Herd immunity refers to the indirect protection conferred on susceptible individuals against infection when a sufficiently large proportion of the population is immune [1]. Herd immunity results from individual immunity and hence depends on it. Individual immunity is triggered by natural exposure to the disease vector or vaccination. The mechanisms of action and failure of vaccine response is not well understood and it is unknown what is the optimal combination of factors — type of vaccine, the presence of adjuvants and the application route and frequency — for best immune response. However, immune response to vaccination has been found to decrease with increasing age [2].
Many models of vaccination depend on a term that summarizes the effect of multiple factors into one, known as the basic reproductive number R0 [4]. It is the number of secondary cases caused by one infected individual in a population [4]. In the simplest case, perfect and life-long vaccine efficacy is assumed, yielding the new basic reproductive number under vaccination R0'=(1-p)R0. Since a R0 of <1 will lead to the infection being eradicated, rearranging we obtain p=1–1/R0 as the critical vaccination population that will achieve eradication [4]. For an R0 of 2, the critical vaccination population is theoretically 50%, however, this figure is clearly very optimistic.
Despite its highly simplifying assumptions, this model successfully predicts features of pandemics such as waves of disease outbreak [4]. More complex models account for waning immunity [5] and imperfect vaccine protection [6]. More recently, models have begun to account for spatial structure in terms of vaccine distribution rather than assume uniform random distribution of the proportion of vaccinated individuals [7, 8]. Accounting for the spatial structure, the optimal vaccination distribution strategy can be as much as 30% more effective at averting infection (according to the model) in one study [9]. It is important to note that R0 itself is based on many other factors such as pathogen type, the mode of transmission, population density and many other factors both social and biological that affect how easily the infection is transmitted.
Another challenge is that the relationship between herd immunity and the pathogen is non-linear. While the pathogen triggers immunising response, herd immunity can also lead to a selective pressure on the pathogen. In children that received the pneumococcal conjugate vaccine, a shift in serotypes of Streptococcus pneumoniae colonizing their nasopharynx to non-vaccine serotypes has been observed [10]. This leads to vaccine resistance and is the reason why vaccines do not yet exist for fast mutating viruses such as HIV [11].
An important question is whether the vaccine-adapted strains are more or less virulent than the wildtype. A common view is that vaccine escaped strains will be less transmissible, otherwise, they would have evolved regardless of the vaccine. Experimental observations of immune escaped mutants in hepatitis B virus [12] and the experimental substitution of amino acids in multiple epitopes of the influenza A virus support the view that viral replication is hindered in immune or vaccine escaped mutants [13].
However, it cannot be assumed that this vaccine escaped variants will necessarily be less virulent. Indeed, it has been observed in Marek’s Disease Virus that the vaccine escaped strains cause more severe disease in unvaccinated birds [14] and the vaccine protection was eroded though still significant for vaccinated birds [15]. It is possible that a vaccine-escaped strain might have more immune-evading epitope conformations that make it highly efficient at binding host cells [11]. In fact, it is possible that high vaccination coverage can select for more virulence as without vaccination, the vaccine-escaped strain might be too pathogenic to be transmissible.
It is extremely difficult to predict how a vaccination strategy could affect pathogen evolution. Attempts at modelling the evolutionary dynamics of pathogens under vaccination need to account for all fitness costs and benefits of escape in the state space of all possible mutations [16]. Mackinnon et al.’s model of this process in Malaria parasite suggests that the selection pressure from vaccination may allow the higher virulence strain to become more prevalent and in the case of moderate vaccine coverage could still lead to worse outcome in terms of overall mortality due to the higher virulence experienced by unvaccinated individuals [17]. However, in general vaccination had led to significant reduction in disease, even in the presence of vaccine resistance [15].
In summary, vaccinations have led to great reduction in disease mortality and in some cases eradicated the disease. Their use also confers herd immunity to susceptible members of the population. The modelling of the effect of vaccination and in general disease transmission needs to account for many non-linear factors and is still constantly being improved.
References
[1] S. B. Omer, I. Yildirim, and H. P. Forman, “Herd Immunity and Implications for SARS-CoV-2 Control,” JAMA, vol. 324, pp. 2095–2096, 2020.
[2] S. S. Shen-Orr and D. Furman, “Variability in the immune system: of vaccine responses and immune states,” Current opinion in immunology, vol. 25, pp. 542–547, 2013.
[4] A. Scherer and A. McLean, “Mathematical models of vaccination,” British Medical Bulletin, vol. 62, pp. 187–199, 2002.
[5] A. R. McLean and S. M. Blower, “Imperfect Vaccines and Herd Immunity to HIV,” Proceedings: Biological Sciences, vol. 253, pp. 9–13, 1993.
[6] E. Massad, F. A. B. Coutinho, M. N. Burattini, L. F. Lopez, and C. J. Struchiner, “Modeling the impact of imperfect HIV vaccines on the incidence of the infection,” Mathematical and Computer Modelling, vol. 34, pp. 345–351, 2001/08/01/ 2001.
[7] A. Litvak-Hinenzon and L. Stone, “Spatio-temporal waves and targeted vaccination in recurrent epidemic network models,” Journal of the Royal Society Interface, vol. 6, pp. 749–760, 2009.
[8] S. Venkatramanan, J. Chen, S. Gupta, B. Lewis, M. Marathe, H. Mortveit, et al., “Spatio-temporal optimization of seasonal vaccination using a metapopulation model of influenza,” in 2017 IEEE International Conference on Healthcare Informatics (ICHI), 2017, pp. 134–143.
[9] J. C. Lemaitre, D. Pasetto, M. Zanon, E. Bertuzzo, L. Mari, S. Miccoli, et al., “Optimizing the spatio-temporal allocation of COVID-19 vaccines: Italy as a case study,” medRxiv, p. 2021.05.06.21256732, 2021.
[10] S. I. Pelton, “Acute otitis media in the era of effective pneumococcal conjugate vaccine: will new pathogens emerge?,” Vaccine, vol. 19, pp. S96-S99, 2000/12/08/ 2000.
[11] A. F. Read and M. J. Mackinnon, “Pathogen evolution in a vaccinated world,” Evolution in health and disease, vol. 2, pp. 139–52, 2008.
[12] T. Kalinina, A. Iwanski, H. Will, and M. Sterneck, “Deficiency in virion secretion and decreased stability of the hepatitis B virus immune escape mutant G145R,” Hepatology, vol. 38, pp. 1274–1281, 2003/11/01/ 2003.
[13] E. G. M. Berkhoff, E. de Wit, M. M. Geelhoed-Mieras, A. C. M. Boon, J. Symons, R. A. M. Fouchier, et al., “Fitness costs limit escape from cytotoxic T lymphocytes by influenza A viruses,” Vaccine, vol. 24, pp. 6594–6596, 2006/11/10/ 2006.
[14] N. Osterrieder, J. P. Kamil, D. Schumacher, B. K. Tischer, and S. Trapp, “Marek’s disease virus: from miasma to model,” Nature Reviews Microbiology, vol. 4, pp. 283–294, 2006/04/01 2006.
[15] D. A. Kennedy and A. F. Read, “Why the evolution of vaccine resistance is less of a concern than the evolution of drug resistance,” Proceedings of the National Academy of Sciences, vol. 115, pp. 12878–12886, 2018.
[16] S. Gandon and T. Day, “The evolutionary epidemiology of vaccination,” Journal of the Royal Society, Interface, vol. 4, pp. 803–817, 2007.
[17] M. J. Mackinnon, S. Gandon, and A. F. Read, “Virulence evolution in response to vaccination: The case of malaria,” Vaccine, vol. 26, pp. C42-C52, 2008/07/18/ 2008.
