Multistability and chaos in SEIRS epidemic model with a periodic time-dependent transmission rate

In this work, we study the dynamics of a SEIRS epidemic model with a periodic time-dependent transmission rate. Emphasizing the influence of the seasonality frequency on the system dynamics, we analyze the largest Lyapunov exponent along parameter planes finding large chaotic regions. Furthermore, in some ranges there are shrimp-like periodic strutures. We highlight the system multistability, identifying the coexistence of periodic orbits for the same parameter values, with the infections maximum distinguishing by up one order of magnitude, depending only on the initial conditions. In this case, the basins of attraction has self-similarity. Parametric configurations, for which both periodic and non-periodic orbits occur, cover $13.20\%$ of the evaluated range. We also identified the coexistence of periodic and chaotic attractors with different maxima of infectious cases, where the periodic scenario peak reaching approximately $50\%$ higher than the chaotic one

Mathematical models for chemotaxis and their applications in self-organisation phenomena

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and mathematicians into biology. The Patlak-Keller-Segel (PKS) system forms part of the bedrock of mathematical biology, a go-to-choice for modellers and analysts alike. For the former it is simple yet recapitulates numerous phenomena; the latter are attracted to these rich dynamics. Here I review the adoption of PKS systems when explaining self-organisation processes. I consider their foundation, returning to the initial efforts of Patlak and Keller and Segel, and briefly describe their patterning properties. Applications of PKS systems are considered in their diverse areas, including microbiology, development, immunology, cancer, ecology and crime. In each case a historical perspective is provided on the evidence for chemotactic behaviour, followed by a review of modelling efforts; a compendium of the models is included as an Appendix. Finally, a half-serious/half-tongue-in-cheek model is developed to explain how cliques form in academia. Assumptions in which scholars alter their research line according to available problems leads to clustering of academics and the formation of "hot" research topics.Comment: 35 pages, 8 figures, Submitted to Journal of Theoretical Biolog

Parallel processing in immune networks

In this work we adopt a statistical mechanics approach to investigate basic, systemic features exhibited by adaptive immune systems. The lymphocyte network made by B-cells and T-cells is modeled by a bipartite spin-glass, where, following biological prescriptions, links connecting B-cells and T-cells are sparse. Interestingly, the dilution performed on links is shown to make the system able to orchestrate parallel strategies to fight several pathogens at the same time; this multitasking capability constitutes a remarkable, key property of immune systems as multiple antigens are always present within the host. We also define the stochastic process ruling the temporal evolution of lymphocyte activity, and show its relaxation toward an equilibrium measure allowing statistical mechanics investigations. Analytical results are compared with Monte Carlo simulations and signal-to-noise outcomes showing overall excellent agreement. Finally, within our model, a rationale for the experimentally well-evidenced correlation between lymphocytosis and autoimmunity is achieved; this sheds further light on the systemic features exhibited by immune networks.Comment: 21 pages, 9 figures; to appear in Phys. Rev.

Physical Principles of Retroviral Integration in the Human Genome

Some retroviruses, including HIV, insert their DNA in a non-random manner in the host genome through a poorly understood selection mechanism. Here the authors develop a biophysical model of retroviral integration, identifying previously unnoticed universal principles that regulate this phenomenon

Applications of Dynamic Modeling and Statistical Analysis to Infectious Diseases

In this dissertation, I explore the disproportionate burden of infectious disease outbreaks, epidemics, and pandemics and the projected impact of interventions for mitigating their harm on populations in Cameroon and the United States. The spatial heterogeneity in vaccination coverage and access to care in Cameroon creates areas that are highly susceptible to measles transmission. In the US, the HIV epidemic is increasingly concentrated in the southern states in addition to larger cities with variable levels of prevention and linkage to sustained treatment. Disparities in COVID-19 burden exist by race and geography across Michigan, in part due to systemic racism and underlying health burdens.In Chapter One, I model the spatiotemporal dynamics of a large outbreak of measles in Cameroon by using several multivariate time-series models at the health district, department, and region levels. By assessing the spatiotemporal dynamics at different geographical scales, it was possible to determine the respective contribution of each administrative division to measles transmission throughout the country. The model including long-distance population mobility optimally reflected the spatial spread of measles. Population movement between departments within regions was estimated to contribute to 9.1% of all cases and movement between regions contributed to 18.1% of cases at the health district level. These findings demonstrate the need to improve our understanding of the roles of population mobility and local heterogeneity of vaccination coverage in the spread and control of measles in Cameroon. In Chapter Two, I develop a mathematical model of HIV transmission and progression to evaluate the impact of expanding HIV prevention, diagnosis, treatment, and viral suppression levels in 57 priority counties and states in the United States, as identified by the federal government initiative “Ending the HIV Epidemic”. This plan aims to increase access to diagnosis, linkage to treatment, maintenance of treatment and pre-exposure prophylaxis uptake in high-incidence counties as well as states with high burdens of disease in rural areas between 2020 and 2030. I project that the number of annual new infections could be reduced by 58% and that over 157,000 cumulative new infectious could be averted over the next decade nationwide upon successful implementation of this initiative. Despite the substantial benefit incurred by this HIV care continuum expansion, additional concerted efforts beyond its scope such as community-specific interventions benefiting disproportionately affected populations, stigma erasure, HIV criminalization elimination, and ending systemic oppression will be needed to truly stop HIV transmission in the US. In Chapter Three, I examined racial disparities in COVID-19 mortality in Michigan, US, stratified by age, sex, and comorbidity prevalence. Using individual-level linked death certificate and surveillance data on all COVID-19 deaths statewide, I calculated that the mortality rate for Black populations overall was 3.6 times that of White populations, with heterogeneity across neighbourhoods. Strikingly, the mortality rate for Black individuals under 65 years lacking comorbidities was 12.6 times that of their White counterparts. Prevalence of comorbidities, age, and sex did not account for the elevated mortality rate experienced by Black individuals in Michigan. Even after accounting for demographic and underlying health characteristics, my work highlights that disparities across race resulting from systemic racism are compounded in crises. This dissertation contributes to our understanding of the inequitable impacts of epidemics on under-resourced or historically marginalized communities within the United States and Cameroon, with analyses focused on racial and geographic disparities. Addressing the root causes of these disparities through elimination of systemic racism, improved access to care, and healthcare reform is necessary to prevent further infections and deaths. Furthermore, these changes have the capacity to reduce the impact of future infectious disease epidemics on the populations that are consistently and disproportionately affected