in livestock regions where laboratory capacity is limited (e.g., use of PCR or gene sequencing techniques) and/or molecular tests are not cost-effective. Therefore, when prevalence of infection is high, the removal of PL cattle should be engaged to control BLV within-herds.

The low-lethal concentrations of rotenone and pyrethrins suppress the population growth of Rhopalosiphum padi

As an important pest on winter wheat, Rhopalosiphum padi (L.) causes damage to the wheat yield by sucking plant nutrients, transmitting plant viruses and producing mildew. R. padi has been reported to develop resistance to pyrethroids and neonicotinoids. To explore potential alternative approaches for R. padi control, the activity of 10 botanical insecticides was evaluated. Results suggested that the toxicity of rotenone and pyrethrins to R. padi were the highest and near to the commonly used chemical insecticides. When exposed to the low-lethal concentrations (LC10, LC30) of rotenone or pyrethrins for 24 h, the lifespan and fecundity of adults in F0 generation decreased significantly compared to control. The negative effect could also be observed in the F1 generation, including the decreased average offspring, longevity of adult, and prolonged nymph period. The population parameters in F1 generation of R. padi were also inhibited by exposing to the low-lethal concentrations of rotenone or pyrethrins, including the decreased net reproductive rate, intrinsic rate of natural increase, finite rate of population increase, and gross reproduction rate. Co-toxocity factor results showed that mixtures of rotenone and thiamethoxam, pyrethrins and thiamethoxam showed synergistic effect. Our work suggested that rotenone and pyrethrins showed negative effect on the population growth under low-lethal concentrations. They are suitable for R. padi control as foliar spraying without causing population resurgence.