On the solution of mathematical models of herd immunity in human helminth infections

The general solution of the mathematical model of herd immunity to human helminth infections recently proposed by Anderson and May [3] is obtained. The numerical solution of a more accurate biological model is indistinguishable from the corresponding exact solution of a more tractable mathematical model. Computer simulations of some particular cases of this model support the notion that both ecological and immunological factors determine the observed convex patterns of age-prevalence and age-intensity curves of human helminth infections.This work was made thanks to the advise and support of Dr. Robert M. May while the author was Postdoctoral Fellow at Princeton University     

Analysis of a disease transmission model in a population with varying size

An S I R S epidemiological model with vital dynamics in a population of varying size is discussed. A complete global analysis is given which uses a new result to establish the nonexistence of periodic solutions. Results are discussed in terms of three explicit threshold parameters which respectively govern the increase of the total population, the existence and stability of an endemic proportion equilibrium and the growth of the infective population. These lead to two distinct concepts of disease eradication which involve the total number of infectives and their proportion in the population.Partially supported by NSF Grant No. DMS-8703631. This work was done while this author was visiting the University of VictoriaResearch supported in part by NSERC A-8965     

A threshold result for an epidemiological model

A threshold parameter R ₀ is identified for an SIRS epidemiological model which has nonlinear incidence and a distributed delay for transfer out of the removed class. For R ₀ < 1, the disease free equilibrium is proved to be the global attractor for all solutions.Research supplied in part by NSERC A-8965     

Some epidemiological models with nonlinear incidence

Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the equilibria and stability are investigated, it is found that multiple equilibria exist for some parameter values and periodic solutions can arise by Hopf bifurcation from the larger endemic equilibrium. Many results analogous to those in the first model are obtained for the second model which has a delay in the removed class but no exposed class.Research supported in part by Centers for Disease Control Contract 200-87-0515. Support services provided at University House Research Center at the University of IowaResearch supported in part by NSERC A-8965 and the University of Victoria President's Committee on Faculty Research and Travel     

On some formulas in a partnership model from the perspective of a semi-Markov process

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways,for extensions to the age-dependent case.This research was partially supported by NATO Grant D.890350     

Modelling the effect of treatment and behavioral change in HIV transmission dynamics

In this paper we analyze a model for the HIV-infection transmission in a male homosexual population. In the model we consider two types of infected individuals. Those that are infected but do not know their serological status and/or are not under any sort of clinical /therapeutical treatment, and those who are. The two groups of infectives differ in their incubation time, contact rate with susceptible individuals, and probability of disease transmission. The aim of this article is to study the roles played by detection and changes in sexual behavior in the incidence and prevalence of HIV. The analytical results show that there exists a unique endemic equilibrium which is globally asymptotically stable under a range of parameter values whenever a detection /treatment rate and an indirect measure of the level of infection risk are sufficiently large. However, any level of detection/ treatment rate coupled with a decrease of the transmission probability lowers the incidence rate and prevalence level in the population. In general, only significant reductions in the transmission probability (achieved through, for example, the adoption of safe sexual practices) can contain effectively the spread of the disease.     

The effect of immunosuppression on secondary Echinococcus multilocularis infections in mice.

Baron R. W. and Tanner C. E. 1976. The effect of immunosuppression on secondary Echinococcus multilocularis infections in mice. International Journal for Parasitology6: 37–42. The growth of cysts of Echinococcus multilocularis in T-cell depleted A/J mice was studied. Adult thymectomy enhances the metastasis of hydatid cysts but does not significantly affect the total cyst weight. Combined thymectomy and antithymocyte serum (ATS) treatment also increases the metastatic dissemination of the parasite and also significantly increases cyst loads. It is suggested that cell-mediated immunity controls the early phase of Echinococcus infection.     

Peritoneal mesothelioma mortality in Italy: Spatial analysis and search for asbestos exposure sources

BackgroundThis study is part of a national plan of epidemiological surveillance of malignant mesothelioma (MM) mortality in Italy. The paper shows the results of malignant peritoneal mesothelioma (MPeM) mortality study in Italian Regions and municipalities.MethodsNational Bureau of Statistics data for MPeM municipal mortality (ICD-10, Code C45.1) were analyzed in the time-window 2003–2014: mortality standardized rates (reference Italian population, census 2011), temporal trends of the annual national rates, Standardized Mortality Ratios and a municipal clustering analysis were performed.Results747 deaths for MPeM were recorded (0.10/100,000): 464 in men (0.14/100,000) and in 283 women (0.07/100,000). No significant MPeM mortality temporal trend was found.Seventeen municipalities showed excesses of mortality for MPeM in at least one gender and/or overall population.Four clusters in male population, and one in women were identified.ConclusionsThe study identifies some areas where remediation activities and/or health care actions may be warranted.     

Aedes albopictus oviposits with other Aedes species in artificial oviposition cups: a case study in Knox County,Tennessee, U.S.A.

Interspecific associations between two mosquito species can lead to effects such as competition, species displacement, and species stability. To better understand Aedes albopictus (Skuse) and other Aedes species, we monitored eggs in artificial oviposition cups (ovitraps) within Knox County, TN, U.S.A., during the 2016 and 2017 mosquito seasons. In 2016, one black and one white ovitrap were placed at 18 sites for 21 weeks, while in 2017 black and white ovitraps baited with grass‐infused or deionized water were placed at 11 sites for nine weeks. Eggs were identified to species and resulting counts were used to determine the degree of interspecific association using Cole's coefficients (C₇) and the degree of heterogeneity across space and time using generalized linear mixed models (GLMM). Here, Aedes mosquitoes are generally ovipositing in black cups with grass‐infused water, and Ae. albopictus eggs co‐occurred with other Aedes species more often than would be expected. Finding a positive significant interspecific association between Ae. albopictus and other Aedes eggs suggests that methods used to control Ae. albopictus may also control other Aedes mosquitoes. Finding that Ae. albopictus co‐occurs with other Aedes mosquitoes warrants additional research to evaluate outcomes associated with co‐occurrence within the study area.     

Elimination of Aedes aegypti in northern Australia, 2004–2006

The Northern Territory (NT) of Australia is currently free of the dengue mosquito Aedes (Stegomyia) aegypti (L). However, on 17 February 2004, two Ae. aegypti adults were captured in two routine CO₂‐baited encephalitis virus surveillance traps in Tennant Creek, located 990 km south of Darwin in the NT. The detection triggered an immediate survey and control response undertaken by the NT Department of Health and Community Services, followed by a Commonwealth of Australia‐funded Ae. aegypti elimination program. This report details the methods and results of the detection and subsequent elimination activities that were carried out between 2004 and 2006, returning the NT to its dengue vector‐free status. There have been very few successful Ae. aegypti elimination programs in the world. This purposeful mosquito elimination for Australia was officially declared on 5 April 2006.