On a Pandemic Threshold Theorem of the Early Kermack–McKendrick Model with Individual Heterogeneity

A pandemic threshold theorem of the Kermack–McKendrick epidemic system with individual heterogeneity is proved from the definition of R ₀ by Diekmann, Heesterbeek, and Metz. The early Kermack–McKendrick epidemic model is extended to recognize individual heterogeneity, where the state variable indicates an epidemiological state or genetic, physiological, or behavioral characteristics such as risk of infection. With the basic reproduction number R ₀ for the heterogeneous population, the final size equation of the limit epidemic starting from a completely susceptible steady state at t = ?∞ has a unique positive solution if and only if R ₀  > 1. The main result is that the positive solution of the final size equation gives the lower bound of the intensity of any epidemic starting from a host population composed of susceptible and a few infected individuals who spread on a noncompact domain of the trait variable.     

Stability Analysis and Dynamics Preserving Nonstandard Finite Difference Schemes for a Malaria Model

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number R ₀ is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough, R ₀ = 1 is a subcritical backward bifurcation point. The domain for the study of the dynamics is reduced to a compact and feasible region, where the system admits a specific algebraic decomposition into infective and non-infected humans and mosquitoes. Stability results are extended and the possibility of backward bifurcation is clarified. A dynamically consistent nonstandard finite difference scheme is designed.     

Analysis of changes of insect-plant ratio-improvement of key-factor analysis for evaluating bottom-up effects in insect population dynamics

A revised key-factor analysis was presented for analyzing the temporal changes in the ratio of insect absolute number to plant resource. Ten data sets for 5 insect species were then analyzed. In this key-factor analysis, the key factor is defined as the factor contributing highly to between-year variation inR _r , the log rate of the inter-year change of the insect-plant ratio. The yearly change of plant resource was handled as a separate factor, expressed byr _pl , log ratio of plant resource in yearn to plant resource in yearn+1. The following was revealed: 1) In 7 of the 10 data sets examined,r _pl influenced variations ofR _r ; in particular in 3 casesr _pl was the main key factor. 2) Generation-to-generation fluctuations of absolute insect densities showed density dependence in 4 cases, while those of insect-plant ratios, in 8 cases. 3) The Royama model or a linear model, explained well the relationship between log insect-plant ratio (X _r ) andR _r and the relationship betweenX _r and log yearly change rate of absolute insect density (R _abs ). However, in the 7 cases in whichr _pl was a critical factor for variations ofR _r , with, increase ofX _r ,R _r showed a steeper, decrease around the equilibrium point (the point for whichR _r is 0) thanR _abs . This occurred becauser _pl tended to be negatively correlated withX _r . Consequently, in two casesX _r fluctuated cyclicly or chaotically although without the changes in plant resource, fluctuations ofX _r would be damped oscillations approaching equilibrium.     

Dynamics of Mixed Coalitions Under Social Cohesion Constraints

ABSTRACT

Parameters for the birth and death diffusion life table model subject to downward jumps randomly occurring at a constant rate are estimated. The jump magnitudes have a beta distribution with support [0, l_x ], where l_x is the total number of survivors prior to the jump. The estimation method is maximum likelihood. The Cramer–Rao Lower bound and the asymptotic distribution for the MLE are derived. The model is applied to the U.S. men′s population from 1900 to 1999.     

Theoretical studies on the role of food exploitation for the competition of scaamble type

Summary A model was made to clarify the basic processes of competition to occur among larvae by the exploitation as defined byBakker (1969). It was found that this model is applicable to the experimental results on the food exploitation amongDroshophila larvae obtained byBakker (1961). In the model the preimaginal stage is divided into two periods;T _f which is the time that a group of larvae spends in exhausting the food after hatching, andT _s which is the duration of the starvation period afterT _f .T _f and thenW _l (larval body weight) just after the end ofT _f are decided byF _s (amount of food supplied per larva at larval hatching) andF _c (amount of food consumed per larva).T _f affects on the onset ofT _s as well asR _l (rate of decrease in the individual body weight duringT _s ).W _a (weight of emerging adults) is gotten by a subtraction ofR _l fromW _l just after the end ofT _f ,R _e is affected directly by these components ofW _l andR _l . As a result,W _a andR _e are expressed by functions ofF _s . This model confirmed that the food exploitation lead to the competition of scramble type. Finally it was suggested that there exist some strategies which prevent ill-effects owing to the food exploitation.     

Influence of instantaneous fertility decline to replacement level on population growth: An alternative model

If age-specific birth rates m, of a stable population drop abruptly tom _x/R ₀, whereR ₀ is the net reproduction rate, then, according to Keyfitz, the size of the ultimate stationary population relative to.that at the beginning of the process is given byI =be ⁰ ₀ R ₀ ? 1)/(rμR ₀, whereb andr are the birth rate and the rate of growth, respectively, of the stable population,e ₀ ⁰ the life expectancy at birth, andμ the average age at childbirth in the resulting stationary population. Noting that the decline inm _x need not necessarily be uniform, investigation has been carried out to examine the effect on Iwhen fertility decline is more rapid at higher ages. In particular, the effect of the reduced age-specific rates such asm _xe^? rx (which also produces a stationary population) has been analyzed, and simplifications of the results carried out separately for three different models of the net maternity function. It has also been shown that when m, drops abruptly to somem _x ^*, where the form ofm _x ^* need not be specified except for the restriction that the resulting population will be stationary, the value of the index can be approximately obtained fromI ^* =be ₀ ⁰ (1 -rμ/2), whereμ is the average age at childbearing of the initial stable population.     

Some extensions of the keyfitz momentum relationship

A stable population, such that the total birthrateB(t) =B _o e ^ro^t, is abruptly altered by modifying the age-specific birth rate,m(x). The survivor function remains unaltered. The modified population ultimately settles down to a stable behavior, such thatB(t) =B ₁ e ^r ₁ ^t . It is shown thatB ₁/B ₀ = (R ₀ ?R ₁)/[(r ₀ ?r ₁)R ₀ Z ₁], whereR ₀,R ₁ are the net reproduction rates before and after the change, and \(\bar Z_1 \) expected age giving birth for the stable population after the change. The age structure and transients resulting from the change are also described. The effect of an abrupt change in the survivor functionl(x) is also investigated for the simple case where the change is caused by alteringl(x) toe ^?λx l(x). It is shown that the above ratio becomes \(B_1 /B_0 = N_1 /N_0 = [1 - \smallint _0^\infty e^{ - kx} g(x)dx]/\bar Z_1 \lambda \) , whereN refers to the numbers in the population,k =r ₀ + λ, andg(x) =m(x)l(x), the value before the change. A measure for the reproductive worth of the population is also established.     

Modeling Acute Rheumatic Fever

Acute rheumatic fever (ARF) is a major cause of heart disease, rare in developed countries, but of concern in New Zealand, where a unique feature is the prevalence of ARF among Maori and Pacific Island peoples. The incidence and prevalence of ARF in a population are modeled for the New Zealand case, where risks of contracting Group A Streptococcus or developing ARF are allowed to vary according to ethnicity, age, and ARF history. The critical parameter R₀ determines whether a disease will become epidemic or not. A proportional treatment protocol is the most effective at reducing ARF.     

Relationship between female body size and demographic parameters inBactrocera Malaysian A (Diptera: Tephritidae)

Summary The effect of body size, as measured by the head width, of the femaleBactrocera sp. Malaysian A (kept separately in sexual pairs) on the demographic parameters was investigated in the laboratory under ambient conditions of 28–30°C, 78–85% RH and natural photoperiod. Body size was shown to influence significantly all the demographic parameters. The expectation of life of females at eclosion from pupae was respectively for head widths of 1.6, 1.8, 1.9, 2.0 and 2.1 mm: 76.2, 73.4, 73.8, 102.4 and 115.2 days. The mean number of eggs laid per female in its life time was respectively: 86.4±48.7, 181.8±56.1, 229.7±72.6, 364.3±69.4 and 477.5±109.3 which was significantly different from one another (F=3.73,P<0.05) especially the two smaller sizes from the two larger sizes. The regression line for total eggs laid (Y) against head width (X) wasY=785.2X−1208.7 (R ²=0.35,P<0.001). The net reproductive rate (R ₀) was respectively 15.8, 34.0, 43.5, 66.9 and 88.8 eggs, while the intrinsic rate of increase (r) was respectivley 0.0435, 0.0538, 0.0670, 0.0665 and 0.0711. The results confirm that for mass rearing purposes, larger females which produce more offspring are to be preferred.     

Sex-Structured Dynamic of Multi-Group Herpes Simplex Virus 2

A 3(n + l)-dimensional ordinary differential equation for HSV-2 includes l groups of men and n groups of women with different risks of infection. Global Lyapunov functions based on graph theory and on LaSalle invariance principle show that the model dynamics are completely determined by the basic reproduction number ?₀. The disease-free equilibrium is globally asymptotically stable when ?₀ ≤ 1; a unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region when ?₀ > 1.     

Bayesian Estimation for Quantification by Real-time Polymerase Chain Reaction Under a Branching Process Model of the DNA Molecules Amplification Process

The aim of Quantitative Polymerase Chain Reaction is to determine the initial amount X ₀ of specific nucleic acids from an observed trajectory of the amplification process, the amplification being achieved through successive replication cycles. This process depends on the efficiency {p _n } _n of replication of the DNA molecules, p _n being the probability that a molecule will duplicate at replication cycle n. Assuming p _n  = p for all n, Bayesian estimators of the unknown parameter θ = (p, X ₀) are constructed by Markov Chain Monte Carlo methods under a Bienaymé-Galton-Watson branching model of the amplification process. The Bayesian approach takes into account some prior information on the parameter. Relying on simulated data, the proposed Bayesian estimators and their credibility sets are shown to be quite accurate.     

Transmission Probabilities and Reproduction Numbers for Sexually Transmitted Infections with Variable Infectivity: Application to the Spread of HIV Between Low- and High-Activity Populations

Probabilities of transmission and numbers of secondary cases are given for an infection which is transmitted sexually by individuals engaged in multiple partnerships with specified durations and timings. The results applied to the human immunodeficiency virus (HIV) hinge on a function which captures the dependence of the per coital act probability of transmission on the time since disease onset and on the duration of infection at death. Reproduction numbers are derived in a heterogeneous population consisting of low- and high-activity men and women. An expression for the basic reproduction number R ₀ of this system sheds light on the role of concurrency, on the timing of the partnerships, and on bridging effects. A high-activity group can cause a significant epidemic outbreak no matter how small the bridging effect, as long as it is not 0. Only if the bridging effect is eliminated altogether can the growth factor in the low-activity group be reduced independently of what happens in the high-activity group. The role of the relationship between client and sex worker and the role of bridging populations in sub-Saharan Africa are assessed.     

Counter-Examples about Lower- and Upper-Bounded Population Growth

ABSTRACT

For a unimodal growth function f having its maximum at a critical state x _c , the interval bounding the population size asymptotically is usually presented as being equal to [f ^○2(x _c ), f(x _c )]. This interval however does not represent the maximum range within which the population size can vary, even asymptotically. The actual invariant interval containing the population size is equal to: [min(x*, f ^○2(x _c )), f(x _c )], where x* denotes the non-zero fixed point, assumed to be unique, of the iteration of f.     

Estimation of life expectancy — cohort life table

Life tables are traditionally built with linear assumptions for the survival curve. Here, considering that survivors can remain at the end of the observation period, the author shows that non linear modeling is more appropriate. With data on cervix uteri cancer, e0 ≈ 12.5 years with standard error ≈ 2.8 years with infinite time horizon, but e0 ≈ 6.0 years with standard error ≈ 0.1 year in interval with finite time horizon [0, 12 years]. The average hazard function is introduced to estimate the life expectancy, and the actuarial estimate of the hazard function is showed to under‐estimate the true hazard values under the exponential distribution. Finally, a sensitivity analysis of the probabilities of death on the estimation of life expectancy completes the study.     

The feeding from edge towards inner part in soybean plot in rufous turtle dove,Streptopellia orientalis (Latham) and the estimation of passing rate of the flock

Summary Rufous turtle dove,Streptopelia orientalis, coming to the soybean field entered it from the outer part to eat soybean cotyledons. As a result, the injured plants extended from the outer to inner parts in the field. A model expressing these behaviours was constructed here, by assuming that the amount of food birds can eat in one block determines whether they stay there or move into neighbour block. As the food decrease due to exploitation of them by birds, birds enter into farther parts with the passage of time. The rate of feeding in all visiting birds (an ₀ wherea is the rate of feeding per individual andn ₀ the number of birds visiting) and the rate of staying at a block,b, was estimated from the field experimental results, using the above model. The value ofan ₀ fluctuated greatly, depending upon the season in which soybean seeds sowed. The value ofb also fluctuated inversely with that ofan ₀, suggesting the the staying rate decreases with an increase in the number of doves coming, probably because of interference among individuals.     

Analysis of spatial association between two species based on the interspecies mean crowding

Summary and Conclusion The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ andC _p, are derived as geometric and weighted arithmetic means of the same component ratios related to inter-and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita's (1959)C _σ index. Indices to measure the degree of spatial correlation between species, Ω andR _μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra-and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested. This study was supported by Science Research Fund (No. 148041) from the Ministry of Education.     

Prey capture tactics of spiders: An analysis based on a simulation model for spider's growth

Summary The prey capture tactics of spiders was analyzed, considering the energy gained by the capture of prey and that required for it. For the purpose of it, a growth model of spiders was constructed, expressing the flow rate of prey biomass to the spider's body by differential equations. Solving these equations under the differing values of three parameters, growth curves of spiders was obtained. These three parameters are the amount of prey biomass supplied daily to spiders,x ₀, the rate of prey capture of spiders, α, and a coefficient of the respiration rate required for the capture of prey,k. When the value ofk increased, spiders could grow only at high value ofx ₀. These results suggest that habitats with small prey biomass are preferred by spiders adopting a sit-and-wait tactics for prey capture, which requires small values ofk. Wolf spiders are one of these spiders showing that tactics. On the other hand, web-builders which require large amount of energy for spinning webs (namely, take large value ofk), are able to grow only in the habitats with large prey biomass. Each species of spiders are considered to locate in a certain point between both extremes of these tactics for the capture of prey.     

Measurement of non-randomness in spatial distributions

Summary The measurement of departure from randomness in spatial distributions has widespread application in ecological work. Several “indices of non-randomness” are compared with regard to their dependence on sample number, sample size and density. Criteria for the best choice of index for specific situations are discussed. A new coefficientC _x is proposed for use with positively contagious distributions and tests of significance are given. WhenC _x and another index (S ²/m−1) are used for positive and negative contagion respectively, values ranging from −1 through 0 (random) to +1 are obtained, regardless of sample number, sample size or density.     

My quitting stories: A qualitative study exploring Aboriginal women’s experiences of smoking cessation and preventing relapse in the context of pregnancy

BackgroundMost women who give up smoking during pregnancy relapse to smoking postnatally. Evidence on strategies that are helpful in maintaining smoking cessation during and beyond pregnancy is limited.AimThis paper aims to explore Aboriginal women’s experiences of quitting smoking, relapsing, and preventing relapse, focusing on the strategies they applied for attaining and maintaining abstinence and the support they received.MethodsQualitative interviews were conducted between October 2020 and June 2021, in urban New South Wales, Australia, with 12 Aboriginal women who either smoked tobacco or quit smoking and had been pregnant in the last five years. Aboriginal Research Assistants recruited participants, participated in data collection and data analysis. Data were thematically analysed.ResultsMajor themes that emerged from the data include: a) aspiration to be abstinent; b) strong mindset; c) strategies to stay smoke-free; d) supports received; and e) service and policy recommendations. Protecting children from second-hand smoke had salience for the maintenance of abstinence. Having a strong mindset was perceived as a prerequisite to staying smoke-free. Use of multiple coping strategies in combination was frequently expressed. Knowledge about tobacco-related harms, the way nicotine dependence works, and the available support options was empowering and enabled informed decision making and actions around smoking cessation.ConclusionThis qualitative study conducted with 12 Aboriginal women revealed that Aboriginal women employ multiple strategies (cognitive, behavioural and social) to quit smoking and stay smoke-free. The strategies warrant further exploration with different Aboriginal communities across Australia and consideration of inclusion in smoking cessation care.