The control of vector-borne disease epidemics

The theoretical underpinning of our struggle with vector-borne disease, and still our strongest tool, remains the basic reproduction number, R₀, the measure of long term endemicity. Despite its widespread application, R₀ does not address the dynamics of epidemics in a model that has an endemic equilibrium. We use the concept of reactivity to derive a threshold index for epidemicity, E₀, which gives the maximum number of new infections produced by an infective individual at a disease free equilibrium. This index describes the transitory behavior of disease following a temporary perturbation in prevalence. We demonstrate that if the threshold for epidemicity is surpassed, then an epidemic peak can occur, that is, prevalence can increase further, even when the disease is not endemic and so dies out. The relative influence of parameters on E₀ and R₀ may differ and lead to different strategies for control. We apply this new threshold index for epidemicity to models of vector-borne disease because these models have a long history of mathematical analysis and application. We find that both the transmission efficiency from hosts to vectors and the vector-host ratio may have a stronger effect on epidemicity than endemicity. The duration of the extrinsic incubation period required by the pathogen to transform an infected vector to an infectious vector, however, may have a stronger effect on endemicity than epidemicity. We use the index E₀ to examine how vector behavior affects epidemicity. We find that parasite modified behavior, feeding bias by vectors for infected hosts, and heterogeneous host attractiveness contribute significantly to transitory epidemics. We anticipate that the epidemicity index will lead to a reevaluation of control strategies for vector-borne disease and be applicable to other disease transmission models.     

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.     

The serogroup B meningococcal outer membrane vesicle-based vaccine 4CMenB induces cross-species protection against Neisseria gonorrhoeae

There is a pressing need for a gonorrhea vaccine due to the high disease burden associated with gonococcal infections globally and the rapid evolution of antibiotic resistance in Neisseria gonorrhoeae (Ng). Current gonorrhea vaccine research is in the stages of antigen discovery and the identification of protective immune responses, and no vaccine has been tested in clinical trials in over 30 years. Recently, however, it was reported in a retrospective case-control study that vaccination of humans with a serogroup B Neisseria meningitidis (Nm) outer membrane vesicle (OMV) vaccine (MeNZB) was associated with reduced rates of gonorrhea. Here we directly tested the hypothesis that Nm OMVs induce cross-protection against gonorrhea in a well-characterized female mouse model of Ng genital tract infection. We found that immunization with the licensed Nm OMV-based vaccine 4CMenB (Bexsero) significantly accelerated clearance and reduced the Ng bacterial burden compared to administration of alum or PBS. Serum IgG and vaginal IgA and IgG that cross-reacted with Ng OMVs were induced by 4CMenB vaccination by either the subcutaneous or intraperitoneal routes. Antibodies from vaccinated mice recognized several Ng surface proteins, including PilQ, BamA, MtrE, NHBA (known to be recognized by humans), PorB, and Opa. Immune sera from both mice and humans recognized Ng PilQ and several proteins of similar apparent molecular weight, but MtrE was only recognized by mouse serum. Pooled sera from 4CMenB-immunized mice showed a 4-fold increase in serum bactericidal₅₀ titers against the challenge strain; in contrast, no significant difference in bactericidal activity was detected when sera from 4CMenB-immunized and unimmunized subjects were compared. Our findings directly support epidemiological evidence that Nm OMVs confer cross-species protection against gonorrhea, and implicate several Ng surface antigens as potentially protective targets. Additionally, this study further defines the usefulness of murine infection model as a relevant experimental system for gonorrhea vaccine development.     

Establishment of a human CEACAM1 transgenic mouse model for the study of gonococcal infections

Neisseria gonorrhoeae is the causative microorganism for the sexually transmitted disease (STD) gonorrhea and humans are its only natural host. An animal model would be a useful tool for gonorrhea research, therefore we developed the hCEACAM1 transgenic mice, using an eukaryotic expression vector, pCDPCAM1-GI. This construct was microinjected into the zygotes of C57BL/6 mice and 22 F0 generation transgenic mice were obtained. Four (lines 50, 53, 54, and 59) of the F0 generation were found to carry the transgene by PCR and sequence analysis, respectively. Western blotting and Fluorescence-Activated Cell Sorting Analysis demonstrated that hCEACAM1 was expressed on the cell membrane of various tissues in the line 53 transgenic mouse. To initiate the disease in the animal model, the F2 or F3 transgenic mice were inoculated with N. gonorrhoeae intravaginally. Compared with normal mice, N. gonorrhoeae can successfully infect and cause inflammation in the transgenic mice. These data suggested the feasibility of using hCEACAM1 transgenic mice as an animal model for gonococcal infections.     

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

For infections for which the perceived risk of serious disease is steadily low, the perceived risk of suffering some vaccine side effects might become the driving force of the vaccine demand. We investigate the dynamics of SIR infections in homogeneously mixing populations where the vaccine uptake is a decreasing function of the current (or past) incidence, or prevalence, of vaccine side effects. We define an appropriate model where vaccine side-effects are modelled as functions of the age since vaccination.It happens that the vaccine uptake follows its own dynamics independent of epidemiological variables. We show the conditions under which the vaccine uptake lands on a globally stable equilibrium, or steadily oscillates, and the implications of such behaviour for the dynamics of epidemiological variables. We finally report some unexpected scenarios caused by trends in vaccine side effects.     

Establishment of a human CEACAM1 transgenic mouse model for the study of gonococcal infections

Neisseria gonorrhoeae is the causative microorganism for the sexually transmitted disease (STD) gonorrhea and humans are its only natural host. An animal model would be a useful tool for gonorrhea research, therefore we developed the hCEACAM1 transgenic mice, using an eukaryotic expression vector, pCDPCAM1-GI. This construct was microinjected into the zygotes of C57BL/6 mice and 22 F0 generation transgenic mice were obtained. Four (lines 50, 53, 54, and 59) of the F0 generation were found to carry the transgene by PCR and sequence analysis, respectively. Western blotting and Fluorescence-Activated Cell Sorting Analysis demonstrated that hCEACAM1 was expressed on the cell membrane of various tissues in the line 53 transgenic mouse. To initiate the disease in the animal model, the F2 or F3 transgenic mice were inoculated with N. gonorrhoeae intravaginally. Compared with normal mice, N. gonorrhoeae can successfully infect and cause inflammation in the transgenic mice. These data suggested the feasibility of using hCEACAM1 transgenic mice as an animal model for gonococcal infections.     

Computationally exact methods for stochastic periodic dynamics: Spatiotemporal dispersal and temporally forced transmission

The dynamics of many diseases and populations possess distinct recurring phases. For example, many species breed only during a subset of the year and the infection dynamics of many pathogens have transmission rates that vary with season. Here I investigate computational methods for studying transient and long-term behaviour of stochastic models which have periodic phases—several different potential techniques for studying long-term behaviour will be contrasted. I illustrate the results with two studies: The first is of a spatially realistic metapopulation model of malleefowl (Leipoa ocellata), a species which disperses only during a quarter of the year; this model is used to highlight the advantages and disadvantages of the particular methods presented. The second study is of a model for disease dynamics which incorporates seasonality in both the rate of within-population transmission and also in the rate of transmission effected via aerosol importation. This model has applications to studying disease invasion and persistence in captive-breeding populations. We demonstrate, via comparison to appropriately matched models with constant transmission rates and also no aerosol transmission, that seasonality and aerosol importation may alter control choices, with possibly an increase in the threshold population size for local control surveillance, transfer of importance to limiting aerosol transmission, and the use of temporally targetted surveillance. The methodology presented is the gold-standard for dealing with many phased processes in ecology and epidemiology, but its application is limited to systems of small size.     

The effects of human movement on the persistence of vector-borne diseases

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R₀ for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R₀<1) then it is globally stable and if the disease-free equilibrium is unstable (R₀>1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.     

Modeling and Analyzing the Transmission Dynamics of HBV Epidemic in Xinjiang,China

Hepatitis B is an infectious disease caused by the hepatitis B virus (HBV) which affects livers. In this paper, we formulate a hepatitis B model to study the transmission dynamics of hepatitis B in Xinjiang, China. The epidemic model involves an exponential birth rate and vertical transmission. For a better understanding of HBV transmission dynamics, we analyze the dynamic behavior of the model. The modified reproductive number σ is obtained. When σ < 1, the disease-free equilibrium is locally asymptotically stable, when σ > 1, the disease-free equilibrium is unstable and the disease is uniformly persistent. In the simulation, parameters are chosen to fit public data in Xinjiang. The simulation indicates that the cumulated HBV infection number in Xinjiang will attain about 600,000 cases unless there are stronger or more effective control measures by the end of 2017. Sensitive analysis results show that enhancing the vaccination rate for newborns in Xinjiang is very effective to stop the transmission of HBV. Hence, we recommend that all infants in Xinjiang receive the hepatitis B vaccine as soon as possible after birth.     

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.     

Dynamics of plant mosaic disease propagation and the usefulness of roguing as an alternative biological control

In this research article, an epidemiological model is formulated for mosaic disease considering plant and vector populations. Plant host population has been divided into three compartments namely healthy, latently infected and infected ones, and vector population is divided into two compartments: non-infective and infective vectors. The system possesses three equilibria: plant-only, disease-free and endemic equilibrium. Plant-only equilibrium is always unstable; disease-free equilibrium is stable when the basic reproduction number, R₀, is less than unity and unstable for when it crosses unity, and ensure existence of an endemic equilibrium which may be stable or can undergo a Hopf bifurcation. Finally, impulse periodic roguing with varied rate and time interval is adopted for cost effective and eco-friendly disease control and future direction of agriculture management. The dynamics of the impulsive system has also been analysed. Detailed numerical simulations are employed to support the analytical results. We found that roguing is most cost effective and useful management for mosaic disease eradication of plants if applied at proper rate and interval.     

Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin’s maximum principle, and it is observed that full treatment effort should be given while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point.     

Modelling HIV/AIDS in the presence of an HIV testing and screening campaign

Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and beyond. Reduction of new HIV infections by implementing a comprehensive national HIV prevention programme at a sufficient scale to have real impact remains a priority. In this paper, a deterministic HIV/AIDS model that incorporates condom use, screening through HIV counseling and testing (HCT), regular testing and treatment as control strategies is proposed with the objective of quantifying the effectiveness of HCT in preventing new infections and predicting the long-term dynamics of the epidemic. It is found that a backward bifurcation occurs if the rate of screening is below a certain threshold, suggesting that the classical requirement for the basic reproduction number to be below unity though necessary, is not sufficient for disease control in this case. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number R₀. Numerical simulations are performed and the model is fitted to data on HIV prevalence in South Africa. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long-term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed.     

Outside-Host Growth of Pathogens Attenuates Epidemiological Outbreaks

Opportunist saprotrophic pathogens differ from obligatory pathogens due to their capability in host-independent growth in environmental reservoirs. Thus, the outside-host environment potentially influences host-pathogen dynamics. Despite the socio-economical importance of these pathogens, theory on their dynamics is practically missing. We analyzed a novel epidemiological model that couples outside-host density-dependent growth to host-pathogen dynamics. Parameterization was based on columnaris disease, a major hazard in fresh water fish farms caused by saprotrophic Flavobacterium columnare. Stability analysis and numerical simulations revealed that the outside-host growth maintains high proportion of infected individuals, and under some conditions can drive host extinct. The model can show stable or cyclic dynamics, and the outside-host growth regulates the frequency and intensity of outbreaks. This result emerges because the density-dependence stabilizes dynamics. Our analysis demonstrates that coupling of outside-host growth and traditional host-pathogen dynamics has profound influence on disease prevalence and dynamics. This also has implications on the control of these diseases.     

Whether the Weather Drives Patterns of Endemic Amphibian Chytridiomycosis: A Pathogen Proliferation Approach

The pandemic amphibian disease chytridiomycosis often exhibits strong seasonality in both prevalence and disease-associated mortality once it becomes endemic. One hypothesis that could explain this temporal pattern is that simple weather-driven pathogen proliferation (population growth) is a major driver of chytridiomycosis disease dynamics. Despite various elaborations of this hypothesis in the literature for explaining amphibian declines (e.g., the chytrid thermal-optimum hypothesis) it has not been formally tested on infection patterns in the wild. In this study we developed a simple process-based model to simulate the growth of the pathogen Batrachochytrium dendrobatidis (Bd) under varying weather conditions to provide an a priori test of a weather-linked pathogen proliferation hypothesis for endemic chytridiomycosis. We found strong support for several predictions of the proliferation hypothesis when applied to our model species, Litoria pearsoniana, sampled across multiple sites and years: the weather-driven simulations of pathogen growth potential (represented as a growth index in the 30 days prior to sampling; GI₃₀) were positively related to both the prevalence and intensity of Bd infections, which were themselves strongly and positively correlated. In addition, a machine-learning classifier achieved ∼72% success in classifying positive qPCR results when utilising just three informative predictors 1) GI₃₀, 2) frog body size and 3) rain on the day of sampling. Hence, while intrinsic traits of the individuals sampled (species, size, sex) and nuisance sampling variables (rainfall when sampling) influenced infection patterns obtained when sampling via qPCR, our results also strongly suggest that weather-linked pathogen proliferation plays a key role in the infection dynamics of endemic chytridiomycosis in our study system. Predictive applications of the model include surveillance design, outbreak preparedness and response, climate change scenario modelling and the interpretation of historical patterns of amphibian decline.     

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed “cold sites”, which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.     

Modelling Hospitalization,Home-Based Care,and Individual Withdrawal for People Living with HIV/AIDS in High Prevalence Settings

In sub-Saharan Africa, the model of care for people who are living with HIV/AIDS has changed from hospital care to home-based care. In this paper, a mathematical model describing the dynamics of HIV transmission, hospitalization, and home-based care is constructed and analysed. The model reproduction number R _e is determined and discussed. The equilibria are determined and analysed in terms of R _e . It is shown that if R _e <1, the disease free equilibrium is both locally and globally asymptotically stable. The model has a unique endemic equilibrium and is locally asymptotically stable whenever R _e >1. Five cases arise in the discussion of R _e pertaining to intervention strategies. Numerical simulations are done to compare the impact of each strategy on the dynamics of HIV/AIDS. The model is fitted to the prevalence data estimates from UNAIDS on Zimbabwe. The implications of some key epidemiological parameters are investigated numerically. Projections are made to determine the possible long term trends of the prevalence of HIV in Zimbabwe.     

Spatial Variation in an Avian Host Community: Implications for Disease Dynamics

Because many pathogens can infect multiple host species within a community, disease dynamics in a focal host species can be affected by the composition of the host community. We examine the extent to which spatial variation in species’ abundances in an avian host community may contribute to geographically varying prevalence of a recently emerged wildlife pathogen. Mycoplasma gallisepticum is a pathogen novel to songbirds that has caused substantial mortality in house finches (Carpodacus mexicanus) in eastern North America. Though the house finch is the primary host species for M. gallisepticum, the American goldfinch (Spinus tristis) and northern cardinal (Cardinalis cardinalis) are alternate hosts, and laboratory experiments have demonstrated M. gallisepticum transmission between house finches and goldfinches. Still unknown is the real world impact on disease dynamics of variation in abundances of the three hosts. We analyzed data from winter-long bird and disease surveys in the northeastern United States. We found that higher disease prevalence in house finches was associated with higher numbers of northern cardinals and American goldfinches, although only the effect of cardinal abundance was statistically significant. Nevertheless, our results indicate that spatial variation in bird communities has the potential to cause geographic variation in disease prevalence in house finches.     

Empirical Estimation of R 0 for Unknown Transmission Functions: The Case of Chronic Wasting Disease in Alberta

We consider the problem of estimating the basic reproduction number R ₀ from data on prevalence dynamics at the beginning of a disease outbreak. We derive discrete and continuous time models, some coefficients of which are to be fitted from data. We show that prevalence of the disease is sufficient to determine R ₀. We apply this method to chronic wasting disease spread in Alberta determining a range of possible R ₀ and their sensitivity to the probability of deer annual survival.     

Trait-mediated indirect effects, predators, and disease: test of a size-based model

Increasing prevalence of wildlife disease accentuates the need to uncover drivers of epidemics. Predators can directly influence disease prevalence via density-mediated effects (e.g., culling infected hosts leading to reduced disease prevalence). However, trait-mediated indirect effects (TMIEs) of predators can also strongly influence disease—but predicting a priori whether TMIEs should increase or decrease disease prevalence can be challenging, especially since a single predator may elicit responses that have opposing effects on disease prevalence. Here, we pair laboratory experiments with a mechanistic, size-based model of TMIEs in a zooplankton host, fungal parasite, multiple predator system. Kairomones can either increase or decrease body size of the host Daphnia, depending on the predator. These changes in size could influence key traits of fungal disease, since infection risk and spore yield increase with body size. For six host genotypes, we measured five traits that determine an index of disease spread (R ₀). Although host size and disease traits did not respond to kairomones produced by the invertebrate predator Chaoborus, cues from fish reduced body size and birth rate of uninfected hosts and spore yield from infected hosts. These results support the size model for fish; the birth and spore yield responses should depress disease spread. However, infection risk did not decrease with fish kairomones, thus contradicting predictions of the size model. Exposure to kairomones increased per spore susceptibility of hosts, countering size-driven decreases in exposure to spores. Consequently, synthesizing among the relevant traits, there was no net effect of fish kairomones on the R ₀ metric. This result accentuates the need to integrate the TMIE-based response to predators among all key traits involved in disease spread.