Tuberculosis Transmission Model with Chemoprophylaxis and Treatment

A tuberculosis model which incorporates treatment of infectives and chemoprophylaxis is presented. The model assumes that latently infected individuals develop active disease as a result of endogenous re-activation, exogenous re-infection and disease relapse, though a small fraction is assumed to develop active disease soon after infection. We start by formulating and analyzing a TB model without any intervention strategy that we extend to incorporate chemoprophylaxis and treatment of infectives. The epidemic thresholds known as reproduction numbers and equilibria for the models are determined, and stabilities analyzed. The reproduction numbers for the models are compared to assess the possible community benefits achieved by treatment of infectives, chemoprophylaxis and a holistic approach of these intervention strategies. The study shows that treatment of infectives is more effective in the first years of implementation (≈ 10 years) as treatment results in clearing active TB immediately and there after chemoprophylaxis will do better in controlling the number of infectives due to reduced progression to active TB.     

Analysis of Risk-Structured Vaccination Model for the Dynamics of Oncogenic and Warts-Causing HPV Types

A new deterministic model is designed and used to assess the community-wide impact of mass vaccination of new sexually active individuals on the dynamics of the oncogenic and warts-causing HPV types. Rigorous qualitative analyses of the model, which incorporates the two currently available anti-HPV vaccines, reveal that it undergoes competitive exclusion when the reproduction of one HPV risk type (low/high) exceeds unity, while that of the other HPV risk type is less than unity. For the case when the reproduction numbers of the two HPV risk types (low/high) exceed unity, the two risk types co-exist. It is shown that the sub-model with the low-risk HPV types only has at least one endemic equilibrium whenever the associated reproduction threshold exceeds unity. Furthermore, this sub-model undergoes a re-infection-induced backward bifurcation under certain conditions. In the absence of the re-infection of recovered individuals and cancer-induced mortality in males, the associated disease-free equilibrium of the full (risk-structured) model is shown to be globally asymptotically stable whenever the reproduction number of the model is less than unity (that is, the full model does not undergo backward bifurcation under this setting). It is shown, via numerical simulations, that the use of the Gardasil vaccine could lead to the effective control of HPV in the community if the coverage rate is in the range of 73–95 % (84 %). If 70 % of the new sexually active susceptible females are vaccinated with the Gardasil vaccine, additionally vaccinating 34–56 % (45 %) of the new sexually active susceptible males can lead to the effective community-wide control (or elimination) of the HPV types.     

Not to wake a sleeping giant: new insights into host-pathogen interactions identify new targets for vaccination against latent Mycobacterium tuberculosis infection

Mycobacterium tuberculosis is one of the worlds' most successful and sophisticated pathogens. It is estimated that over 2 billion people today harbour latent M. tuberculosis infection without any clinical symptoms. As most new cases of active tuberculosis (TB) arise from this (growing) number of latently infected individuals, urgent measures to control TB reactivation are required, including post-exposure/therapeutic vaccines. The current bacille Calmette-Guérin (BCG) vaccine and all new generation TB vaccines being developed and tested are essentially designed as prophylactic vaccines. Unfortunately, these vaccines are unlikely to be effective in individuals already latently infected with M. tuberculosis. Here, we argue that detailed analysis of M. tuberculosis genes that are switched on predominantly during latent stage infection may lead to the identification of new antigenic targets for anti-TB strategies. We will describe essential host-pathogen interactions in TB with particular emphasis on TB latency and persistent infection. Subsequently, we will focus on novel groups of late-stage specific genes, encoded amongst others by the M. tuberculosis dormancy (dosR) regulon, and summarise recent studies describing human T-cell recognition of these dormancy antigens in relation to (latent) M. tuberculosis infection. We will discuss the possible relevance of these new classes of antigens for vaccine development against TB.     

Global Stability of Equilibria in a Two-Sex HPV Vaccination Model

Human papillomavirus (HPV) is the primary cause of cervical carcinoma and its precursor lesions, and is associated with a variety of other cancers and diseases. A prophylactic quadrivalent vaccine against oncogenic HPV 16/18 and warts-causing genital HPV 6/11 types is currently available in several countries. Licensure of a bivalent vaccine against oncogenic HPV 16/18 is expected in the near future. This paper presents a two-sex, deterministic model for assessing the potential impact of a prophylactic HPV vaccine with several properties. The model is based on the susceptible-infective-removed (SIR) compartmental structure. Important epidemiological thresholds such as the basic and effective reproduction numbers and a measure of vaccine impact are derived. We find that if the effective reproduction number is greater than unity, there is a locally unstable infection-free equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the effective reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable, and HPV will be eliminated.     

Analysis of SIR epidemic models with nonlinear incidence rate and treatment

This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the number of infectives reaches the capacity. Under some conditions, it is shown that there exists a backward bifurcation from an endemic equilibrium, which implies that the disease-free equilibrium coexists with an endemic equilibrium. In such a case, reducing the basic reproduction number less than unity is not enough to control and eradicate the disease, extra measures are needed to ensure that the solutions approach the disease-free equilibrium. When the basic reproduction number is greater than unity, the model can have multiple endemic equilibria due to the effect of treatment, vaccination and other parameters. The existence and stability of the endemic equilibria of the model are analyzed and sufficient conditions on the existence and stability of a limit cycle are obtained. Numerical simulations are presented to illustrate the analytical results.     

Immunization Against Rabies

The methods used for both pre-exposure and post-exposure immunization against rabies were studied. In pre-exposure immunization duck embryo vaccine should be used. In post-exposure immunization either duck embryo or Semple-type vaccine appears to be effective in stimulating antibody production. Both vaccines may cause neurological sequelae. A dose of vaccine should be given 20-50 days after completion of the primary course of vaccination. Immune serum should be used in all severe exposures especially of the head and neck, and in individuals in whom the commencement of vaccination has been unduly delayed. In individuals who have been previously vaccinated reinforcing doses have been found to be effective even as long as 20 years after the primary vaccination. A tissue culture vaccine has been developed and is about to undergo field trials.     

Modeling AIDS vaccines: the cellular level.

This paper discusses current strategies for the development of AIDS vaccines which allow immunization to disturb the natural course of HIV at different detailed stages of its life cycle. Mathematical models describing the main biological phenomena (i.e. virus and vaccine induced T4 cell growth; virus and vaccine induced activation of latently infected T4 cells; incremental changes in immune response as infection progresses; antibody dependent enhancement and neutralization of infection) and allowing for different vaccination strategies serve as a background for computer simulations. The mathematical models reproduce updated information on the behavior of immune cells, antibody concentrations and free viruses. The results point to some controversial outcomes of an AIDS vaccine such as an early increase in virus concentration among vaccinated when compared to nonvaccinated individuals.     

Theoretical Assessment of Public Health Impact of Imperfect Prophylactic HIV-1 Vaccines with Therapeutic Benefits

This paper presents a number of deterministic models for theoretically assessing the potential impact of an imperfect prophylactic HIV-1 vaccine that has five biological modes of action, namely “take,” “degree,” “duration,” “infectiousness,” and “progression,” and can lead to increased risky behavior. The models, which are of the form of systems of nonlinear differential equations, are constructed via a progressive refinement of a basic model to incorporate more realistic features of HIV pathogenesis and epidemiology such as staged progression, differential infectivity, and HIV transmission by AIDS patients. The models are analyzed to gain insights into the qualitative features of the associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction numbers and a measure for vaccine impact or efficacy. The key findings of the study include the following (i) if the vaccinated reproduction number is greater than unity, each of the models considered has a locally unstable disease-free equilibrium and a unique endemic equilibrium; (ii) owing to the vaccine-induced backward bifurcation in these models, the classical epidemiological requirement of vaccinated reproduction number being less than unity does not guarantee disease elimination in these models; (iii) an imperfect vaccine will reduce HIV prevalence and mortality if the reproduction number for a wholly vaccinated population is less than the corresponding reproduction number in the absence of vaccination; (iv) the expressions for the vaccine characteristics of the refined models take the same general structure as those of the basic model.     

Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use.     

Decentralized resource allocation to control an epidemic: A game theoretic approach

This paper examines how two countries would allocate resources at the onset of an epidemic when they seek to protect their own populations by minimizing the total number of infectives over the entire time horizon. We model this situation as a game between selfish countries, where players strategically allocate their resources in order to minimize the total number of infected individuals in their respective populations during the epidemic. We study this problem when the initial number of infectives is very small, which greatly simplifies the analysis. We show in this framework that selfish countries always allocate their resources so as to bring the effective reproduction ratio below one and avoid a major outbreak. When a major outbreak is avoidable, we further identify the necessary and sufficient conditions under which the individual allocation decisions of selfish countries match the decision that a central planner would make in order to minimize the total number of infectives in the whole population (without distinguishing between countries).     

Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic

The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits a vaccine-induced backward bifurcation when the associated reproduction number is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the reproduction number is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model. For the case where the vaccine is perfect, it is shown that having the reproduction number less than unity is necessary and sufficient for effective control of H1N1 in the population (in such a case, the associated disease-free equilibrium is globally asymptotically stable). The model has a unique endemic equilibrium when the reproduction number exceeds unity. Numerical simulations of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a mass vaccination program together with the size of the Manitoban population that have preexisting infection-acquired immunity (from the first wave) are crucial to the magnitude of the expected burden of disease associated with the second wave of the H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally, it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and that the second wave would last until the end of January or early February, 2010.     

Saturation recovery leads to multiple endemic equilibria and backward bifurcation

The number of patients need to be treated may exceed the carry capacity of local hospitals during the spreading of a severe infectious disease. We propose an epidemic model with saturation recovery from infective individuals to understand the effect of limited resources for treatment of infectives on the emergency disease control. It is shown that saturation recovery from infective individuals leads to vital dynamics, such as bistability and periodicity, when the basic reproduction number R₀ is less than unity. An interesting dynamical behavior of the model is a backward bifurcation which raises many new challenges to effective infection control.     

Impact of Travel Between Patches for Spatial Spread of Disease

A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ₀. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ₀ on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.     

New vaccines for immunization of man: new approaches towards the prevention of rabies in man

Cell culture rabies vaccines for human use, highly immunogenic and well tolerated, are now used for pre-exposure immunization as well as for post-exposure treatment. Presently available cell culture rabies vaccines induce immunity against the SAD modified live rabies virus used for oral immunization of foxes. They also induce immunity against the newly identified European bat rabies virus (Duvenhage).     

Infection-age structured epidemic models with behavior change or treatment

We formulate infection-age structured susceptible-infective-removed (SIR) models with behavior change or treatment of infections. Individuals change their behavior or have treatment after they are infected. Using infection age as a continuous variable, and dividing infectives into discrete groups with different infection stages, respectively, we formulate a partial differential equation model and an ordinary differential equation model with behavior change or treatment. We derive explicit formulas for the reproductive number by linear stability analysis of the infection-free equilibrium, and explicit formulas for the unique endemic equilibrium, when it exists, for both models. These formulas provide mathematical theoretical frameworks for analysis of impact of behavior change or treatment of infection to the transmission dynamics of infectious diseases. We study several special cases and provide sensitivity analysis for the reproductive numbers with respect to model parameters based on those formulas.     

Infection-age structured epidemic models with behavior change or treatment

We formulate infection-age structured susceptible-infective-removed (SIR) models with behavior change or treatment of infections. Individuals change their behavior or have treatment after they are infected. Using infection age as a continuous variable, and dividing infectives into discrete groups with different infection stages, respectively, we formulate a partial differential equation model and an ordinary differential equation model with behavior change or treatment. We derive explicit formulas for the reproductive number by linear stability analysis of the infection-free equilibrium, and explicit formulas for the unique endemic equilibrium, when it exists, for both models. These formulas provide mathematical theoretical frameworks for analysis of impact of behavior change or treatment of infection to the transmission dynamics of infectious diseases. We study several special cases and provide sensitivity analysis for the reproductive numbers with respect to model parameters based on those formulas.     

Comprehensive quantification of herpes simplex virus latency at the single-cell level.

To date, characterization of latently infected tissue with respect to the number of cells in the tissue harboring the viral genome and the number of viral genomes contained within individual latently infected cells has not been possible. This level of cellular quantification is a critical step in determining (i) viral or host cell factors which function in the establishment and maintenance of latency, (ii) the relationship between latency burden and reactivation, and (iii) the effectiveness of vaccines or antivirals in reducing or preventing the establishment of latent infections. Presented here is a novel approach for the quantitative analysis of nucleic acids within the individual cells comprising complex solid tissues. One unique feature is that the analysis reflects the nucleic acids within the individual cells as they were in the context of the intact tissue-hence the name CXA, for contextual analysis. Trigeminal ganglia latently infected with herpes simplex virus (HSV) were analyzed by CXA of viral DNA. Both the type and the number of cells harboring the viral genome as well as the number of viral genomes within the individual latently infected cells were determined. Here it is demonstrated that (i) the long-term repository of HSV-1 DNA in the ganglion is the neuron, (ii) the viral-genome copy number within individual latently infected neurons is variable, ranging over 3 orders of magnitude from <10 to >1,000, (iii) there is a direct correlation between increasing viral input titer and the number of neurons in which latency is established in the ganglion, (iv) increasing viral input titer results in more neurons with greater numbers of viral-genome copies, (v) treatment with acyclovir (ACV) during acute infection reduces the number of latently infected ganglionic neurons 20-fold, and (vi) ACV treatment results in uniformly low (<10)-copy-number latency. This report represents the first comprehensive quantification of HSV latency at the level of single cells. Beyond viral latency, CXA has the potential to advance many studies in which rare cellular events occur in the background of a complex solid tissue mass, including microbial pathogenesis, tumorigenesis, and analysis of gene transfer.     

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.     

Identification of a Major Dimorphic Region in the Functionally Critical N-Terminal ID1 Domain of VAR2CSA

The VAR2CSA protein of Plasmodium falciparum is transported to and expressed on the infected erythrocyte surface where it plays a key role in placental malaria (PM). It is the current leading candidate for a vaccine to prevent PM. However, the antigenic polymorphism integral to VAR2CSA poses a challenge for vaccine development. Based on detailed analysis of polymorphisms in the sequence of its ligand-binding N-terminal region, currently the main focus for vaccine development, we assessed var2csa from parasite isolates infecting pregnant women. The results reveal for the first time the presence of a major dimorphic region in the functionally critical N-terminal ID1 domain. Parasite isolates expressing VAR2CSA with particular motifs present within this domain are associated with gravidity- and parasite density-related effects. These observations are of particular interest in guiding efforts with respect to optimization of the VAR2CSA-based vaccines currently under development.     

Development of vaccines for prevention of Ebola virus infection

Ebola virus infection causes severe hemorrhagic fevers with high fatality rates up to 90% in humans, for which no effective treatment is currently available. The ongoing Ebola outbreak in West Africa that has caused over 14,000 human infections and over 5000 deaths underscores its serious threat to the public health. While licensed vaccines against Ebola virus infection are still not available, a number of vaccine approaches have been developed and shown to protect against lethal Ebola virus infection in animal models. This review aims to summarize the advancement of different strategies for Ebola vaccine development with a focus on the discussion of their protective efficacies and possible limitations. In addition, the development of animal models for efficacy evaluation of Ebola vaccines and the mechanism of immune protection against Ebola virus infection are also discussed.