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Mathematical Biosciences

Leonid Bunimovich, Longmei Shu
Some basic aspects of the recently discovered phenomenon of local immunodeficiency [1] generated by antigenic cooperation in cross-immunoreactivity (CR) networks are investigated. We prove that local immunodeficiency (LI) that's stable under perturbations already occurs in very small networks and under general conditions on their parameters. Therefore our results are applicable not only to Hepatitis C where CR networks are known to be large [1], but also to other diseases with CR. A major necessary feature of such networks is the non-homogeneity of their topology...
February 14, 2019: Mathematical Biosciences
Jing Zhao, Shaopeng Gu, Adam McDermaid
Chronic kidney disease (CKD) is prevalent across the world, and kidney function is well defined by an estimated glomerular filtration rate (eGFR). The progression of kidney disease can be predicted if the future eGFR can be accurately estimated using predictive analytics. In this study, we developed and validated a prediction model of eGFR by data extracted from a regional health system. This dataset includes demographic, clinical and laboratory information from primary care clinics. The model was built using Random Forest regression and evaluated using Goodness-of-fit statistics and discrimination metrics...
February 12, 2019: Mathematical Biosciences
Baoling Ma, Chuan Li, Jack Warner
Malaria infection has posed a major health threat for hundreds of years in human history. Yet, due to the complex interactions between a host immune response and the parasite, no sophisticated mathematical models exist to study its dynamics. In this work, we propose a new system of structured partial differential equations that account for the dependence of red blood cell infectivity on maturation level. These equations are coupled with another set of differential equations for investigating the population dynamics of Plasmodium falciparum and its interaction with red blood cells and cells of the immune system...
February 12, 2019: Mathematical Biosciences
Regina Padmanabhan, Nader Meskin, Wassim M Haddad
In this paper, a reinforcement learning (RL)-based optimal adaptive control approach is proposed for the continuous infusion of a sedative drug to maintain a required level of sedation. To illustrate the proposed method, we use the common anesthetic drug propofol used in intensive care units (ICUs). The proposed online integral reinforcement learning (IRL) algorithm is designed to provide optimal drug dosing for a given performance measure that iteratively updates the control solution with respect to the pharmacology of the patient while guaranteeing convergence to the optimal solution...
February 5, 2019: Mathematical Biosciences
Clara Champagne, Bernard Cazelles
We perform estimations of compartment models for dengue transmission in rural Cambodia with increasing complexity regarding both model structure and the account for stochasticity. On the one hand, we successively account for three embedded sources of stochasticity: observation noise, demographic variability and environmental hazard. On the other hand, complexity in the model structure is increased by introducing vector-borne transmission, explicit asymptomatic infections and interacting virus serotypes. Using two sources of case data from dengue epidemics in Kampong Cham (Cambodia), models are estimated in the bayesian framework, with Markov Chain Monte Carlo and Particle Markov Chain Monte Carlo...
February 5, 2019: Mathematical Biosciences
Swadesh Pal, S Ghorai, Malay Banerjee
Non-local interaction describes the effects of mobility of a population species in their spatial locations. Non-local interaction is incorporated into a prey-predator model by introducing an integral term with appropriate kernel function. The kernel function determines the nature and range of the accessibility of the resources. We consider a nonlocal spatio-temporal prey-predator model with additive weak Allee effect in prey growth and density-dependent predator mortality. The dynamics of the model is examined in presence of a parabolic and a triangular kernel functions...
February 5, 2019: Mathematical Biosciences
Talal Alzahrani, Raluca Eftimie, Dumitru Trucu
Oncolytic viruses (OV) are viruses that can replicate selectively within cancer cells and destroy them. While the past few decades have seen significant progress related to the use of these viruses in clinical contexts, the success of oncolytic therapies is dampened by the complex spatial tumour-OV interactions. In this work, we present a novel multiscale moving boundary modelling for the tumour-OV interactions, which is based on coupled systems of partial differential equations both at macro-scale (tissue-scale) and at micro-scale (cell-scale) that are connected through a double feedback link...
February 4, 2019: Mathematical Biosciences
Abdulaziz Y A Mukhtar, Justin B Munyakazi, Rachid Ouifki
Malaria is endemic in South Sudan and it is one of the most severe diseases in the war-torn nation. There has been much concern about whether the severity of its transmission might depend upon climatic conditions that are related to the reproduction of the single-cell parasite attaching to female mosquitoes, especially in high altitude areas. The country experiences two different climatic conditions; namely one tropical and the other hot and semi-arid. In this study, we aim to assess the potential impact of climatic conditions on malaria prevalence in these two climatically distinct regions of South Sudan...
January 31, 2019: Mathematical Biosciences
Leonid Hanin, Burkhard Jandrig, Lyudmila Pavlova, Karen Seidel
The goal of this study is to uncover some unobservable aspects of the individual-patient natural history of metastatic renal cell carcinoma (RCC) through mathematical modeling. We analyzed four clear cell RCC patients who at the time of primary tumor resection already had pulmonary metastases. Our description of the natural history of cancer in these patients was based on a parameterized version of a previously proposed very general mathematical model adjusted to these clinical cases. For each patient, identifiable model parameters were estimated by the method of maximum likelihood from the volumes of lung metastases computed from CT scans taken at or around the time of surgery...
January 28, 2019: Mathematical Biosciences
Mingwang Shen, Yanni Xiao, Libin Rong, Lauren Ancel Meyers
Most of previous studies investigated the optimal control of HIV infection at either within-host or between-host level. However, the optimal treatment strategy for the individual may not be optimal for the population and vice versa. To determine when the two-level optimal controls are in accord or conflict, we develop a multi-scale model using various functions that link the viral load within host and the transmission rate between hosts, calibrated by cohort data. We obtain the within-host optimal treatment scheme that minimizes the viral load and maximizes the count of healthy cells at the individual level, and the coupled optimal scheme that minimizes the basic reproduction number at the population level...
January 23, 2019: Mathematical Biosciences
Simopekka Vänskä, Johannes A Bogaards, Kari Auranen, Matti Lehtinen, Johannes Berkhof
Cervical cancer arises differentially from infections with up to 14 high-risk human papillomavirus (HPV) types, making model-based evaluations of cervical cancer screening strategies computationally heavy and structurally complex. Thus, with the high number of HPV types, microsimulation is typically used to investigate cervical cancer screening strategies. We developed a feasible deterministic model that integrates varying natural history of cervical cancer by the different high-risk HPV types with compressed mixture representations of the screened population, allowing for fast computation of screening interventions...
January 16, 2019: Mathematical Biosciences
Michèle Breton, Ilyass Dahmouni, Georges Zaccour
In this paper, we consider a two-species fishery model where the species can have different biological interactions, namely, competitive, symbiotic or prey-predator relationships. Each species is harvested by a group of fisherpersons. We characterize and compare equilibrium harvesting strategies, steady-state stocks and total discounted utilities under different modes of play, that is, noncooperation in both groups, cooperation in each of the groups and cooperation in only one group of fisherpersons. Our main results are as follows: (i) In all scenarios, the equilibrium strategy of an agent fishing either species consists of harvesting, in each period, a proportion of the available stock...
January 15, 2019: Mathematical Biosciences
J P Gutiérrez-Jara, F D Córdova-Lepe, M T Muñoz-Quezada
This paper presents a novel epidemiological model of a population affected by two different susceptible-infected-susceptible infectious diseases. For each disease, individuals fall into one of the two susceptibility conditions in which one of the diseases has the highest occurrence level. This model is unique in assuming that: (a) if an individual is infected by one disease, their susceptibility to the other disease is increased; (b) when an individual recovers from a disease they become less susceptible to it, i...
January 15, 2019: Mathematical Biosciences
Xin Liu, Anuj Mubayi, Dominik Reinhold, Liu Zhu
Stochastic epidemic models, generally more realistic than deterministic counterparts, have often been seen too complex for rigorous mathematical analysis because of level of details it requires to comprehensively capture the dynamics of diseases. This problem further becomes intense when complexity of diseases increases as in the case of vector-borne diseases (VBD). The VBDs are human illnesses caused by pathogens transmitted among humans by intermediate species, which are primarily arthropods. In this study, a stochastic VBD model is developed and novel mathematical methods are described and evaluated to systematically analyze the model and understand its complex dynamics...
January 15, 2019: Mathematical Biosciences
Alexis Erich S Almocera, Esteban A Hernandez-Vargas
Multiscale models that link within-host infection to between-host transmission are valuable tools to progress understanding of viral infectious diseases. In this paper, we present two multiscale models that couple within-host infection to a susceptible-infected-recovered (SIR) model. A disease-induced transmission rate bridges the scales from within to between-host. Our stability analysis on the first model (influenza infection) reveals two equilibrium points for the SIR model that describe endemic scenarios where both susceptible and infected cases maintain nonzero population sizes...
January 15, 2019: Mathematical Biosciences
J A Guerrero, J E Macías-Díaz
In this work, we consider the problem of identifying activity phases in electromyography signals, and various other potential types of electrical and non-electrical biological signals such as electroneurograms, electroencephalograms, voice and ultrasounds. The solution to this problem has been provided under relatively limited scenarios. The purpose of the present work is to propose an optimal Bayesian classifier to solve the problem of detecting bursts on biological signals. To that end, a parametrization of the distribution of samples in signals is presented...
December 28, 2018: Mathematical Biosciences
I Akushevich, A Yashkin, J Kravchenko, F Fang, K Arbeev, F Sloan, A I Yashin
A new model for disease prevalence based on the analytical solutions of McKendrick-von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data...
December 28, 2018: Mathematical Biosciences
E Bonyah, M A Khan, K O Okosun, J F Gómez-Aguilar
Alcoholism has become a global threat and has a serious health consequence in the society. In this paper, a deterministic alcohol model is formulated, analyzed and the basic properties established. The reproduction number R0 of system is determined. The steady states examined and local stability is found to be both locally and globally stable. The endemic state exhibit three equilibra solutions. Furthermore, time dependent control is incorporated into the system in order to establish the best strategy in controlling the alcohol consumption and gonorrhea dynamics, using Pontryagin's Maximum Principle...
December 28, 2018: Mathematical Biosciences
Marthe Måløy, Frode Måløy, Rafael Lahoz-Beltrá, Juan Carlos Nuño, Antonio Bru
When a new type of individual appears in a stable population, the newcomer is typically not advantageous. Due to stochasticity, the new type can grow in numbers, but the newcomers can only become advantageous if they manage to change the environment in such a way that they increase their fitness. This dynamics is observed in several situations in which a relatively stable population is invaded by an alternative strategy, for instance the evolution of cooperation among bacteria, the invasion of cancer in a multicellular organism and the evolution of ideas that contradict social norms...
December 24, 2018: Mathematical Biosciences
Vinicius Weide, Maria C Varriale, Frank M Hilker
We develop three discrete-time predator-prey models from the Nicholson-Bailey host-parasitoid framework, assuming a type II functional response and logistic prey growth in form of the Beverton-Holt map. Our models show many similarities with the continuous-time Rosenzweig-MacArthur model, not only the same equilibria and sequence of bifurcations, but also phenomena such as the hydra effect and paradox of enrichment. Our three models differ in the order of events, in which the processes of density-dependent prey regulation and predation take place...
December 21, 2018: Mathematical Biosciences
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