# [CT187]

## [00044] Final size and infectious cases estimate for two-group SEIRD model

• Session Date & Time : 2D (Aug.22, 15:30-17:10)
• Type : Contributed Talk
• Abstract : For a two-group SEIRD model with asymmetric interaction and an approximated solution, we estimate the error of this approximation in the second group based on the error in the first one. We also study the final size of the epidemic for each group. The results are illustrated with the spread of COVID-19 pandemic in the New York County-USA for the initial stage of the contamination, and in the cities of Petrolina and Juazeiro-Brazil.
• Classification : 92D25, 92D30, 34C60
• Author(s) :
• Matheus Correia dos Santos (Federal University of Rio Grande do Sul - UFRGS)
• Alison Marcelo Van der Laan Melo (Federal University of the São Francisco Valley - UNIVASF)

## [00078] A higher order numerical scheme to a nonlinear McKendrick-Von Foerster equation with singular mortality

• Session Date & Time : 2D (Aug.22, 15:30-17:10)
• Type : Contributed Talk
• Abstract : In this paper, higher-order numerical schemes to the McKendrick-Von Foerster equation are presented when the death rate has singularity at the maximum age. The third, fourth-order schemes that are proposed are based on the characteristics, which are non-intersecting lines in this case, and are multi-step methods with appropriate corrections at each step. In fact, the convergence analysis of the schemes is discussed in detail. Moreover, numerical experiments are provided to validate the orders of convergence of the proposed third-order and fourth-order schemes.
• Classification : 92D25, 65M25, 65M12
• Author(s) :
• Joydev Halder (School of Mathematics and Statistics, University of Hyderabad)
• Suman Kumar Tumuluri (School of Mathematics and Statistics, University of Hyderabad)

## [01314] Final Size and estimated number of infections two-group SEIRD model

• Session Date & Time : 2D (Aug.22, 15:30-17:10)
• Type : Contributed Talk
• Abstract : We consider a two-group SEIRD epidemic model. We show that the final state of susceptible individuals is always positive and present a way to obtain it. Also, we show how to estimate the number of infections in a group, based on the number of infections in the other group and on the number of deaths in the whole population. We illustrate our results with the spread of the COVID-19 pandemic in the USA and Brazil.
• Classification : 92D25, 92D30, 34C60
• Author(s) :
• Matheus Correia dos Santos (Federal University of Rio Grande do Sul - UFRGS)
• Alison Marcelo Van Der Laan Melo (Federal University of the São Francisco Valley)

## [01762] Generalized proofs of positivity of the solutions to population models

• Session Date & Time : 2D (Aug.22, 15:30-17:10)
• Type : Contributed Talk
• Abstract : Dynamic models of many processes in the biological and physical sciences are governed by systems of ordinary differential equations called compartmental systems. Since the dependent variables in such models denote population size, the solutions that start from positive initial conditions remain positive for all time. In this study, two generalized proofs of positivity of the solutions to compartmental models are presented. These compartmental models can be used in many applications including epidemiology and population dynamics.
• Classification : 92D25, 92-10
• Author(s) :
• AUNI ASLAH MAT DAUD (Universiti Malaysia Terengganu)

## [01826] Environmental Feedbacks from the Warburg Effect in Pre-Metastatic Neoplasms

• Session Date & Time : 2D (Aug.22, 15:30-17:10)
• Type : Contributed Talk
• Abstract : Unusual metabolism is a hallmark of cancer know as the Warburg effect. The methodology of eco-evolutionary games can describe this effect. We mathematically model the game between two metabolic strategies in the neoplasm: oxidative phosphorylation vs glycolysis. We show that our model results in 5 possible dynamic regimes. We conclude that lower glucose uptake rates for glycolytic cells help maintain less dangerous non-glycolytic tumors and hinder early tumor progression. This conclusion provides new treatment insights.
• Classification : 92D25, 92D40, 91A22
• Author(s) :
• Mark Steven Lovett (Dartmouth College)
• Erol Akçay (University of Pennsylvania)
• Andrew Tilman (USDA: Forestry service)
• Artem Kaznatcheev (Department of Mathematics and Department of Information and Computing Sciences, Utrecht University.)

## [01964] Competitions between stage-structured species in a patchy environment

• Session Date & Time : 2E (Aug.22, 17:40-19:20)
• Type : Contributed Talk
• Abstract : In this study, an ecological model with two life stages, immature and mature, and incorporating both intra- and inter-competitions between two species is explored to study invasion of species in a two-patch environment. It can be applied to exploring evolution of insects like Drosophila and beetles, which experience larva and adult (immature and mature life stages). The monotone dynamics in such a model provides us a property to explore its local and global dynamics. The model can also admit complex dynamics with multiple positive equilibria and limit point bifurcation when both species persist.
• Classification : 92D25, 92D40, 37N25
• Author(s) :
• Chang-Yuan Cheng (National Pingtung University National Pingtung University)

## [02455] Transient indicator and asymptotic dynamics of Bazykin's predator-prey model

• Session Date & Time : 2E (Aug.22, 17:40-19:20)
• Type : Contributed Talk
• Abstract : Transient dynamics are just as important as the asymptotic dynamics of ecological models. Motivated by this, we investigate both the transient and asymptotic dynamics of Bazykin’s model. Due to the presence of a bistable region, reactivity and resilience analysis are performed for both the coexisting states. The system is highly reactive and less resilient in the vicinity of the saddle-node bifurcation. The sensitivity analysis is examined using matrix calculus to identify the most sensitive parameter.
• Classification : 92D25, 34C23, 91B76, 90C31, 34D05
• Author(s) :
• TAPAN KUMAR KAR (Indian Institute of Engineering Science and Technology, Shibpur)

## [02460] Oxygen-plankton model to study a catastrophic event: ocean anoxia

• Session Date & Time : 2E (Aug.22, 17:40-19:20)
• Type : Contributed Talk
• Abstract : The dissolved oxygen in the ocean has decreased significantly during the past few decades. It is distributed heterogeneously in the ocean, forming large patches of oxygen-depleted zones known as Oxygen Minimum Zones (OMZ). This talk will consider a conceptual plankton-oxygen model that accounts for the difference in the timescales for phyto- and zooplankton. It will emphasize the impact of the plankton's timescale separation and nonlinear mortality rate in addressing the growth and expansion of OMZs.
• Classification : 92D25, 34D45, 35Q92
• Author(s) :
• Pranali Roy Chowdhury (Indian Institute of Technology Kanpur)

## [00205] `Period doubling' induced by optimal control in a behavioral SIR epidemic model.

• Session Date & Time : 2E (Aug.22, 17:40-19:20)
• Type : Contributed Talk
• Abstract : We consider a behavioral SIR epidemic model to describe the action of the public health system aimed at enhancing the social distancing during an epidemic outbreak. An optimal control problem is proposed where the control acts in a specific way on the contact rate. We show that the optimal control of social distancing is able to generate a period doubling–like phenomenon. Namely, the ‘period’ of the prevalence is double the ‘period’ of the control, and an alternation of small and large peaks of disease prevalence can be observed.
• Classification : 92D30, 34C60, 93C15
• Author(s) :
• Sileshi Sintayehu Sharbayta (Addis Ababa University)
• Bruno Buonomo (University of Naples Federico II)
• Alberto d'Onofrio (University of Trieste)
• Tadesse Abdi (Addis Ababa University)