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On the Origin of Complex Dynamics in Multi-strain Models: Insights for Public Health Intervention Measures

Periodic Reporting for period 1 - COMPLEXDYNAMICS-PHIM (On the Origin of Complex Dynamics in Multi-strain Models: Insights for Public Health Intervention Measures)

Reporting period: 2019-01-01 to 2020-12-31

The dynamics of infectious diseases are by nature non-linear and the understanding of such non-linear processes is vital, both for medical and economic reasons. The problem is mathematically difficult and to make the urgently needed progress in our understanding of such dynamics, concepts from various fields of mathematics as well the availability of good data for model evaluation are needed.

Dengue fever (DF) is one example of a viral mosquito-borne infection, a major international public health concern. With 2.5 billion people at risk of acquiring the infection, it is estimated that around 400 million dengue infections occur every year, of which 96 million manifest symptoms with any level of disease severity. DF is caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). Infection by one serotype confers life-long immunity to that serotype and a period of temporary cross-immunity to other serotypes. The clinical response on exposure to a second serotype is complex and there is good evidence that sequential infection increases the risk of developing severe disease, due to a process described as antibody-dependent enhancement (ADE), where the pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection.

DF epidemiological dynamics shows large fluctuations in disease incidence, and several mathematical models describing the transmission of dengue viruses have been proposed to explain the irregular behavior of dengue epidemics. Multi-strain dengue dynamics have been modeled with extended SIR-type models including immunological aspects of the disease such as ADE phenomenology. A minimalistic two-infection dengue model (with at least two different serotypes to describe differences between primary and secondary infections), developed by Maíra Aguiar and collaborators (JTB, 2011) has found deterministic chaos in much wider parameter regions (not predicted by previous models), indicating that deterministic chaos is much more important in multi-strain models than previously thought and opening new ways to the analysis of existing data sets.

The mechanisms described for dengue, where complex dynamics were observed to happen in a very simple models, are likely to be present in other diseases caused by multiple strains where large fluctuations have been observed and up to now not well understood. Led by Marie Sklodowska-Curie Research Fellow Maíra Aguiar, the EU-funded COMPLEXDYNAMICS-PHIM project has developed simple mathematical models able to address specific public health questions. The main objective of this project was to study the origin of the chaotic dynamics in multi-strain epidemiological models, identifying the mechanisms needed to generate the complex behavior found in the well studied minimalistic dengue models (Aguiar et al, JTB, 2011).
The COMPLEXDYNAMICS-PHIM has three general work-packages covering research on vector-host-pathogens interactions, data analysis, and modelling public health intervention measures. Various sources of data, from different countries and on different time scales were accessed to validate, parametrize and test these models.

Starting from a non-seasonal model with direct transmission, seasonality and vector dynamics were added separately in order to disentangle its effects. By using parameter values obtained from empirical data (or from the literature, when data is not available), chaotic vs. simple behavior has been identified in areas where dengue viruses are co-circulating. This work is still ongoing with delay due to my involvement on COVID-19 Modeling Task Force (Basque Modeling Task Force - BMTF).

The scientific work performed was based in models on dengue fever epidemiology that have previously shown deterministic chaos in some parameter regions due to the multi-strain structure of the disease pathogen. Starting from well studied minimalistic dengue models, which have the function of a paradigmatic study system of much wider interest, extensions were added gradually to include relevant aspects of the disease epidemiology and biological aspects of the host-pathogen interactions. Disease transmission models combined with intervention measures were developed to address specific public health questions, combining knowledge about the immune components involved in the progression of the disease and the most recently information in respect to the newly licensed vaccine. From a microscopic perspective, I have developed an within-host modeling framework to describe viral clearance mediated by antibodies, exploring the impact of ADE in disease severity. Time-scale separation via center-manifold analysis was performed to investigate vector dynamics and human immunological response was also studied.

The main results achieved so far are published in refereed international journals and presented at international scientific meetings and to general public. COMPLEXDYNAMICS-PHIM counts with 20 publications so far, 7 in refereed international journals, 4 preprints, 6 abstracts published in conference proceedings and 3 edited books. Moreover, 3 manuscripts are in preparation and will be available as a preprint soon. Project results were presented internationally in conferences and courses. It is important to note that all the presential meetings scheduled in 2020 were postponed for late 2021 and 2022. The yearly International Conference DSABNS was organized three times withing the project period, attracting hundreds of participants worldwide. Moreover, a COVID-19 modeling dashboard was created during my secondment period with results published monthly, free to access by researchers and the general audience.
The COMPLEXDYNAMICS-PHIM scope was extended in January 2020, after a new respiratory syndrome (COVID-19) caused by a new coronavirus (SARS-CoV-2), was identified in China and spread rapidly around the globe. COVID-19 was declared a pandemic by the World Health Organization (WHO) in March, 2020. Maíra Aguiar became part of a modeling task force and has developed a stochastic mathematical modeling framework to describe the dynamics of COVID-19 and to assist public health managers and Government during the COVID-19 responses.

The different modelling levels described in this project framework have been compared in their ability to describe and predict outbreaks in endemic countries and invasion scenarios into new “disease free” world regions. This is specially important now, with the ongoing pandemic, as well as that the threat of a possible outbreak of dengue fever in Europe exists. Intervention strategies for disease-prevention and control have been and are continually studied, applied to both, endemic situations and invasion scenarios, and the risks of infection as well the efficacy of a given control measure provided by both, industry and public health authorities.

Impact on modeling dengue fever and COVID-19 vaccine trials and vaccination program implementation to be suggested to public health authorities and industry based on positive results obtained by the modeling analysis are considered potentially one of the most important and timely research results in this project.

Scientific collaboration on mathematical techniques, notification data collection, and laboratory data interpretation are still ongoing, where data referring to some of the disease pathogens will be provided to be used to continue parametrizing the refined models.
complexdynamics_phim dengue_covid19