Jane M. Heffernan

Perspectives on the basic reproductive ratio

The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R0 often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R0. In this paper we give a brief overview of common methods of formulating R0 and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R0 from epidemiological data. Finally, we survey the recent use of R0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.

Oscillatory viral dynamics in a delayed HIV pathogenesis model

We consider an HIV pathogenesis model incorporating antiretroviral therapy and HIV replication time. We investigate the existence and stability of equilibria, as well as Hopf bifurcations to sustained oscillations when drug efficacy is less than 100%. We derive sufficient conditions for the global asymptotic stability of the uninfected steady state. We show that time delay has no effect on the local asymptotic stability of the uninfected steady state, but can destabilize the infected steady state, leading to a Hopf bifurcation to periodic solutions in the realistic parameter ranges.

Influence of backward bifurcation in a model of hepatitis B and C viruses.

In the 1990 s, liver transplantation for hepatitis B and C virus (HBV and HCV) related-liver diseases was a very controversial issue since recurrent infection of the graft was inevitable. Significant progress has been made in the prophylaxis and treatment of recurrent hepatitis B/C (or HBV/HCV infection) after liver transplantation. In this paper, we propose a mathematical model of ordinary differential equations describing the dynamics of the HBV/HCV and its interaction with both liver and blood cells. A single model is used to describe infection of either virus since the dynamics in-host (infected of the liver) are similar. Analyzing the model, we observe that the system shows either a transcritical or a backward bifurcation. Explicit conditions on the model parameters are given for the backward bifurcation to be present. Consequently, we investigate possible factors that are responsible for HBV/HCV infection and assess control strategies to reduce HBV/HCV reinfection and improve graft survival after liver transplantation.

Can we spend our way out of the AIDS epidemic? A world halting AIDS model

BackgroundThere has been a sudden increase in the amount of money donors are willing to spend on the worldwide HIV/AIDS epidemic. Present plans are to hold most of the money in reserve and spend it slowly. However, rapid spending may be the best strategy for halting this disease.MethodsWe develop a mathematical model that predicts eradication or persistence of HIV/AIDS on a world scale. Dividing the world into regions (continents, countries etc), we develop a linear differential equation model of infectives which has the same eradication properties as more complex models.ResultsWe show that, even if HIV/AIDS can be eradicated in each region independently, travel/immigration of infectives could still sustain the epidemic. We use a continent-level example to demonstrate that eradication is possible if preventive intervention methods (such as condoms or education) reduced the infection rate to two fifths of what it is currently. We show that, for HIV/AIDS to be eradicated within five years, the total cost would be ≈

Implications of vaccination and waning immunity

63 billion, which is within the existing

Interval Between Infections and Viral Hierarchy Are Determinants of Viral Interference Following Influenza Virus Infection in a Ferret Model

60 billion (plus interest) amount raised by the donor community. However, if this action is spread over a twenty year period, as currently planned, then eradication is no longer possible, due to population growth, and the costs would exceed

Viral dynamics model with CTL immune response incorporating antiretroviral therapy

90 billion.ConclusionEradication of AIDS is feasible, using the tools that we have currently to hand, but action needs to occur immediately. If not, then HIV/AIDS will race beyond our ability to afford it.

Highly conserved cross-reactive CD4+ T-cell HA-epitopes of seasonal and the 2009 pandemic influenza viruses.

For infectious diseases where immunization can offer lifelong protection, a variety of simple models can be used to explain the utility of vaccination as a control method. However, for many diseases, immunity wanes over time and is subsequently enhanced (boosted) by asymptomatic encounters with the infection. The study of this type of epidemiological process requires a model formulation that can capture both the within-host dynamics of the pathogen and immune system as well as the associated population-level transmission dynamics. Here, we parametrize such a model for measles and show how vaccination can have a range of unexpected consequences as it reduces the natural boosting of immunity as well as reducing the number of naive susceptibles. In particular, we show that moderate waning times (40–80 years) and high levels of vaccination (greater than 70%) can induce large-scale oscillations with substantial numbers of symptomatic cases being generated at the peak. In addition, we predict that, after a long disease-free period, the introduction of infection will lead to far larger epidemics than that predicted by standard models. These results have clear implications for the long-term success of any vaccination campaign and highlight the need for a sound understanding of the immunological mechanisms of immunity and vaccination.

The effects of genetic drift in experimental evolution

Abstract Background. Epidemiological studies suggest that, following infection with influenza virus, there is a short period during which a host experiences a lower susceptibility to infection with other influenza viruses. This viral interference appears to be independent of any antigenic similarities between the viruses. We used the ferret model of human influenza to systematically investigate viral interference. Methods. Ferrets were first infected then challenged 1–14 days later with pairs of influenza A(H1N1)pdm09, influenza A(H3N2), and influenza B viruses circulating in 2009 and 2010. Results. Viral interference was observed when the interval between initiation of primary infection and subsequent challenge was <1 week. This effect was virus specific and occurred between antigenically related and unrelated viruses. Coinfections occurred when 1 or 3 days separated infections. Ongoing shedding from the primary virus infection was associated with viral interference after the secondary challenge. Conclusions. The interval between infections and the sequential combination of viruses were important determinants of viral interference. The influenza viruses in this study appear to have an ordered hierarchy according to their ability to block or delay infection, which may contribute to the dominance of different viruses often seen in an influenza season.

Improving estimates of the basic reproductive ratio: Using both the mean and the dispersal of transition times

We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected