On the probability of strain invasion in endemic settings: Accounting for individual heterogeneity and control in multi-strain dynamics

Abstract

a b s t r a c tPathogen evolution is an imminent threat to global health that has warranted, and duly received, considerable attention within the medical, microbiological and modelling communities. Outbreaks of new pathogens are often ignited by the emergence and transmission of mutant variants descended from wildtype strains circulating in the community. In this work we investigate the stochastic dynamics of the emergence of a novel disease strain, introduced into a population in which it must compete with an existing endemic strain. In analogy with past work on single-strain epidemic outbreaks, we apply a branching process approximation to calculate the probability that the new strain becomes established. As expected, a critical determinant of the survival prospects of any invading strain is the magnitude of its reproduction number relative to that of the background endemic strain. Whilst in most circumstances this ratio must exceed unity in order for invasion to be viable, we show that differential control scenarios can lead to less-fit novel strains invading populations hosting a fitter endemic one. This analysis and the accompanying findings will inform our understanding of the mechanisms that have led to past instances of successful strain invasion, and provide valuable lessons for thwarting future drug-resistant strain incursions.

Evolutionary Pathways and Trajectories in Antibiotic Resistance

“…Exogenous invasion by a resistant clone does not necessarily require antibiotic selection if the clone is well-endowed with colonization factors. Invader strains generally succeed when their reproductive numbers exceed that of the background established strain; however, there are scenarios in which the less fit succeed in replacing the previous colonizer (353). The second process leading to clonal replacements is endogenous conversion.…”

A Review of Using Mathematical Modeling to Improve Our Understanding of Bacteriophage, Bacteria, and Eukaryotic Interactions

“…Stochastic variations may therefore appear as biological ‘noise’ ( Wilkinson, 2009 ) and can relate to diffusion in complex cellular environments ( Bressloff, 2014 ), variations in individual cell division times or the production of heterogeneous cell populations ( Wilkinson, 2009 ), both through differentiation ( Gog et al, 2012 ) and genetic mutation. Although historically deterministic modeling has been very popular ( Gill, 2009 ; Meehan et al, 2020 ), if one thing has become apparent from previous experimental and modeling research into phage therapy, it is that the biological world is stochastic by nature ( Beiting and Roos, 2011 ). Models therefore have sometimes been too deterministic to fully represent an in vivo scenario ( Gill, 2009 ).…”

“…This means that the model accounts for biological ‘decisions,’ e.g., a mutation event, where an outcome will alter the path an individual may follow, resulting in a model which looks similar to a family tree. By analyzing two possible outcomes (survival versus extinction; Lashari and Trapman, 2018 ) at each branch point, this kind of model can, for example, provide information on fluctuations in population size and the differential effects of control mechanisms (e.g., transcriptional regulation) on individuals over time ( Athreya, 2006 ; Meehan et al, 2020 ) based on the different routes individuals follow (and such information is not accessible to deterministic models). For this reason, branching processes have historically been used to study long term evolution, reproduction and extinction, for example in the study of the spread of epidemics ( Lashari and Trapman, 2018 ; Fyles et al, 2021 ).…”

“…Due to the stochasticity associated with genetic heterogeneity, models with multiple ‘decision points’ (branching processes) and stochastic differential equations (SDEs) would also be helpful, studying processes in the context of a ‘memory’ of previous events ( Gog et al, 2012 ; Wood et al, 2014 ; see previous section). For example, branching processes have already been used to better understand the development of AMR ( Meehan et al, 2020 ). Modeling data also needs to be analyzed in the context of changes to ‘payoffs’ and probabilities over time ( Tago and Meyer, 2016 ), depending on the resistance phenotype developed.…”

Impact of Behavioural Changes in Mosquito Feeding on Malaria Invasion: A Model-Based Approach

“…Loss of immunity of human (+1, 0, −1, 0, 0) ξr h ∆t + o(∆t)(E6) Recovery of human (0, −1, +1, 0, 0) γi h ∆t + o(∆t) (E7) Death of susceptible human (−1, 0, 0, 0, 0) µ h s h + o(∆t) (E8) Death of infectious human (0, −1, 0, 0, 0) µ h i h + o(∆t) (E9) Death of recovered human (0, 0, −1, 0, 0) µ h r h + o(∆t) (E10) Death of susceptible mosquito (0, 0, 0, −1, 0) µvsv + o(∆t) (E11) Death of infectious mosquito (0, 0, 0, 0, −1) µviv + o(∆t)secondary infections. The heterogeneity increases as s << 1[42,45]. Note that this model includes the Poisson model (s → ∞).…”