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The COVID-19 pandemic has represented an unprecedented challenge for the humanity, and scientists around the world provided a huge effort to elucidate critical aspects in the fight against the pathogen, useful in designing public health strategies, vaccines and therapeutic approaches. One of the first pieces of evidence characterizing the SARS-CoV-2 infection has been its breadth of clinical presentation, ranging from asymptomatic to severe/deadly disease, and the indication of the key role played by the immune response in influencing disease severity. This review is aimed at summarizing what the SARS-CoV-2 infection taught us about the immune response, highlighting its features of a double-edged sword mediating both protective and pathogenic processes. We will discuss the protective role of soluble and cellular innate immunity and the detrimental power of a hyper-inflammation-shaped immune response, resulting in tissue injury and immunothrombotic events. We will review the importance of B- and T-cell immunity in reducing the clinical severity and their ability to cross-recognize viral variants.

The vertebrate immune system is capable of strong, focused adaptive responses that depend on T-cell speci city in recognizing antigenic sequences of a pathogen. Recognition tolerance and anti- genic convergence cause cross-immune reactions that extend prompt, speci c responses to rather similar pathogens. This suggests that reaching herd-immunity might be facilitated during suc- cessive epidemic outbreaks (e.g., SARS-CoV-2 waves with di erent variants). Qualitative studies play down this possibility because cross-immune protection is seldom sterilizing. We use minimal quantitative models to study how cross-immunity a ects epidemic dynamics over short and long timescales. In the short scale, we investigate models of sterilizing and attenuating immunity, nd- ing equivalences between both mechanisms|thus suggesting a key role of attenuating protection in achieving herd immunity. Our models render maps in epidemic-parameter space that discern threatening variants depending on acquired cross-immunity levels. We illustrate this application with SARS-CoV-2 data, including protection due to vaccination rates across countries. In the long-time scale, we model sterilizing cross-immunity between rolling pathogens to characterize statistical properties of successful strains. We nd that sustained cross-immune protection alters the regions of epidemic-parameter space where large outbreaks happen. Our results suggest an optimistic revision concerning prospects for herd protection based on cross-immunity, including for the SARS-CoV-2 pandemics.

A mathematical model which captures how the immune response controls influenza infection is essential for predicting the effects of pharmaceutical interventions, and alleviating the public health burden of the disease. However, current models do not agree on how immune response components work together to control infection. Hence, the predicted effects of existing treatments differ between models, implying that predictions of the effects of novel treatments may be unreliable. The discrepancies between models arise because many models are only fit to viral load data from a single infection, from which it is difficult to distinguish between competing models. This study focuses on the construction of a viral dynamics model which reproduces experimental observations of the protection conferred by a primary infection against a subsequent infection. Incorporating observations from multiple experimental conditions enables more accurate extraction of the timing and strength of cross-immunity, and thus quantification of the roles of each component of the immune response. Following a literature review and mathematical preliminaries (Chapters 1-4), Chapter 5 details the analysis of data from experiments where ferrets are sequentially infected with two different influenza strains. The analysis shows that the protection conferred by a primary infection against a subsequent infection depends on the time between exposures as well as the strains used. Chapters 6 and 7 then present the construction of a viral dynamics model to show that the innate immune response can explain the delay of a secondary infection by a primary infection, and that both cross-reactivity and memory in the cellular adaptive immune response are required to explain the shortening of a secondary infection by a primary infection. The model also reproduces qualitative observations from a range of knockout experiments. To quantify the roles of each immune component, the model must be fitted to experimental data. H

Centre de Recerca Matemàtica

Epidemiological models concerned with the control of malaria using interventions such as bed nets and vaccines increasingly incorporate realistic aspects of malaria biology. The increasing complexity of these models limits their ability to abstract ecological processes and to address questions on the regulation of population dynamics using time-series data, particularly in regards to interactions between different pathogens and the regulatory role of innate (bottom-up) and acquired (top-down) immunity. We use a theoretical framework to test hypotheses on the importance of population-level immunity and parasite abundance in regulating the population dynamics of malaria. We use qualitative loop analyses to examine the sign of the interaction between Plasmodium falciparum and P. vivax at the population level, and we discuss implications of this sign for the within-host regulation of parasites. Our analyses of monthly malaria time-series data from the island of Espirito Santo, Vanuatu (1983-1997), show that the dynamics of P. falciparum are not sensitive to P. vivax, whereas infections by the latter increase in response to those of the former. These results support a differential use of resources inside the hosts, a resource-consumer interaction between hosts and their immune system, and within-host regulation of parasites. Finally, our results emphasize the need to better understand factors regulating malaria dynamics before developing control strategies and call for the use of control strategies directed at the interruption of transmission, such as vector control and the use of bed nets., Copyright by the Ecological Society of America, Ecology, 90(9), pp.2414-2425; 2009

Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is su ciently complex, admits several cluster structures of di erent types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organization having many features in common with pattern formation.

Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is su ciently complex, admits several cluster structures of di erent types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organization having many features in common with pattern formation.

Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is su ciently complex, admits several cluster structures of di erent types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organization having many features in common with pattern formation.

Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is su ciently complex, admits several cluster structures of di erent types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organization having many features in common with pattern formation.