Mathematical model for Zika virus dynamics with sexual transmission route

Zika virus is a flavivirus transmitted to humans primarily through the bite of infected Aedes mosquitoes. In addition to vector-borne spread, however, the virus can also be transmitted through sexual contact. In this paper, we formulate and analyze a new system of ordinary differential equations which incorporates both vector and sexual transmission routes. Theoretical analysis of this model when there is no disease induced mortality shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the associated reproduction number is less than unity and unstable otherwise. However, when we extend this same model to include Zika induced mortality, which have been documented in Latin America, we find that the model exhibits a backward bifurcation. Specifically, a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. To further explore model predictions, we use numerical simulations to assess the importance of sexual transmission to disease dynamics. This analysis shows that risky behavior involving multiple sexual partners, particularly among male populations, substantially increases the number of infected individuals in the population, contributing significantly to the disease burden in the community.     

A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

Background

Mathematical modeling has become a tool used to address many emerging diseases. One of the most basic and popular modeling frameworks is the compartmental model. Unfortunately, most of the available compartmental models developed for Zika virus (ZIKV) transmission were designed to describe and reconstruct only past, short-time ZIKV outbreaks in which the effects of seasonal change to entomological parameters can be ignored. To make an accurate long-term prediction of ZIKV transmission, the inclusion of seasonal effects into an epidemic model is unavoidable.

Methods

We developed a vector-borne compartmental model to analyze the spread of the ZIKV during the 2015–2016 outbreaks in Bahia, Brazil and to investigate the impact of two vector control strategies, namely, reducing mosquito biting rates and reducing mosquito population size. The model considered the influences of seasonal change on the ZIKV transmission dynamics via the time-varying mosquito biting rate. The model was also validated by comparing the model prediction with reported data that were not used to calibrate the model.

Results

We found that the model can give a very good fit between the simulation results and the reported Zika cases in Bahia (R-square?=?0.9989). At the end of 2016, the total number of ZIKV infected people was predicted to be 1.2087 million. The model also predicted that there would not be a large outbreak from May 2016 to December 2016 due to the decrease of the susceptible pool. Implementing disease mitigation by reducing the mosquito biting rates was found to be more effective than reducing the mosquito population size. Finally, the correlation between the time series of estimated mosquito biting rates and the average temperature was also suggested.

Conclusions

The proposed ZIKV transmission model together with the estimated weekly biting rates can reconstruct the past long-time multi-peak ZIKV outbreaks in Bahia.

     

The effect of sexual transmission on Zika virus dynamics

Journal of Mathematical Biology - Zika virus is a human disease that may lead to neurological disorders in affected individuals, and may be transmitted vectorially (by mosquitoes) or sexually. A...     

The transmission dynamics of a within-and between-hosts malaria model

In this paper, we developed a novel deterministic coupled model tying together the effects of within-host and population level dynamics on malaria transmission dynamics. We develop within-host and within-vector dynamic models, population level between-hosts models, and a nested coupled model combining these levels. The unique feature of this work is the way the coupling and feedback for the model use the various life stages of the malaria parasite both in the human host and the mosquito vector. Analysis of the coupled and the within-human host models indicate the existence of locally asymptotically stable infection- and parasite-free equilibria when the associated reproduction numbers are less than one. The population-level model, on the other hand, exhibits backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium. A global sensitivity analysis was carried out to measure the effects of the sensitivity and uncertainty in the various model parameters estimates. The results indicate that the most important parameters driving the pathogen level within an infected human are the production rate of the red blood cells from the bone marrow, the infection rate, the immunogenicity of the infected red blood cells, merozoites and gametocytes, and the immunosensitivity of the merozoites and gametocytes. The key parameters identified at the population level are the human recovery rate, the death rate of the mosquitoes, the recruitment rate of susceptible humans into the population, the mosquito biting rate, the transmission probabilities per contact in mosquitoes and in humans, and the parasite production and clearance rates in the mosquitoes. Defining the feedback functions as a linear function of the mosquito biting rate, numerical exploration of the coupled model reveals oscillations in the parasite populations within a human host in the presence of the host immune response. These oscillations dampen as the mosquito biting rate increases. We also observed that the oscillation and damping effect seen in the within-human host dynamics fed back into the population level dynamics; this in turn amplifies the oscillations in the parasite population within the mosquito-host.     

寨卡病毒与性传播

寨卡病毒是蚊源性虫媒病毒,归属于黄病毒科黄病毒属。1947年在乌干达寨卡森林的一头哨猴(恒河猴)中首次分离到。上世纪60年代在亚洲和非洲报告有散发性病例。2007年,在密克罗尼西亚雅浦岛发生以发热与皮疹为特征的第一次大流行;2013年10月在法属波利尼西亚发生了南太平洋最大的寨卡病毒爆发流行;在2015年引入巴西的寨卡病毒引起爆发。迄今,巴西已有150万人感染,并扩展到世界上30多个国家,大多数在南美洲。由于在巴西不正常地密集出现新生儿小头畸形,而母亲在孕期曾感染过寨卡病毒,因此世界卫生组织宣布世界范围内流行的寨卡病毒是国际关注的突发公共卫生事件。寨卡病毒感染是酷似登革热的、自限性的发热、皮疹、关节痛综合征,我国称寨卡病毒病。大多数病例是轻症,主要症状是皮疹、发热、关节痛、肌痛、头痛和结膜炎。寨卡病毒自然传播中的媒介为伊蚊,但也存在非生物媒介传播的危险。曾从血清中分离到寨卡病毒,并证实性交传播。最近有更多的由性传播的病例报告。寨卡病毒由病毒携带的男性经性行为传染给女方。如果最近刚从寨卡病毒流行区来的男性,在性生活中应使用安全套;如果女方已经怀孕,最好是放弃性接触,以保护胎儿。     

Periodic oscillations and backward bifurcation in a model for the dynamics of malaria transmission

A deterministic ordinary differential equation model for the dynamics of malaria transmission that explicitly integrates the demography and life style of the malaria vector and its interaction with the human population is developed and analyzed. The model is different from standard malaria transmission models in that the vectors involved in disease transmission are those that are questing for human blood. Model results indicate the existence of nontrivial disease free and endemic steady states, which can be driven to instability via a Hopf bifurcation as a parameter is varied in parameter space. Our model therefore captures oscillations that are known to exist in the dynamics of malaria transmission without recourse to external seasonal forcing. Additionally, our model exhibits the phenomenon of backward bifurcation. Two threshold parameters that can be used for purposes of control are identified and studied, and possible reasons why it has been difficult to eradicate malaria are advanced.     

Global dynamics of a cholera model with age structures and multiple transmission modes

In this paper,we propose and analyze a cholera model.The model incorporates both direct transmission (person-to-person transmission) and indirect transmission (contaminated environment-to-person transmission: hyper-infectivity and lower-infcctivity).Moreover,we employ general nonlinear incidences and introduce infection age of infectious individuals and biological ages of pathogens in the environment.After considering the well-posedness of the system,we study the existence and local stability of steady states,which is determined by the basic reproduction number.To establish the attractivity of the infection steady state,we also get the uniform persistence and existence of compact global attractors.The main result is a threshold dynamics obtained by applying the Fluctuation Lemma and the approach of Lyapunov functionals.When the basic reproduction number is less than one,the infection-free steady state is globally asymptotically stable while when the basic reproduction number is larger than one,the infection steady state attracts each solution with nonzero infection force at some time point.The effect of multiple transmission modes on the disease dynamics is also discussed.     

Stability analysis of a deterministic model of Zika/Dengue co-circulation

We consider a deterministic model of Zika and Dengue viruses co-circulating in a human population. We study the system of differential equations modeling the dynamics of the diseases that can either be transmitted directly (host-to-host) or indirectly (host-vectorhost).We use an SIR model for hosts and an SI model for vectors in the homogeneous populations. The stability of the model has been analyzed both qualitatively and quantitatively.     

Wolbachia strain wAlbA blocks Zika virus transmission in Aedes aegypti

Transinfections of the maternally transmitted endosymbiont Wolbachia pipientis can reduce RNA virus replication and prevent transmission by Aedes aegypti, and also have the capacity to invade wild-type populations, potentially reaching and maintaining high infection frequencies. Levels of virus transmission blocking are positively correlated with Wolbachia intracellular density. Despite reaching high densities in Ae. aegypti, transinfections of wAlbA, a strain native to Aedes albopictus, showed no blocking of Semliki Forest Virus in previous intrathoracic injection challenges. To further characterize wAlbA blocking in Ae. aegypti, adult females were intrathoracically challenged with Zika (ZIKV) and dengue viruses, and then fed a ZIKV-containing bloodmeal. No blocking was observed with either virus when challenged by intrathoracic injection. However, when ZIKV was delivered orally, wAlbA-infected females showed a significant reduction in viral replication and dissemination compared with uninfected controls, as well as a complete absence of virus in saliva. Although other Wolbachia strains have been shown to cause more robust viral blocking in Ae. aegypti, these findings demonstrate that, in principle, wAlbA could be used to reduce virus transmission in this species. Moreover, the results highlight the potential for underestimation of the strength of virus-blocking when based on intrathoracic injection compared with more natural oral challenges.     

Transplacental Zika virus transmission in ex vivo perfused human placentas

A Zika virus (ZIKV) infection during pregnancy can result in severe birth defects such as microcephaly. To date, it is incompletely understood how ZIKV can cross the human placenta. Furthermore, results from studies in pregnant mice and non-human primates are conflicting regarding the role of cross-reactive dengue virus (DENV) antibodies on transplacental ZIKV transmission. Elucidating how ZIKV can cross the placenta and which risk factors contribute to this is important for risk assessment and for potential intervention strategies for transplacental ZIKV transmission. In this study we use an ex vivo human placental perfusion model to study transplacental ZIKV transmission and the effect that cross-reactive DENV antibodies have on this transmission. By using this model, we demonstrate that DENV antibodies significantly increase ZIKV uptake in perfused human placentas and that this increased uptake is neonatal Fc-receptor-dependent. Furthermore, we show that cross-reactive DENV antibodies enhance ZIKV infection in term human placental explants and in primary fetal macrophages but not in primary trophoblasts. Our data supports the hypothesis that presence of cross-reactive DENV antibodies could be an important risk factor for transplacental ZIKV transmission. Furthermore, we demonstrate that the ex vivo placental perfusion model is a relevant and animal friendly model to study transplacental pathogen transmission.     

Molecular genetic data provide support for a model of transmission dynamics in an Australian reptile tick, Bothriocroton hydrosauri

Bothriocroton hydrosauri is a three-host ixodid tick that infests large reptiles in southeastern Australia, where its most common host is a large scincid lizard Tiliqua rugosa . Based on previous ecological and behavioural studies of this system, we propose a 'ripple' model of tick population dynamics, where only a few female ticks succeed in producing surviving offspring. These females then are the centres of ripples of their progeny spreading into the broader landscape. The model predicts higher relatedness among larvae than among nymphs or adults on a host, and significant spatial autocorrelation in larvae extending further than for the later life stages. The model also predicts that adult ticks are likely to encounter related partners and that this will generate inbreeding within the population. We tested those predictions using nine polymorphic microsatellite loci on a sample of 848 ticks (464 larvae, 140 nymphs and 244 adults) collected from 98 lizard hosts from near Bundey Bore Station in South Australia. Our data support the predictions and indicate that the dynamics of transmission among hosts play an important role in parasite population structure.     

A model for aggregation-dispersion dynamics of a population

An important feature that distinguishes the movement of living systems from the random motion of inorganic material is a delicate balance between spreading and concentrating. This movement is based on the kind of interactions which a bacterial colony may establish during migration. Namely, the antagonistic effects of dispersal which take place preferentially down the population gradient and the tendency in grouping together. In this work a model is proposed which considers these effects. The phase plane analysis and the numerical calculations reveal the existence of stable sharp wave front solutions. The speed of the wave front is modulated by the compromise between the tendencies of spreading and aggregating. The results obtained were compared with experimental observations in cultures of Escherichia coli and Streptococcus faecalis. The agreement between both types of results supports the hypothesis on which the model was based.     

A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.     

A model of bi-mode transmission dynamics of hepatitis C with optimal control

In this paper, we present a rigorous mathematical analysis of a deterministic model for the transmission dynamics of hepatitis C. The model is suitable for populations where two frequent modes of transmission of hepatitis C virus, namely unsafe blood transfusions and intravenous drug use, are dominant. The susceptible population is divided into two distinct compartments, the intravenous drug users and individuals undergoing unsafe blood transfusions. Individuals belonging to each compartment may develop acute and then possibly chronic infections. Chronically infected individuals may be quarantined. The analysis indicates that the eradication and persistence of the disease is completely determined by the magnitude of basic reproduction number R _c. It is shown that for the basic reproduction number R _c < 1, the disease-free equilibrium is locally and globally asymptotically stable. For R _c > 1, an endemic equilibrium exists and the disease is uniformly persistent. In addition, we present the uncertainty and sensitivity analyses to investigate the influence of different important model parameters on the disease prevalence. When the infected population persists, we have designed a time-dependent optimal quarantine strategy to minimize it. The Pontryagin’s Maximum Principle is used to characterize the optimal control in terms of an optimality system which is solved numerically. Numerical results for the optimal control are compared against the constant controls and their efficiency is discussed.     

A simulation model of African Anopheles ecology and population dynamics for the analysis of malaria transmission

Background

Malaria is one of the oldest and deadliest infectious diseases in humans. Many mathematical models of malaria have been developed during the past century, and applied to potential interventions. However, malaria remains uncontrolled and is increasing in many areas, as are vector and parasite resistance to insecticides and drugs.

Methods

This study presents a simulation model of African malaria vectors. This individual-based model incorporates current knowledge of the mechanisms underlying Anopheles population dynamics and their relations to the environment. One of its main strengths is that it is based on both biological and environmental variables.

Results

The model made it possible to structure existing knowledge, assembled in a comprehensive review of the literature, and also pointed out important aspects of basic Anopheles biology about which knowledge is lacking. One simulation showed several patterns similar to those seen in the field, and made it possible to examine different analyses and hypotheses for these patterns; sensitivity analyses on temperature, moisture, predation and preliminary investigations of nutrient competition were also conducted.

Conclusions

Although based on some mathematical formulae and parameters, this new tool has been developed in order to be as explicit as possible, transparent in use, close to reality and amenable to direct use by field workers. It allows a better understanding of the mechanisms underlying Anopheles population dynamics in general and also a better understanding of the dynamics in specific local geographic environments. It points out many important areas for new investigations that will be critical to effective, efficient, sustainable interventions.     

Chancroid transmission dynamics: a mathematical modeling approach

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.     

Modelling the transmission dynamics of Theileria annulata: model structure and validation for the Turkish context

A mathematical model that describes the transmission dynamics of Theileria annulata is proposed that consists of 2 host components: the Hyalomma tick population and a compartmental model of T. annulata infection in the cattle population. The model was parameterized using data describing tick infestation and the infection status of cattle in Turkey from 2006 to 2008. The tick attachment rates are highly seasonal and because of the temporal separation of infectious and susceptible ticks virtually all ticks are infected by carrier cattle, so that annual peaks of disease in cattle do not impact on infection in the Hyalomma tick population. The impact of intervention measures that target the tick population both on the host and in the environment and their impact on the transmission of T. annulata were investigated. Interventions that have a limited 'one-off' impact and interventions that have a more permanent impact were both considered. The results from the model show the importance of targeting ticks during the period when they have left their first host as nymphs but have yet to feed on their second host.     

Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.     

How seasonal variations in birth and transmission rates impact population dynamics in a basic SIR model

The changing climate is expected to alter the timings of key events in species life-histories. These shifts are likely to have important consequences for infectious disease dynamics, as the distribution and abundance of host species will lead to a different environment for parasites. Previous work has shown how seasonality in single host traits - most commonly the reproduction rate or transmission rate - can lead to an array of complex epidemiological dynamics, including chaos and multiple-stable states, with changes to the timing and amplitude of the seasonal peaks often driving drastic changes in behaviour. However, more than one life-history trait is likely to be seasonal, and changing environmental conditions may impact each of them in different ways, yet there have been few studies of host-parasite dynamics that include more than one seasonal trait. Here we examine a Susceptible-Infected-Recovered epidemiological model in which both reproduction and transmission exhibit seasonal fluctuations. We examine how the amplitude and timing of these seasonal peaks impact disease dynamics. We show that the relative timing of the two events is key, with the most stable dynamics when births peak a few months before transmission. We also show that chaotic dynamics become more likely when transmission in particular has a high amplitude, and when baseline transmission and virulence are high. Our results emphasise the importance of seasonality and timing of host life-history events to disease dynamics.