MEPI Subgroup Contributed Talks

Rosemary Omoregie

University of Benin, Nigeria

"Mathematical Model For Dengue and its Co-Endemicity with Chikungunya virus"

A deterministic nonlinear mathematical model describing the population dynamics for Dengue and Chikungunya virus taken into consideration the effect of misdiagnosis due to the co-endemicity of the two viruses in the human population. It is necessary to understand the most important parameters involved in their dynamics that may help in developing strategies for prevention, control and joint treatments. The model is rigorously analyzed qualitatively and thresholds for eradication are established.

---

Binod Pant

Northeastern University

"Could malaria mosquitoes be controlled by periodic release of transgenic mosquitocidal Metarhizium pingshaense? A mathematical modeling approach"

Mosquito-borne diseases, such as malaria, remain a major global health challenge, necessitating the exploration of innovative vector control strategies. Naturally occurring entomopathogenic fungi have been shown to reduce mosquito lifespan, but their slow-acting nature has limited their practical application. Advances in biotechnology have led to the development of transgenic fungus strains (this study will focus on Metarhizium pingshaense strain) engineered to express insecticidal toxins, significantly increasing their efficacy against malaria vector mosquitoes. To our knowledge, this is the first deterministic model designed to assess the impact of fungal-based mosquito control. The proposed model accounts for multiple transmission pathways of the fungal infection, including mating-based transmission from infected males to females and indirect transmission via contact with infectious mosquito carcasses. The model is analyzed to determine equilibrium states, local stability conditions, and the reproduction number. Numerical simulations explore various release scenarios, evaluating the effectiveness of periodic versus continuous fungal release in different ecological settings. The results indicate that transgenic Metarhizium pingshaense has the potential to significantly reduce mosquito populations, particularly when release strategies are optimized.

---

Soyoung Park

University of Maryland

"Mathematical assessment of the roles of vaccination and Pap screening on the incidence of HPV and related cancers in South Korea"

Human Papillomavirus (HPV) is a major sexually-transmitted infection that causes various cancers and genital warts in humans. In addition to accounting for about 99% of cervical cancer cases, it significantly contributes to anal, penile, vaginal, and head and neck cancers. Although HPV is vaccine-preventable (and highly efficacious vaccines exist for preventing infection with some of the most oncogenic HPV subtypes in the targeted population), the disease continues to cause major public health burden globally (largely due to inequity in access to the main control resources (i.e., access to Pap smear and vaccination) and low vaccination coverage in most communities that implement routine HPV vaccination). This lecture is based on the use of a new mathematical model (for the natural history of HPV, together with the associated neoplasia) for assessing the combined population-level impacts of Pap cytology screening and vaccination against the spread of HPV in a heterogeneous (heterosexual and homosexual) population. The model, which takes the form of a deterministic system of nonlinear differential equations, will be calibrated and validated using HPV-related cancer data from South Korea. Theoretical and numerical simulation results will be presented. Conditions for achieving vaccine-derived herd-immunity threshold (for achieving HPV elimination in Korea) will be derived.

---

somdata sina

IISER Kolkata, India

"Compositional Complexity in Genomic Patterns and Classification"

A genome consists of a long string of four letters (bases A, T, C, G). How the information of biochemical processes stored in this string of bases is an open question. Are their higher order structures, such as, words, sentences, semantics, and a grammar in the DNA language (compositional complexity)? DNA from different species exhibit differences in global sequence composition, and this is used as markers to align larger sequences - grouping of genomes based on homology. Classification of genomes through similarity and dissimilarity is at the heart of Phylogenetics/Genomic Epidemiology. It uses several statistical-mathematical methods to align and compare the base sequences of multiple genomes, which are both computational resource intensive and time consuming for similar sequences. We develop and use an “alignment-free” method based on the Chaos-Game-Representation (CGR) of Statistical Physics, to successfully classify very closely related genomes of sub and sub-sub-species of HIV1 and mutants of Covid19. This useful approach requires less computational resources and time for analysis.

---

Woldegebriel Assefa Woldegerima

York University

"Singular Perturbation Analysis of a Two-Time Scale Model of Vector-Borne Disease"

Biological systems evolve across different spatial and temporal scales. Modeling such complex systems gives rise to multi-scale differential equations that may be written as ODEs, PDEs, DDEs, SDEs, or Difference Equations. Particularly, vector-borne disease models are often described using ordinary differential equations with multiple time scales, which can involve singular perturbations—situations where rapid transitions or significant changes in system behavior occur due to small parameter variations or the interaction between fast and slow dynamics. To analyze these multi- time scale problems, we employ tools such as Geometric Singular Perturbation Theory (GSPT), Tikhonov’s Theorem, and Fenichel’s Theory. These methods provide insights into complex phenomena, including the loss of normal hyperbolicity and other intricate behaviors. Particularly, applying singular perturbation theory to vector-borne diseases allows us to reduce the dynamics to a one-time scale and understand their dynamics. To illustrate this, we present a Zika virus model and apply Tikhonov’s theorem and GSPT to investigate the model’s asymptotic behavior. Additionally, we conduct a bifurcation analysis to explore how the system’s behavior changes with variations in the parameter . We illustrate the various qualitative scenarios of the reduced system under singular perturbation. We will show that the fast–slow models, even though in nonstandard form, can be studied by means of GSPT.

---