26536486
Modeling co-infection of Ixodes tick-borne pathogens.
Ticks, including the Ixodes ricinus and Ixodes scapularis hard tick species, are regarded as the most common arthropod vectors of both human and animal diseases in Europe and the United States capable of transmitting a large number of bacteria, viruses and parasites. Since ticks in larval and nymphal stages share the same host community which can harbor multiple pathogens, they may be co-infected with two or more pathogens, with a subsequent high likelihood of co-transmission to humans or animals. This paper is devoted to the modeling of co-infection of tick-borne pathogens, with special focus on the co-infection of Borrelia burgdorferi (agent of Lyme disease) and Babesia microti (agent of human babesiosis). Considering the effect of co-infection, we illustrate that co-infection with B. burgdorferi increases the likelihood of B. microti transmission, by increasing the basic reproduction number of B. microti below the threshold smaller than one to be possibly above the threshold for persistence. The study confirms a mechanism of the ecological fitness paradox, the establishment of B. microti which has weak fitness (basic reproduction number less than one). Furthermore, co-infection could facilitate range expansion of both pathogens.
27222897
Coinfecting deer-associated zoonoses: Lyme disease, babesiosis, and ehrlichiosis.
The heightened worldwide recognition of the health burden of tickborne infection derives largely from the increasing incidence of Lyme disease, human babesiosis, and human granulocytic ehrlichiosis, both individually and in concert. Because these infections share the same rodent reservoir and tick vector hosts, they can be cotransmitted to human hosts. Indeed, human coinfections involving various combinations of these pathogens are common, and some tend to be particularly severe. Diagnostic procedures and clinical management of the resulting disease syndrome is rendered complex by the diversity of pathogens involved and by the unusual diversity and duration of symptoms.
8691889
Immunoserologic evidence of coinfection with Borrelia burgdorferi, Babesia microti, and human granulocytic Ehrlichia species in residents of Wisconsin and Minnesota
In Wisconsin and Minnesota, Ixodes scapularis (Ixodes dammini) ticks are the vector of three microorganisms that may cause significant disease in humans and lower mammals. These diseases include Lyme borreliosis, which is caused by Borrelia burgdorferi, babesiosis, which is caused by Babesia microti, and human granulocytic ehrlichiosis (HGE), which is caused by an apparently new species in the genus Ehrlichia. Immunoserologic testing was performed on sera from patients with a diagnosis of one of these diseases to determine if there was evidence of coinfection with one or more of the other agents. Of 96 patients with Lyme borreliosis, 9 (9.4%) demonstrated immunoserologic evidence of coinfection: 5 (5.2%) with the agent of HGE, 2 (2.1%) with B. microti, and 2 (2.1%) with both microorganisms. Of 19 patients diagnosed with HGE, 3 (15.8%) showed immunoserologic evidence of coinfection: 1 (5.3%) with B. burgdorferi, 1 (5.3%) with B. microti, and 1 (5.3%) with both microorganisms. One patient diagnosed with babesiosis was also seropositive for ehrlichiosis. These results provide evidence for coinfection, perhaps explaining the variable manifestations and clinical responses noted in some patients with tick-transmitted diseases. In certain clinical settings, laboratory testing for coinfection is indicated to ensure that appropriate antimicrobial treatment is given.
5922905
Risk maps for range expansion of the Lyme disease vector, Ixodes scapularis, in Canada now and with climate change
BackgroundLyme disease is the commonest vector-borne zoonosis in the temperate world, and an emerging infectious disease in Canada due to expansion of the geographic range of the tick vector Ixodes scapularis. Studies suggest that climate change will accelerate Lyme disease emergence by enhancing climatic suitability for I. scapularis. Risk maps will help to meet the public health challenge of Lyme disease by allowing targeting of surveillance and intervention activities.ResultsA risk map for possible Lyme endemicity was created using a simple risk algorithm for occurrence of I. scapularis populations. The algorithm was calculated for each census sub-division in central and eastern Canada from interpolated output of a temperature-driven simulation model of I. scapularis populations and an index of tick immigration. The latter was calculated from estimates of tick dispersion distances by migratory birds and recent knowledge of the current geographic range of endemic I. scapularis populations. The index of tick immigration closely predicted passive surveillance data on I. scapularis occurrence, and the risk algorithm was a significant predictor of the occurrence of I. scapularis populations in a prospective field study. Risk maps for I. scapularis occurrence in Canada under future projected climate (in the 2020s, 2050s and 2080s) were produced using temperature output from the Canadian Coupled Global Climate Model 2 with greenhouse gas emission scenario enforcing 'A2' of the Intergovernmental Panel on Climate Change.ConclusionWe have prepared risk maps for the occurrence of I. scapularis in eastern and central Canada under current and future projected climate. Validation of the risk maps provides some confidence that they provide a useful first step in predicting the occurrence of I. scapularis populations, and directing public health objectives in minimizing risk from Lyme disease. Further field studies are needed, however, to continue validation and refinement of the risk maps.
3650331
Coinfection by Ixodes Tick-Borne Pathogens: Ecological, Epidemiological, and Clinical Consequences.
Ixodes ticks maintain a large and diverse array of human pathogens in the enzootic cycle, including Borrelia burgdorferi and Babesia microti. Despite the poor ecological fitness of B. microti, babesiosis has recently emerged in areas endemic for Lyme disease. Studies in ticks, reservoir hosts, and humans indicate that coinfection with B. burgdorferi and B. microti is common, promotes transmission and emergence of B. microti in the enzootic cycle, and causes greater disease severity and duration in humans. These interdisciplinary studies may serve as a paradigm for the study of other vector-borne coinfections. Identifying ecological drivers of pathogen emergence and host factors that fuel disease severity in coinfected individuals will help guide the design of effective preventative and therapeutic strategies.
27095760
A model for the coupled disease dynamics of HIV and HSV-2 with mixing among and between genders.
Evidence indicates that those with genital herpes (HSV-2) infections have greater risks of infection by HIV; and, once co-infected, are more likely to transmit HIV. To better understand the interactions between HIV and HSV-2, we construct a mathematical model that describes the joint dynamics. A new feature of this model is the inclusion of both heterosexual and homosexual interactions. We derive and interpret the basic and invasion reproduction numbers for HIV and HSV-2 using the approach of next-generation matrices. We then perform scenario analyses and conduct a sensitivity analysis to investigate the impact of the model parameters on the reproduction numbers and disease prevalences. We conclude that homosexual transmission drastically changes the disease prevalences; hence, it is important to account for this interaction as models that ignore homosexuality may greatly underestimate the disease burden.
25367173
Coinfection Dynamics of Two Diseases in a Single Host Population.
A susceptible-infectious-susceptible (SIS) epidemic model that describes the coinfection and cotransmission of two infectious diseases spreading through a single population is studied. The host population consists of two subclasses: susceptible and infectious, and the infectious individuals are further divided into three subgroups: those infected by the first agent/pathogen, the second agent/pathogen, and both. The basic reproduction numbers for all cases are derived which completely determine the global stability of the system if the presence of one agent/pathogen does not affect the transmission of the other. When the constraint on the transmissibility of the dually infected hosts is removed, we introduce the invasion reproduction number, compare it with two other types of reproduction number and show the uniform persistence of both diseases under certain conditions. Numerical simulations suggest that the system can display much richer dynamics such as backward bifurcation, bistability and Hopf bifurcation.
25991284
Modeling malaria and typhoid fever co-infection dynamics.
Malaria and typhoid are among the most endemic diseases, and thus, of major public health concerns in tropical developing countries. In addition to true co-infection of malaria and typhoid, false diagnoses due to similar signs and symptoms and false positive results in testing methods, leading to improper controls, are the major challenges on managing these diseases. In this study, we develop novel mathematical models describing the co-infection dynamics of malaria and typhoid. Through mathematical analyses of our models, we identify distinct features of typhoid and malaria infection dynamics as well as relationships associated to their co-infection. The global dynamics of typhoid can be determined by a single threshold (the typhoid basic reproduction number, R0(T)) while two thresholds (the malaria basic reproduction number, R0(M), and the extinction index, R0(MM)) are needed to determine the global dynamics of malaria. We demonstrate that by using efficient simultaneous prevention programs, the co-infection basic reproduction number, R0, can be brought down to below one, thereby eradicating the diseases. Using our model, we present illustrative numerical results with a case study in the Eastern Province of Kenya to quantify the possible false diagnosis resulting from this co-infection. In Kenya, despite having higher prevalence of typhoid, malaria is more problematic in terms of new infections and disease deaths. We find that false diagnosis-with higher possible cases for typhoid than malaria-cause significant devastating impacts on Kenyan societies. Our results demonstrate that both diseases need to be simultaneously managed for successful control of co-epidemics.
14785324
Modelling Co-Infection with Malaria and Lymphatic Filariasis
Malaria and lymphatic filariasis (LF) continue to cause a considerable public health burden globally and are co-endemic in many regions of sub-Saharan Africa. These infections are transmitted by the same mosquito species which raises important questions about optimal vector control strategies in co-endemic regions, as well as the effect of the presence of each infection on endemicity of the other; there is currently little consensus on the latter. The need for comprehensive modelling studies to address such questions is therefore significant, yet very few have been undertaken to date despite the recognised explanatory power of reliable dynamic mathematical models. Here, we develop a malaria-LF co-infection modelling framework that accounts for two key interactions between these infections, namely the increase in vector mortality as LF mosquito prevalence increases and the antagonistic Th1/Th2 immune response that occurs in co-infected hosts. We consider the crucial interplay between these interactions on the resulting endemic prevalence when introducing each infection in regions where the other is already endemic (e.g. due to regional environmental change), and the associated timescale for such changes, as well as effects on the basic reproduction number R0 of each disease. We also highlight potential perverse effects of vector controls on human infection prevalence in co-endemic regions, noting that understanding such effects is critical in designing optimal integrated control programmes. Hence, as well as highlighting where better data are required to more reliably address such questions, we provide an important framework that will form the basis of future scenario analysis tools used to plan and inform policy decisions on intervention measures in different transmission settings.
2315902
Implication of vaccination against dengue for Zika outbreak
Zika virus co-circulates with dengue in tropical and sub-tropical regions. Cases of co-infection by dengue and Zika have been reported, the implication of this co-infection for an integrated intervention program for controlling both dengue and Zika must be addressed urgently. Here, we formulate a mathematical model to describe the transmission dynamics of co-infection of dengue and Zika with particular focus on the effects of Zika outbreak by vaccination against dengue among human hosts. Our analysis determines specific conditions under which vaccination against dengue can significantly increase the Zika outbreak peak, and speed up the Zika outbreak peak timing. Our results call for further study about the co-infection to direct an integrated control to balance the benefits for dengue control and the damages of Zika outbreak.
36266953
Delay differential systems for tick population dynamics
Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks. Here, we formulate a system of delay differential equations which models the stage structure of the tick population. Temperature can alter the length of time delays in each developmental stage, and so the time delays can vary geographically (and seasonally which we do not consider). We define the basic reproduction number $${\mathcal R}_0$$R0 of stage structured tick populations. The tick population is uniformly persistent if $${\mathcal R}_0>1$$R0>1 and dies out if $${\mathcal R}_0<1$$R0<1. We present sufficient conditions under which the unique positive equilibrium point is globally asymptotically stable. In general, the positive equilibrium can be unstable and the system show oscillatory behavior. These oscillations are primarily due to negative feedback within the tick system, but can be enhanced by the time delays of the different developmental stages.
24583366
Developing a temperature-driven map of the basic reproductive number of the emerging tick vector of Lyme disease Ixodes scapularis in Canada.
A mechanistic model of the tick vector of Lyme disease, Ixodes scapularis, was adapted to a deterministic structure. Using temperature normals smoothed by Fourier analysis to generate seasonal temperature-driven development rates and host biting rates, and a next generation matrix approach, the model was used to obtain values for the basic reproduction number (R(0)) for I. scapularis at locations in southern Canada where the tick is established and emerging. The R(0) at Long Point, Point Pelee and Chatham sites where I. scapularis are established, was estimated at 1.5, 3.19 and 3.65, respectively. The threshold temperature conditions for tick population survival (R(0)=1) were shown to be the same as those identified using the mechanistic model (2800-3100 cumulative annual degree days >0°C), and a map of R(0) for I. scapularis, the first such map for an arthropod vector, was drawn for Canada east of the Rocky Mountains. This map supports current risk assessments for Lyme disease risk emergence in Canada. Sensitivity analysis identified host abundance, tick development rates and summer temperatures as highly influential variables in the model, which is consistent with our current knowledge of the biology of this tick. The development of a deterministic model for I. scapularis that is capable of providing values for R(0) is a key step in our evolving ability to develop tools for assessment of Lyme disease risk emergence and for development of public health policies on surveillance, prevention and control.
121654204
Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds
Recent studies have suggested that the risk of exposure to Lyme disease is emerging in Canada because of the expanding range of I. scapularis ticks. The wide geographic breeding range of I. scapularis-carrying migratory birds is consistent with the widespread geographical occurrence of I. scapularis in Canada. However, how important migratory birds from the United States are for the establishment and the stable endemic transmission cycle of Lyme disease in Canada remains an issue of theoretical challenge and practical significance. In this paper, we design and analyze a periodic model of differential equations with a forcing term modeling the annual bird migration to address the aforementioned issue. Our results show that ticks can establish in any migratory bird stopovers and breeding sites. Moreover, bird-transported ticks may increase the probability of B. 
burgdorferi establishment in a tick-endemic habitat.
37208956
Stability and persistence in ODE models for populations with many stages.
A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
9272867
The construction of next-generation matrices for compartmental epidemic models
The basic reproduction number ℛ0 is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of ℛ0 where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of ℛ0. We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number ℛ0. Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that ℛ0 defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that ℛ0 > 1 if and only if r > 0, and ℛ0 = 1 if and only if r = 0.
17313221
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.
A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable. Thus, R0 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 R0 near one. This criterion, together with the definition of R0, 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.
15552602
GLOBAL ASYMPTOTIC BEHAVIOR IN SOME COOPERATIVE SYSTEMS OF FUNCTIONAL DIFFERENTIAL EQUATIONS
This paper is devoted to the study of global asymptotic behavior in some cooperative systems of functional differential equations. We first prove a general global result for both discrete-time and continuous dynamical systems on the subset of a strongly ordered Banach space. Then we discuss cooperative systems of functional differential equations and further obtain a threshold theorem on their global asymptotic behavior under the sublinearity assumption. Finally, we give some application examples in epidemic and population dynamics. Some related earlier results are generalized and improved.
123574961
Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
Conditions are presented under which the solutions of asymptotically autonomous differential equations have the same asymptotic behavior as the solutions of the associated limit equations. An example displays that this does not hold in general.
121024940
Chain Transitivity, Attractivity, and Strong Repellors for Semidynamical Systems
Some properties of internally chain transitive sets for continuous maps in metric spaces are presented. Applications are made to attractivity, convergence, strong repellors, uniform persistence, and permanence. A result of Schreiber on robust permanence is improved.
117466402
Dynamical systems in population biology
Introduction.- Discrete Dynamical Systems.- Monotone Dynamics.- Nonautonomous Semiflows.- A Discrete-time Chemostat Model.- N-species Competition in a Periodic Chemostat.- Almost Periodic Competitive Systems.- Competitor-Competitor-Mutualist Systems.- A Periodically Pulsed Bioreactor Model.- A Nonlocal and Delayed Predator-Prey Model.- Traveling Waves in Bistable Nonlinearities.- Bibliography.- Index.
18695464
A PERIODIC ROSS-MACDONALD MODEL IN A PATCHY ENVIRONMENT.
Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number [Formula: see text] and show that either the disease-free periodic solution is globally asymptotically stable if [Formula: see text] or the positive periodic solution is globally asymptotically stable if [Formula: see text]. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.
43863630
Modelling Malaria Control by Introduction of Larvivorous Fish
Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host–vector interaction and the predator–prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.
8820835
Co-Infection of Blacklegged Ticks with Babesia microti and Borrelia burgdorferi Is Higher than Expected and Acquired from Small Mammal Hosts
Humans in the northeastern and midwestern United States are at increasing risk of acquiring tickborne diseases – not only Lyme disease, but also two emerging diseases, human granulocytic anaplasmosis and human babesiosis. Co-infection with two or more of these pathogens can increase the severity of health impacts. The risk of co-infection is intensified by the ecology of these three diseases because all three pathogens (Borrelia burgdorferi, Anaplasma phagocytophilum, and Babesia microti) are transmitted by the same vector, blacklegged ticks (Ixodes scapularis), and are carried by many of the same reservoir hosts. The risk of exposure to multiple pathogens from a single tick bite and the sources of co-infected ticks are not well understood. In this study, we quantify the risk of co-infection by measuring infection prevalence in 4,368 questing nymphs throughout an endemic region for all three diseases (Dutchess County, NY) to determine if co-infections occur at frequencies other than predicted by independent assortment of pathogens. Further, we identify sources of co-infection by quantifying rates of co-infection on 3,275 larval ticks fed on known hosts. We find significant deviations of levels of co-infection in questing nymphs, most notably 83% more co-infection with Babesia microti and Borrelia burgdorferi than predicted by chance alone. Further, this pattern of increased co-infection was observed in larval ticks that fed on small mammal hosts, but not on meso-mammal, sciurid, or avian hosts. Co-infections involving A. phagocytophilum were less common, and fewer co-infections of A. phagocytophilum and B. microti than predicted by chance were observed in both questing nymphs and larvae fed on small mammals. Medical practitioners should be aware of the elevated risk of B. microti/B. burgdorferi co-infection.
6734708
How Host Population Dynamics Translate into Time-Lagged Prevalence: An Investigation of Sin Nombre Virus in Deer Mice
Abstract
Human cases of hantavirus pulmonary syndrome caused by Sin Nombre virus are the endpoint of complex ecological cascade from weather conditions, population dynamics of deer mice, to prevalence of SNV in deer mice. Using population trajectories from the literature and mathematical modeling, we analyze the time lag between deer mouse population peaks and peaks in SNV antibody prevalence in deer mice. Because the virus is not transmitted vertically, rapid population growth can lead initially to reduced prevalence, but the resulting higher population size may later increase contact rates and generate increased prevalence. Incorporating these factors, the predicted time lag ranges from 0 to 18 months, and takes on larger values when host population size varies with a longer period or higher amplitude, when mean prevalence is low and when transmission is frequency-dependent. Population size variation due to variation in birth rates rather than death rates also increases the lag. Predicting future human outbreaks of hantavirus pulmonary syndrome may require taking these effects into account.

4232854
Co-infection of Ticks: The Rule Rather Than the Exception
Introduction Ticks are the most common arthropod vectors of both human and animal diseases in Europe, and the Ixodes ricinus tick species is able to transmit a large number of bacteria, viruses and parasites. Ticks may also be co-infected with several pathogens, with a subsequent high likelihood of co-transmission to humans or animals. However few data exist regarding co-infection prevalences, and these studies only focus on certain well-known pathogens. In addition to pathogens, ticks also carry symbionts that may play important roles in tick biology, and could interfere with pathogen maintenance and transmission. In this study we evaluated the prevalence of 38 pathogens and four symbionts and their co-infection levels as well as possible interactions between pathogens, or between pathogens and symbionts. Methodology/principal findings A total of 267 Ixodes ricinus female specimens were collected in the French Ardennes and analyzed by high-throughput real-time PCR for the presence of 37 pathogens (bacteria and parasites), by rRT-PCR to detect the presence of Tick-Borne encephalitis virus (TBEV) and by nested PCR to detect four symbionts. Possible multipartite interactions between pathogens, or between pathogens and symbionts were statistically evaluated. Among the infected ticks, 45% were co-infected, and carried up to five different pathogens. When adding symbiont prevalences, all ticks were infected by at least one microorganism, and up to eight microorganisms were identified in the same tick. When considering possible interactions between pathogens, the results suggested a strong association between Borrelia garinii and B. afzelii, whereas there were no significant interactions between symbionts and pathogens. Conclusion/significance Our study reveals high pathogen co-infection rates in ticks, raising questions about possible co-transmission of these agents to humans or animals, and their consequences to human and animal health. We also demonstrated high prevalence rates of symbionts co-existing with pathogens, opening new avenues of enquiry regarding their effects on pathogen transmission and vector competence.
8431503
Spatial Invasion Threshold of Lyme Disease
A mathematical model of Lyme disease is formulated to incorporate a spatially heterogenous structure. The basic reproduction number $R_0$ of the disease and its computational formulae are established. It is shown that $R_0$ serves as a threshold value between extinction and persistence in the evolution of Lyme disease. Numerical simulations indicate that spatial heterogeneity of the disease transmission coefficient increases the basic reproduction number, but spatial heterogeneity of the carrying capacity of mice alleviates the value of $R_0$. Moreover, the influence of host population in size, destruction of tick habitats, and deployment of vaccinations is studied to give insights into optimal control of the disease.