Like all organisms, pathogens evolve. Antigenic variation occurs when a pathogen undergoes a mutation that changes the structure of its surface proteins, which confers it the capability to elude the host's immune response. In a mixed pathogen population, where the surface proteins differ, vaccination can result in previously rare strains suddenly becoming the fittest, in the face of the new selective pressure. Vaccine resistant strains, also called escape mutants, can therefore survive in a population that had been previously immunised, a phenomenon called "antigenic evasion". Historically, vaccines have largely been a powerfull tool for the control of infectious diseases, a fact highlighted by the eradication of several diseases of children, and by smallpox. However, mostly due to antigenic mutations, they have also failed to fully eradicate some pathogens. It is not clearly understood why some pathogens manage to evolve escape mutants, while others fail to do so [1]. Existing antigenic diversity is a major hurdle on the path to the development of vaccines for HIV and malaria.

Epidemiological dynamics in the presence of several strains of the same pathogen have been modelled by several authors. The work of Restif and Grefell [2 (BIOMD0000000249),3 (BIOMD0000000294)], based on the specific datasets available for pertussis (whooping cough), was the first model to investigate the effect of vaccination in the emergence of escape mutants. It demonstrated that stochastic effects can have a profound impact on pathogen population dynamics, which lead to non-obvious conclusions. These stochastic effects need to be considered when devising infection control strategies.

In this work [3 (BIOMD0000000294)], the authors considered the case of a pathogen population where a particular strain within that population was maintained at low incidence levels by the effects of a vaccine. A mutated strain was subsequently added, mimicking an escape mutant, towards which the vaccine only conferred partial immunity. The two strains were assumed to otherwise be identical, for instance displaying the same reproduction rate.

The assumptions of the model are:

• Strain 1 is initially endemic, strain 2 appears in the population at a later stage.
• A fraction p of all newborn babies is immunised by a vaccine that confers immunity from strain 1, but only partial immunity from strain 2.
• Cross-protection is conferred either by vaccine or by recovery from infection, and is modelled either as reduced infection rate, or reduction of infectious period.
• Immunity decreases over time at a constant rate.

Infection dynamics are represented via a modified SIR (susceptible-infected-recovered) model (Figure 1). A susceptible subject (S) can become infected by strain 1 or 2 (I1 or I2) with a certain rate; the subject recovers from the two disease strains with different rates (populations R1 and R2), and upon recovery remains susceptible to infection by the second strain (populations J1 and J2). Vaccinated subjects (V) can only be infected by the second strain (Iv2). The vaccine update acts as a modifier of the infection, recovery and cross-protection parameters.

The desired outcome would be to prevent strain 2 (against which the vaccine is less effective) becoming predominant over strain 1 (antigenic evasion). From the pathogens' point of view, the two strains are competing for a largely overlapping pool of susceptible subjects. Some of the salient results are summarised in Figure 2 and Figure 3.

In summary, this model represents an interesting exploratory study of the poorly understood relation between vaccine efficacy and the dynamics of multi-strain epidemics. Such information could assist in the generation of rational guidelines for healthcare policies. The somewhat counter-intuitive results presented in this paper indicate that the effects of vaccine cross-protection on strain spread and persistence are non-monotonic. In other words, in populations exposed to pathogens that could evolve escape mutants, the highest chances of strain eradication are provided by vaccines with intermediate (rather than high) levels of cross-protection, in particular if this is achieved via a mild reduction of both infectious period and infection susceptibility. Therefore, a high level of cross protection may not be the best strategy, and may simply favour strain replacement.