The transmission mechanism theory of disease dynamics:Its aims,assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process.Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history,dating back to over a century now,that knowledge has not yet been formalized into a scientific theory.In this article,we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system,disease dynamics is determined by transmission as the main dynamic disease process.Therefore,the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now.The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims,assumptions and limitations.

Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration

Stem cell regeneration is an essential biological process in the maintenance of tissue homeostasis;dysregulation of stem cell regeneration may result in dynamic diseases that show oscillations in cell numbers.Cell heterogeneity and plasticity are necessary for the dynamic equilibrium of tissue homeostasis;however,how these features may affect the oscillatory dynamics of the stem cell regeneration process remains poorly understood.Here,based on a mathematical model of heterogeneous stem cell regeneration that includes cell heterogeneity and random transition of epigenetic states,we study the conditions to have oscillation solutions through bifurcation analysis and numerical simulations.Our results show various model system dynamics with changes in different parameters associated with kinetic rates,cellular heterogeneity,and plasticity.We show that introducing heterogeneity and plasticity to cells can result in oscillation dynamics,as we have seen in the homogeneous stem cell regeneration system.However,increasing the cell heterogeneity and plasticity intends to maintain tissue homeostasis under certain conditions.The current study is an initiatory investigation of how cell heterogeneity and plasticity may affect stem cell regeneration dynamics,and many questions remain to be further studied both biologically and mathematically.

A Computer Software-Epitimulator~ for Simulating Temporal Dynamics of Plant Disease Epidemic Progress

The objective of the present study was to develop a computer software for simulating the temporal development of plant disease epidemics using Richards, logistic, Gompertz, monomolecular, and exponential functions, respectively, and for predicting disease with a fitted model. The software was programmed using Visual Basic （VB6.0） and packaged with the Wise Installation System. The Fibonacci （＇0.618＇） section strategy was used to find out the most appropriate value for the shape parameter （m） in Richards function simulation through looping procedures. The software program was repeatedly tested, debugged and edited until it was run through favorably and produced ideal outputs. It was named Epitimulator based on the phrase ＇epidemic time simulator＇ and has been registered by the National Copyright Department of China （Reg. no. 2007SR18489）. It can be installed and run on personal computers with all versions of Windows operational systems. Data of disease index and survey time are keyed in or imported from Access files. The output of fitted models and related data of parameters can be pasted into Microsoft Excel worksheet or into Word document for editing as required and the simulated disease progress curves can be stored in separate graphic files. After being finally tested and completed, Epitimulator was applied to simulate the epidemic progress of corn northern leaf blight （Exserohilum turcicum） with recorded data from field surveys of corn crops and the fitted models were output. Comparison of the simulation results showed that the disease progress was always best described by Richards function, which resulted in the most accurate simulation model. Result also showed that forecast of northern leaf blight development was highly accurate by using the computed progress model from Richards function.

Mathematical modelling for Zoonotic Visceral Leishmaniasis dynamics:A new analysis considering updated parameters and notified human Brazilian data

Brazil is one of the highest endemic countries for Zoonotic Visceral Leishmaniasis:according to the Brazilian Ministry of Health,the annual number of new human cases and deaths due to this disease has been increasing for the last 20 years.In addition,regarding the Americas,the specific relationship between canine and human for Visceral Leishmaniasis dynamics is still not well understood.In this work we propose a new model for Zoonotic Visceral Leishmaniasis,based on the models previously published by Burattini et al.(1998)and Ribas et al.(2013).Herein,we modeled the disease dynamics using a modified set of differential equations from those two authors,considering the same assumptions(inclusion of human,dog and sandfly populations,all constants over time).From this set of equations we were able to calculate the basic reproduction number R 0 and to analyze the stability and sensitivity of the system to the parameters variability.As main result,when the stability of the system is reached,the normalized reporting human cases rate is estimated in 9.12E-08/day.This estimation is very close to the 2015 report from Araçatuba city,5.69E-08/day.We also observed from stability and sensitivity analysis that the activity of sandfly population is critical to introduction and maintenance of Zoonotic Visceral Leishmaniasis in the population.In addition,the importance of dog as source of infection concentrates on latent dog,since it does not show clinical symptoms and signs and,therefore,has a great contribution to disease dissemination.As conclusion,considering the presently ethical issues regarding to elimination of positive dog in Brazil and the highly sensitivity of disease dynamics on sandfly population,we recommend that the sandfly population control should be prioritized.

Dynamic model of tuberculosis considering multi-drug resistance and their applications

Infectious diseases have always been a problem that threatens people's health and tuberculosis is one of the major.With the development of medical scientific research,drug-resistant infectious diseases have become a more intractable threat because various drugs and antibiotics are widely used in the process of fighting against infectious diseases.In this paper,an improved dynamic model of infectious diseases considering population dynamics and drug resistance is established.The feasible region,equilibrium points and stability of the model are analyzed.Based on the existing data,this model can predict the development of the epidemic situation through numerical simulation,and put forward some relevant measures and suggestions.

Addiction as a dynamical rationality disorder

Addiction is frequently modeled as a behavioral disorder resulting from the internal battle between two subsystems:one model describes slow planning versus fast habitual action;another,hot versus cold modes.In another model,one subsystem pushes the individual toward substance abuse,while the other tries to pull him away.These models all describe one side winning over the other at each point of confrontation,represented as a simple binary switch:on or off,win or lose.We propose however,an alternative model,in which opposing systems work in parallel,tipping toward one subsystem or the other,in greater or lesser degree,based on a continuous rationality factor.Our approach results in a dynamical system that qualitatively emulates seeking behavior,cessation,and relapse—enabling the accurate description of a process that can lead to recovery.As an adjunct to the model,we are in the process of creating an associated,interactive website that will enable addicts to journal their thoughts,emotions and actions on a daily basis.The site is not only a potentially rich source of data for our model,but will in its primary function aid addicts to individually identify parameters affecting their decisions and behavior.