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Cross immunity and vaccination against multiple microparasite strains
L J White1, M J Cox, G F Medley
1Department of Biological Sciences, University of Warwick, Coventry, UK.
Abstract:
We explore the equilibrium properties of a series of compartmental, ODE models describing the interaction between different strains of pathogen. The interaction is conceptualized as acting through shared antigens: infection and recovery from one strain leaves the host with a primed immune response against subsequent strains. The models consider the effect of this priming on susceptibility (the ability to be infected) and transmission (the ability to infect) in an SIR model. In these models, the specific past history of infection is encapsulated in different susceptible compartments within the model. In a third, SIS, model, specific past history is not included, but strains have differential abilities to infect previously infected hosts. Equilibrium results include criteria for the coexistence of strains. For the SIR models, the region of coexistence defined by parameters shrinks as the effect of strains on each other (increased antigenic similarity) increases. For the SIS model, coexistence depends critically on the rate at which complete susceptibility is recovered following infection, and coexisting strains must have differential abilities to infect completely and partially susceptible hosts. Interestingly, this model provides analogies to commensalism (the first species gains from the presence of the second; the second neither gains nor loses from the interaction) and symbiosis (the presence of both species benefits the other). Additionally, we show that the maximum number of coexisting strains is two in this model. The effect of vaccination depends on the initial strain structure, the ability of vaccination to mount protection to both strains and the coverage. Vaccination may allow a previously excluded strain to coexist or exist alone, and may allow a previously rarer strain to become more common with the possibility of increasing incidence of disease. We discuss the dynamics of these models, compare model results to observed patterns and consider additional model structures. The importance of these results to specific multi-strain pathogens, in particular rotavirus, is considered.
Insights
Mathematical models reveal how pathogen strains interact via shared antigens, influencing disease spread. Increased similarity between strains reduces coexistence, while vaccination strategies can alter strain prevalence and disease incidence.
Area of Science:
- Mathematical epidemiology
- Theoretical ecology
- Immunology
Background:
- Pathogen evolution involves interactions between different strains.
- Immune priming following infection with one strain can affect subsequent infections.
- Understanding these interactions is crucial for predicting disease dynamics.
Purpose of the Study:
- To explore equilibrium properties of compartmental ODE models for multi-strain pathogen interactions.
- To investigate how antigenic similarity and host immune history affect strain coexistence.
- To analyze the impact of vaccination on multi-strain pathogen dynamics.
Main Methods:
- Development and analysis of compartmental Ordinary Differential Equation (ODE) models.
- Modeling host immune responses, including susceptibility and transmission, based on infection history.
- Examination of equilibrium conditions for strain coexistence in SIR and SIS models.
Main Results:
- In SIR models, increased antigenic similarity between strains reduces the parameter space for coexistence.
- In SIS models, strain coexistence depends on recovery rates and differential infectivity of strains.
- Maximum of two strains can coexist in the SIS model, with analogies to commensalism and symbiosis.
- Vaccination can alter strain dominance, potentially allowing excluded strains to emerge or rare strains to increase.
Conclusions:
- Host immune history and antigenic similarity are key determinants of multi-strain pathogen dynamics.
- SIS models offer insights into ecological interactions like commensalism and symbiosis.
- Vaccination strategies must consider initial strain structure and vaccine efficacy for effective control.
- Findings are relevant to understanding pathogens like rotavirus.