title: Mathematical model on Alzheimer's disease.
abstract: Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually.
  
  
  
  The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials.
  
  
  
  Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.
authors.affiliation: Department of Mathematics, The Penn State University, University Park, 16802, PA, USA. hao.50@mbi.osu.edu.
authors.forename: Wenrui
authors.initials: W
authors.lastname: Hao
authors.affiliation: Mathematical Biosciences Institute & Department of Mathematics, The Ohio State University, Columbus, 43210, OH, USA.
authors.forename: Avner
authors.initials: A
authors.lastname: Friedman
mesh_terms: D000544:Alzheimer Disease / Q000188:drug therapy / Q000378:metabolism* / Q000473:pathology*; D016229:Amyloid beta-Peptides / Q000737:chemistry / Q000378:metabolism; D001253:Astrocytes / Q000187:drug effects / Q000473:pathology; D018932:Chemokine CCL2 / Q000037:antagonists & inhibitors; D018450:Disease Progression; D006801:Humans; D008264:Macrophages / Q000166:cytology / Q000187:drug effects; D017628:Microglia / Q000187:drug effects / Q000473:pathology; D008954:Models, Biological; D009474:Neurons / Q000187:drug effects / Q000473:pathology; D010766:Phosphorylation / Q000187:drug effects; D066329:Protein Aggregates / Q000187:drug effects; D055503:Protein Multimerization; D017433:Protein Structure, Secondary; D016212:Transforming Growth Factor beta / Q000494:pharmacology / Q000627:therapeutic use; D014409:Tumor Necrosis Factor-alpha / Q000037:antagonists & inhibitors; D016875:tau Proteins / Q000378:metabolism
chemical_list: D016229:Amyloid beta-Peptides; C111835:CCL2 protein, human; D018932:Chemokine CCL2; D066329:Protein Aggregates; D016212:Transforming Growth Factor beta; D014409:Tumor Necrosis Factor-alpha; D016875:tau Proteins
keywords: Alzheimer disease; Drug treatment; Mathematical modeling