Recent advances in random and deterministic modeling in biology/health sciences

Thursday, June 17 at 02:15am (PDT)
Thursday, June 17 at 10:15am (BST)
Thursday, June 17 06:15pm (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS17" time block.
Note: this minisymposia has multiple sessions. The second session is MS11-CBBS (click here).

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Maria C.A. Leite, (University of South Florida St.Petersburg), Juan Carlos Cortés López (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain), Rafael J. Villanueva Micó (Instituto Universitario de Matemática Multidisciplinar. Universitat Politècnica de València, Spain)


Mathematical modelling is well-known to be a vital tool for studying complex systems in biology and health sciences. They enable to study mathematically what is costly and/or impossible to do experimentally. There has been a large body of research on this area with amazing contributions in understanding complex biological/health sciences systems. In the spite of such, the innovative development of not only deterministic models but also models that include randomness is still critical for answering crucial questions in mathematical biology. Thus, the talks we envision for this mini-symposium will have a special focus on modeling approaches that have specific application to biology/health sciences, but will also be of interest to researchers in other areas. This mini-symposium will disseminate recent research and open questions in modeling biological/health sciences complex systems. It aims at inspiring mathematicians, modelers, and experimentalists to address several challenges in this field of research.

Francisco Rodríguez

(Dept. of Applied Mathematics and Multidisciplinary Institute for Environmental Studies (IMEM), University of Alicante, Spain)
"Ecohydrological feedbacks, delay responses and random perturbations in mean field dryland vegetation models"
Positive feedbacks between increased connectivity and loss of resources are recognized as potential landscape-scale factors driving degradation and desertification in semiarid regions. Common dryland vegetation models exhibit bistability as the result of different mechanisms yielding local positive feedbacks that reinforce the persistence and growth of vegetation patches, with an unstable equilibrium for vegetation separating the stable equilibria of vegetated and desert states. The existence of bistability allows for abrupt transitions between the alternative stable states, the so called catastrophic shifts, either as the result of gradual worsening of the environmental conditions or due to single or randomly distributed perturbations. Using a spatially explicit cellular automata (CA) dryland model, it has been shown that feedbacks between vegetation pattern and resource loss, measured through an index of spatial bare soil connectivity (Flowlength, FL), dramatically decrease ecosystem resilience and restoration potential. In this work, we considered mean field approximations to this CA model and other common dryland models, and showed that positive global ecohydrological feedbacks mediated by bare-soil connectivity, as captured by the expected value of the FL index, effectively decrease resilience and suffice to induce bistability in absence of additional local feedbacks. We also explored how the presence of delayed responses could affect recovery after random perturbations.

Sandra Delgadillo

(Universidad Autónoma de Aguascalientes, México)
"Full probabilistic analysis of random first-order linear differential equations with Dirac delta impulses (Pre-recorded)"
In this talk, we address, from a probabilistic standpoint, a first-order linear differential equation with an infinite train of Dirac delta impulses. We consider that all its initial condition and coefficients are absolutely continuous random variables with a joint probability density function. We take extensive advantage of the Random Variable Transformation method to determine, first, an explicit expression for the probability density of the solution stochastic process. Secondly, of the random sequences for the maxima and minima for the case, the impulses application times are evenly spaced, with period $T$. From these sequences, we determine the probability of stability of the solution stochastic process. All the theoretical results are illustrated by means of several numerical examples. Finally, we briefly discuss the results of a sensitivity analysis performed, via Sobol indexes, for a fixed and random period T.

Carlos A. Braumann

(Department of Mathematics & CIMA, Universidade de Évora, Portugal)
"Harvesting optimization in a randomly varying environment"
We can describe the dynamics of a harvested population in a randomly varying environment by stochastic differential equations models. Previously [N.M. Brites and C.A. Braumann (2017), Fisheries Res. 195: 238-246; N.M. Brites and C.A. Braumann (2019), Fisheries Res. 216: 196-203], we have compared the profit performance of two harvesting policies, the optimal policy (with variable harvesting effort) and the optimal sustainable policy (with constant harvesting effort). The former is inapplicable in practice due to the fast and abrupt variations of the harvesting effort associated with the frequent environmentally induced variations in population size. Furthermore, it requires the knowledge of the population size at each instant - an inaccurate, lengthy, and expensive task. The optimal sustainable policy considers the application of a constant harvesting effort and, under suitable conditions, leads [see, in a more general setting, C.A. Braumann (1999), Mathem. Biosc. 156: 1-19], to population sustainability and the existence of a stationary probability density. This policy has the advantage of being easily applicable and there is no need to estimate the population size. The performance of the two policies was compared in terms of profit over a finite time horizon. Using data based on real harvested populations and the usual logistic and Gompertz growth models, we show that there is only a slight reduction in profit by using the optimal sustainable policy (based on constant effort) instead of the inapplicable optimal policy (based on variable effort). We also present here stepwise effort policies [introduced in N.M. Brites and C.A. Braumann (2019), Stat. Optim. Inform. Comp. 7(3): 533-544], which are applicable, and compare them with the previous policies. Extensions to Alee effects models can be seen in N.M. Brites and C.A. Braumann (2020), Appl. Stoch. Models Bus. Ind. 36: 825–835. Acknowledgements: Carlos A. Braumann belongs to the research center CIMA - Centro de Investigação em Matemática e Aplicações, Universidade de Évora, supported by FCT (Fundação para a Ciência e a Tecnologia, Portugal), project UID/04674/2020. Nuno M. Brites was partially supported by the Project CEMAPRE/REM - UIDB/05069/2020 - financed by FCT/MCTES through national funds.

Roberto Ku-Carrillo

(Universidad Autónoma de Aguascalientes, Mexico)
"On a linear random differential equation with periodic harvesting and migration"
process. Given the abundance of evidence that evolution is not strictly

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