Modelling the effect of immigration on drinking behaviour

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region.     

Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals

This paper presents a sex-structured model for heterosexual transmission of HIV/AIDS in which the population is divided into three subgroups: susceptibles, infectives and AIDS cases. The subgroups are further divided into two classes, consisting of individuals involved in high-risk sexual activities and individuals involved in low-risk sexual activities. The model considers the movement of individuals from high to low sexual activity groups as a result of public health educational campaigns. Thus, in this case public health educational campaigns are resulting in the split of the population into risk groups. The equilibrium and epidemic threshold, which is known as the basic reproductive number (R0), are obtained, and stability (local and global) of the disease-free equilibrium is investigated. The model is extended to incorporate sex workers, and their role in the spread of HIV/AIDS in settings with heterosexual transmission is explored. Comprehensive analytic and numerical techniques are employed in assessing the possible community benefits of public health educational campaigns in controlling HIV/AIDS. From the study, we conclude that the presence of sex workers enlarges the epidemic threshold R0, thus fuels the epidemic among the heterosexuals, and that public health educational campaigns among the high-risk heterosexual population reduces R0, thus can help slow or eradicate the epidemic.     

Evaluation of the public health risk for autochthonous transmission of mosquito-borne viruses in southern Switzerland

Epidemics of mosquito-borne diseases such as chikungunya and dengue fever are becoming more frequent around the world. In Switzerland, autochthonous cases have not been reported so far, although the presence of the vector Aedes albopictus in urban areas of southern Switzerland increases the risk of indigenous transmissions subsequent to imported cases. In 2018, the potential risk of an outbreak of arboviral diseases was assessed in five municipalities of southern Switzerland. The population abundance of Ae. albopictus was evaluated during the mosquito active season by the mean number of Ae. albopictus bites per day per person (estimated using the human landing collection method) and the risk of outbreak in the case of the introduction of chikungunya, dengue or Zika viruses was estimated. In the five localities investigated, no epidemic risk appeared to be present for any of the arboviruses taken into consideration in the initial months (i.e. mid-May to end of July) of Ae. albopictus activity. In the case of the introduction of chikungunya (mutated or not), dengue (serotype 1) or Zika (African lineage) viruses during mid-end August, an epidemic could have occurred in all the municipalities investigated. In mid-end September, the introduction of same arboviruses could have led to an epidemic in three of the five municipalities investigated.     

Impact of group mixing on disease dynamics

A general mathematical model is proposed to study the impact of group mixing in a heterogeneous host population on the spread of a disease that confers temporary immunity upon recovery. The model contains general distribution functions that account for the probabilities that individuals remain in the recovered class after recovery. For this model, the basic reproduction number R₀ is identified. It is shown that if R₀<1, then the disease dies out in the sense that the disease free equilibrium is globally asymptotically stable; whereas if R₀>1, this equilibrium becomes unstable. In this latter case, depending on the distribution functions and the group mixing strengths, the disease either persists at a constant endemic level or exhibits sustained oscillatory behavior.     

Modeling the transmission dynamics and control of hepatitis B virus in China

Hepatitis B is a potentially life-threatening liver infection caused by the hepatitis B virus (HBV) and is a major global health problem. HBV is the most common serious viral infection and a leading cause of death in mainland China. Around 130 million people in China are carriers of HBV, almost a third of the people infected with HBV worldwide and about 10% of the general population in the country; among them 30 million are chronically infected. Every year, 300,000 people die from HBV-related diseases in China, accounting for 40-50% of HBV-related deaths worldwide. Despite an effective vaccination program for newborn babies since the 1990s, which has reduced chronic HBV infection in children, the incidence of hepatitis B is still increasing in China. We propose a mathematical model to understand the transmission dynamics and prevalence of HBV infection in China. Based on the data reported by the Ministry of Health of China, the model provides an approximate estimate of the basic reproduction number R₀=2.406. This indicates that hepatitis B is endemic in China and is approaching its equilibrium with the current immunization program and control measures. Although China made a great progress in increasing coverage among infants with hepatitis B vaccine, it has a long and hard battle to fight in order to significantly reduce the incidence and eventually eradicate the virus.     

人口流动性对感染性疾病扩散与传播的影响

研究人口流动性对具有斑快结构的感染性疾病传播与扩散的影响,讨论了具有斑块结构感染性疾病SIS模型的全局稳定性,得到了该模型基本再生数的倍增效应．     

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

A precise definition of the basic reproduction number, , is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if , then the disease free equilibrium is locally asymptotically stable; whereas if , then it is unstable. Thus, is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for near one. This criterion, together with the definition of , is illustrated by treatment, multigroup, staged progression, multistrain and vector–host models and can be applied to more complex models. The results are significant for disease control.     

Modelling effects of habitat fragmentation on the ability of trees to respond to climatic warming

The ability of trees to migrate in response to climatic warming was simulated under various conditions of habitat availability. The model uses Holocene tree migration rates to approximate maximum migration rates in a forested landscape. Habitat availability and local population size was varied systematically under two dispersal and colonization models. These dispersal models varied in the likelihood of long-distance dispersal events. The first model used a negative exponential function that severely limited the probability of long-distance dispersal. The results of this model indicate that migration rate could decline an order of magnitude where the habitat availability is reduced from 80 to 20% of the matrix. The second model, using an inverse power function, carried a higher probability of long-distance dispersal events. The results from this model predict relatively small declines in migration rates when habitat availability is reduced to 50% of the simulation matrix. Below 50% habitat availability, mean migration rate was similar to the negative exponential model. These results predict a failure of many trees to respond to future climatic change through range expansion.     

一类具有常数迁入且总入口在变化的SIRI传染病模型的稳定性

讨论一类具有常数迁入率,染病类有病死且有效接触率依赖于总人数的SIRI传染病模型.给出了基本再生数σ的表达式.如果σ≤1,则疾病消除平衡点是全局稳定的;如果σ＞1,则存在唯一的传染病平衡点且是局部渐近稳定的.对具有双线性传染率和标准传染率的相应模型,进一步证明了当σ＞1时传染病平衡点的全局稳定性.     

Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model

In this paper, we introduce a basic reproduction number for a multi-group SIR model with general relapse distribution and nonlinear incidence rate. We find that basic reproduction number plays the role of a key threshold in establishing the global dynamics of the model. By means of appropriate Lyapunov functionals, a subtle grouping technique in estimating the derivatives of Lyapunov functionals guided by graph-theoretical approach and LaSalle invariance principle, it is proven that if it is less than or equal to one, the disease-free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, some sufficient condition is obtained in ensuring that there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Furthermore, our results suggest that general relapse distribution are not the reason of sustained oscillations. Biologically, our model might be realistic for sexually transmitted diseases, such as Herpes, Condyloma acuminatum, etc.     

Modelling the effects of pre-exposure and post-exposure vaccines in tuberculosis control

Epidemic control strategies alter the spread of the disease in the host population. In this paper, we describe and discuss mathematical models that can be used to explore the potential of pre-exposure and post-exposure vaccines currently under development in the control of tuberculosis. A model with bacille Calmette-Guerin (BCG) vaccination for the susceptibles and treatment for the infectives is first presented. The epidemic thresholds known as the basic reproduction numbers and equilibria for the models are determined and stabilities are investigated. The reproduction numbers for the models are compared to assess the impact of the vaccines currently under development. The centre manifold theory is used to show the existence of backward bifurcation when the associated reproduction number is less than unity and that the unique endemic equilibrium is locally asymptotically stable when the associated reproduction number is greater than unity. From the study we conclude that the pre-exposure vaccine currently under development coupled with chemoprophylaxis for the latently infected and treatment of infectives is more effective when compared to the post-exposure vaccine currently under development for the latently infected coupled with treatment of the infectives.     

Neurotensin: effects of hypothalamic and intravenous injections on eating and drinking in rats

To investigate a role for the brain-gut peptide neurotensin (NT) in ingestive behavior, changes in food and water intake of food-deprived rats were examined following injection of NT into the paraventricular hypothalamic nucleus (PVN) or the mesenteric vein. Unilateral PVN NT (2.5, 5.0, 10.0 micrograms/0.3 microliter) produced substantial dose-dependent reductions in total food intake 0.5, 1, and 4 hr postinjection. In contrast, PVN NT had no effect on water intake and produced no change in grooming, rearing, sleeping, resting or locomotor activity. Bilateral PVN NT at a high dose (10.0 micrograms/side) suppressed consumption of solid or liquid diet in food-deprived rats, but did not affect water intake in water-deprived rats. This specificity is consistent with a role for CNS NT in feeding behavior. Intravenous NT (1-1000 pmole/kg/min for 30 min) did not specifically suppress food intake; however, low doses did increase water intake in food-deprived rats. These findings do not support a role for plasma NT in feeding, but do suggest that it may play a role in drinking behavior.     

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R₀=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R₀) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R₀>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).     

Effects of tick population dynamics and host densities on the persistence of tick-borne infections

The transmission and the persistence of tick-borne infections are strongly influenced by the densities and the structure of host populations. By extending previous models and analysis, in this paper we analyse how the persistence of ticks and pathogens, is affected by the dynamics of tick populations, and by their host densities. The effect of host densities on infection persistence is explored through the analysis and simulation of a series of models that include different assumptions on tick-host dynamics and consider different routes of infection transmission. Ticks are assumed to feed on two types of host species which vary in their reservoir competence. Too low densities of competent hosts (i.e., hosts where transmission can occur) do not sustain the infection cycle, while too high densities of incompetent hosts may dilute the competent hosts so much to make infection persistence impossible. A dilution effect may occur also for competent hosts as a consequence of reduced tick to host ratio; this is possible only if the regulation of tick populations is such that tick density does not increase linearly with host densities.