A two-age-classes dengue transmission model

In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination.     

Spatial simulation of malaria transmission and its control by malaria transmission blocking vaccination

A simple, visual representation of spatial aspects of malaria transmission in successive snap-shots in time, is presented. The spatial components of the simulation involve (i) the identification of mosquito vector breeding sites of defined shape and area, (ii) the identification of a zone of malaria transmission determined by the shapes and areas of the vector breeding sites and the distance from these sites that the mosquitoes disperse, (iii) a human population dispersed in relation to the malaria transmission zone, (iv) perimeters around each individual human within which his or her infection can be transmitted by the local vector mosquitoes. The intensity of transmission within a malaria transmission zone is given by a number which is the number of new cases of malaria that each existing case will distribute through the human population within the duration of an infection. The simulation has been used here to examine the effects of vaccination against malaria transmission. Different levels of vaccine coverage are represented under endemic and epidemic malaria. The consequences of full or partial coverage of a zone of malaria transmission are also examined. The results are numerically compatible with the predictions of previous simple mathematical simulations of malaria transmission and interventions. The present simulation allows the nature of malaria transmission and the effects of interventions to be communicated easily and directly to an audience. It could have practical value in discussions of malaria control strategies with health planners.     

Synthetic propeptide inhibits mosquito midgut chitinase and blocks sporogonic development of malaria parasite

Incessant transmission of the parasite by mosquitoes makes most attempts to control malaria fail. Blocking of parasite transmission by mosquitoes therefore is a rational strategy to combat the disease. Upon ingestion of blood meal mosquitoes secrete chitinase into the midgut. This mosquito chitinase is a zymogen which is activated by the removal of a propeptide from the N-terminal. Since the midgut peritrophic matrix acts as a physical barrier, the activated chitinase is likely to contribute to the further development of the malaria parasite in the mosquito. Earlier it has been shown that inhibiting chitinase activity in the mosquito midgut blocked sporogonic development of the malaria parasite. Since synthetic propeptides of several zymogens have been found to be potent inhibitors of their respective enzymes, we tested propeptide of mosquito midgut chitinase as an inhibitor and found that the propeptide almost completely inhibited the recombinant or purified native Anopheles gambiae chitinase. We also examined the effect of the inhibitory peptide on malaria parasite development. The result showed that the synthetic propeptide blocked the development of human malaria parasite Plasmodium falciparum in the African malaria vector An. gambiae and avian malaria parasite Plasmodium gallinaceum in Aedes aegypti mosquitoes. This study implies that the expression of inhibitory mosquito midgut chitinase propeptide in response to blood meal may alter the mosquito's vectorial capacity. This may lead to developing novel strategies for controlling the spread of malaria.     

An SIS patch model with variable transmission coefficients

In this paper, an SIS patch model with non-constant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. The basic reproduction number R₀ is determined. It is shown that the disease-free equilibrium is globally asymptotically stable if R₀?1, and the disease is uniformly persistent and there exists at least one endemic equilibrium if R₀>1. In particular, when the disease is non-fatal and the travel rates of susceptible and infectious individuals in each patch are the same, the endemic equilibrium is unique and is globally asymptotically stable as R₀>1. Numerical calculations are performed to illustrate some results for the case with two patches.     

Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas

We present a mathematical model for malaria treatment and spread of drug resistance in an endemic population. The model considers treated humans that remain infectious for some time and partially immune humans who are also infectious to mosquitoes although their infectiousness is always less than their non immune counterparts. The model is formulated by considering delays in the latent periods in both mosquito and human populations and in the period within which partial immunity is lost. Qualitative analysis of the model including positivity and boundedness of solutions is performed. Analysis of the reproductive numbers shows that if the treated humans become immediately uninfectious to mosquitoes then treatment will always reduce the number of sensitive infections. If however treated humans are infectious then for treatment to effectively reduce the number of sensitive infections, the ratio of the infectious period of the treated humans to the infectious period of the untreated humans multiplied by the ratio of the transmission rate from a treated human to the transmission rate of an untreated human should be less than one. Our results show that the spread of drug resistance with treatment as a control strategy depends on the ratio of the infectious periods of treated and untreated humans and on the transmission rates from infectious humans with resistant and sensitive infections. Numerical analysis is performed to assess the effects of treatment on the spread of resistance and infection. The study provides insight into the possible intervention strategies to be employed in malaria endemic populations with resistant parasites by identifying important parameters.     

A model for predicting the transmission rate of malaria from serological data

A model is developed to estimate the duration for which malaria antibody levels in the blood remain high in a closed population. This estimate can be used to calculate the transmission rate within a region, in conjunction with the serological information contained in the population. The model is used on data obtained from a study of malaria in the Philippines and shows excellent agreement. It is subsequently utilised for predictions and seems to be an appropriate vehicle for this purpose.     

The dilution effect of the domestic animal population on the transmission of P. vivax malaria

The diversion of disease carrying insect from humans to animals may reduce transmission of diseases such as malaria. The use of animals to mitigate mosquito bites on human is called ‘zooprophylaxis’. We introduce a mathematical model for Plasmodium vivax malaria transmission with two bloodmeal hosts (humans and domestic animals) to study the effect of zooprophylaxis. After computing the basic reproduction number from the proposed model, we explore how perturbations in the parameters, sensitive to the effects of control measures, affect its value. Zooprophylaxis is shown to determine whether a basic reproduction becomes bigger than an outbreak threshold value or not. Sensitivity analysis shows that increasing the relative animal population size works better in P. vivax malaria control than decreasing the mosquito population when the relative animal population size is larger than a threshold value.     

Dynamics of malaria transmission model with sterile mosquitoes

In this paper, a malaria transmission model with sterile mosquitoes is considered. We first formulate a simple SEIR malaria transmission model as our baseline model. Then sterile mosquitoes are introduced into the baseline model. We consider the case that the release rate of sterile mosquitoes is proportional to the wild mosquito population size. To investigate the impact of releasing sterile mosquitoes on the malaria transmission, the dynamics of the baseline model and the models with the sterile mosquitoes are discussed. We derive formulas of the reproductive numbers and explore the existence of endemic equilibrium as the reproductive number is more than unity for these models. It is shown that both the baseline model and the models with the sterile mosquitoes undergo backward bifurcations. Based on theoretical analysis and numerical simulation, we investigate the impact of releasing sterile mosquitoes on malaria transmission.     

Diel timing and frequency of sugar feeding in the mosquito Anopheles gambiae, depending on sex, gonotrophic state and resource availability

Little is known about the sugar-feeding behaviour of equatorial Africa's principal vector of malaria, Anopheles gambiae Giles (Diptera: Culicidae). It is suspected to feed on plant sugar infrequently, but possibly the timing depends on environmental circumstances, and males may differ markedly from females. These points of uncertainty were clarified in the laboratory, by monitoring both diel and longterm sugar-feeding activity in both sexes. Males fed on sugar in a nocturnal diel rhythm closely approximating non-specific flight activity. Female diel sugar-feeding patterns resembled published rhythms and cycles of host seeking. Males sugar fed nightly at an average frequency of about twice per night, sustained over 17 days. This was substantially higher than the sugar-feeding frequency of females that were allowed both blood and oviposition sites every night: they averaged about one sugar feed in every 4 nights. These females fed on sugar between gonotrophic cycles, after eggs were mature but before the next bloodmeal. They did not sugar feed during the 2 days after blood feeding, while blood was being digested and the eggs developed. A slight delay in the availability of either the oviposition site or blood led to an increase in female sugar-feeding frequency: they averaged more than once per night until the delayed resource was made available. These observations support the conclusion that sugar feeding is a normal part of the biology of both sexes of An. gambiae.     

A model for the control of malaria using genetically modified vectors

Recent works have considered the problem of using transgenic mosquitoes to control a malaria epidemic. These insects have been genetically engineered to reduce their capacity to infect humans with malaria parasites. We analyze a model of the mosquito population dynamics when genetically modified individuals are introduced into a wild type population so that the effect of their introduction can be assessed. The model describes the dynamics of gene selection under sexual reproduction in a closed vector population. Our results show that the fitness of the resulting heterozygous population is the key parameter for the success of the invasion, independently of the fitness of homozygous vectors. The vector population dynamics model is then combined with an epidemiological model to study the feasibility of controlling a malaria epidemic. Basic reproductive numbers are calculated for both models, and conditions are obtained for preventing reappearance of the epidemic. Simulations on this model show that it may be possible to reduce or even eradicate the epidemic only if the heterozygous population is better adapted than the wild type. They also show that this can be achieved without completely eliminating the wild type mosquitoes.     

A qualitative analysis of a model for the transmission of varicella-zoster virus

Varicella-zoster virus (VZV) is a herpesvirus which is the known agent for causing varicella (chickenpox) in its initial manifestation and zoster (shingles) in a reactivated state. The standard SEIR compartmental model is modified to include the cycle of shingles acquisition, recovery, and possible reacquisition. The basic reproduction number R(0) shows the influence of the zoster cycle and how shingles can be important in maintaining VZV in populations. The model has the typical threshold behavior in the sense that when R(0)1, the virus persists over time and so chickenpox and shingles remain endemic.     

Dynamical behavior of a hepatitis B virus transmission model with vaccination

Hepatitis B virus (HBV) infection is a globally health problem. In 2005, the WHO Western Pacific Regional Office set a goal of reducing chronic HBV infection rate to less than 2% among children five years of age by 2012, as an interim milestone towards the final goal of less than 1%. Many countries made some plans (such as free HBV vaccination program for all neonates in China now) to control the transmission HBV. We develop a model to explore the impact of vaccination and other controlling measures of HBV infection. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R₀≤1, and a globally asymptotically stable endemic equilibrium when R₀>1. Numerical simulation results show that the vaccination is a very effective measure to control the infection and they also give some useful comments on controlling the transmission of HBV.     

Trapping oestrid parasites of reindeer: the relative age, fat body content and gonotrophic conditions of Cephenemyia trompeand Hypoderma tarandifemales caught in baited traps

Abstract. Dissection of flies caught in northern Norway revealed that only mated, gravid females of H.tarandi (L.) and larviparous C.trompe (Modeer) were caught in host-mimicking C0₂-baited traps. Trapped females had the same gonotrophic and fat body (FB) conditions as females caught on and around reindeer. Most trapped females of both species were of middle to old age, having only one-half to no FB reserves left and only a few to moderate numbers of eggs or larvae remaining. Most young females trapped also had previously oviposited or larviposited at least once, and some newly eclosed, mated females were present throughout the fly season. Based on the known location of reindeer herds, it was evident that trapped flies that had recently oviposited or larviposited had dispersed into the trapping area from 25–100 km away. Declining FB reserves sustained wild-caught C.trompe females (and in utero larvae) in the laboratory for 14 days and H.tarandi females for 18 days. Reserve FB also was depleted during long flights. Females of both species that flew for the longest times (5.1–11.7 h) on a laboratory flight mill had low FB reserves, but nearly maximum numbers of eggs or larvae. Conversely, most females that flew for less than 5 h on the flight mill had little or no FB remaining, and few eggs or larvae. The large FB reserves accumulated as larvae feed in the vertebrate host enable the non-feeding adults to survive and infect their hosts even after prolonged periods of flight-inhibiting climatic conditions.     

An SEIS epidemic model with transport-related infection

In this paper, an SEIS epidemic model is proposed to study the effect of transport-related infection on the spread and control of infectious disease. New result implies that traveling of the exposed (means exposed but not yet infectious) individuals can bring disease from one region to other regions even if the infectious individuals are inhibited from traveling among regions. It is shown that transportation among regions will change the disease dynamics and break infection out even if infectious diseases will go to extinction in each isolated region without transport-related infection. In addition, our analysis shows that transport-related infection intensifies the disease spread if infectious diseases break out to cause an endemic situation in each region, in the sense of that both the absolute and relative size of patients increase. This suggests that it is very essential to strengthen restrictions of passengers once we know infectious diseases appeared.     

A model for influenza with vaccination and antiviral treatment

Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models.