diff --git a/odetoolbox/__init__.py b/odetoolbox/__init__.py
index f365d01a..66ee08ea 100644
--- a/odetoolbox/__init__.py
+++ b/odetoolbox/__init__.py
@@ -27,7 +27,7 @@
 from sympy.core.expr import Expr as SympyExpr   # works for both sympy 1.4 and 1.8
 
 from .config import Config
-from .sympy_helpers import _find_in_matrix, _is_zero, _is_sympy_type, SympyPrinter
+from .sympy_helpers import _check_numerical_issue, _check_forbidden_name, _find_in_matrix, _is_zero, _is_sympy_type, SympyPrinter
 from .system_of_shapes import SystemOfShapes
 from .shapes import MalformedInputException, Shape
 
@@ -109,7 +109,7 @@ def _from_json_to_shapes(indict, parameters=None) -> Tuple[List[Shape], Dict[sym
     """
 
     logging.info("Processing input shapes...")
-    shapes = []
+
     # first run for grabbing all the variable names. Coefficients might be incorrect.
     all_variable_symbols = []
     all_parameter_symbols = set()
@@ -124,6 +124,11 @@ def _from_json_to_shapes(indict, parameters=None) -> Tuple[List[Shape], Dict[sym
     assert all([_is_sympy_type(sym) for sym in all_variable_symbols])
     logging.info("All known variables: " + str(all_variable_symbols) + ", all parameters used in ODEs: " + str(all_parameter_symbols))
 
+    # validate input for forbidden names
+    for var in set(all_variable_symbols) | all_parameter_symbols:
+        _check_forbidden_name(var)
+
+    # validate parameters
     for param in all_parameter_symbols:
         if parameters is None:
             parameters = dict()
@@ -135,6 +140,7 @@ def _from_json_to_shapes(indict, parameters=None) -> Tuple[List[Shape], Dict[sym
             parameters[param] = None
 
     # second run with the now-known list of variable symbols
+    shapes = []
     for shape_json in indict["dynamics"]:
         shape = Shape.from_json(shape_json, all_variable_symbols=all_variable_symbols, parameters=parameters, _debug=True)
         shapes.append(shape)
@@ -210,6 +216,9 @@ def _analysis(indict, disable_stiffness_check: bool = False, disable_analytic_so
                 assert type(k) is sympy.Symbol
                 parameters[k] = v
 
+            _check_forbidden_name(k)
+
+
     #
     #   create Shapes and SystemOfShapes
     #
@@ -292,8 +301,12 @@ def _analysis(indict, disable_stiffness_check: bool = False, disable_analytic_so
             all_shape_symbols = [str(sympy.Symbol(str(shape.symbol) + Config().differential_order_symbol * i)) for i in range(shape.order)]
             for sym in all_shape_symbols:
                 if sym in solver_json["state_variables"]:
-                    solver_json["initial_values"][sym] = str(shape.get_initial_value(sym.replace(Config().differential_order_symbol, "'")))
+                    iv_expr = shape.get_initial_value(sym.replace(Config().differential_order_symbol, "'"))
+                    solver_json["initial_values"][sym] = str(iv_expr)
 
+                    # validate output for numerical problems
+                    for var in iv_expr.atoms():
+                        _check_numerical_issue(var)
 
     #
     #   copy the parameter values from the input to the output for convenience; convert into numeric values
@@ -318,7 +331,20 @@ def _analysis(indict, disable_stiffness_check: bool = False, disable_analytic_so
                             break
 
                 if symbol_appears_in_any_expr:
-                    solver_json["parameters"][param_name] = str(sympy.parsing.sympy_parser.parse_expr(param_expr, global_dict=Shape._sympy_globals).n())
+                    sympy_expr = sympy.parsing.sympy_parser.parse_expr(param_expr, global_dict=Shape._sympy_globals)
+
+                    # validate output for numerical problems
+                    for var in sympy_expr.atoms():
+                        _check_numerical_issue(var)
+
+                    # convert to numeric value
+                    sympy_expr = sympy_expr.n()
+
+                    # validate output for numerical problems
+                    for var in sympy_expr.atoms():
+                        _check_numerical_issue(var)
+
+                    solver_json["parameters"][param_name] = str(sympy_expr)
 
 
     #
diff --git a/odetoolbox/config.py b/odetoolbox/config.py
index 8efb3e8c..6f4fe97e 100644
--- a/odetoolbox/config.py
+++ b/odetoolbox/config.py
@@ -34,7 +34,8 @@ class Config:
         "sim_time": 100E-3,
         "max_step_size": 999.,
         "integration_accuracy_abs": 1E-6,
-        "integration_accuracy_rel": 1E-6
+        "integration_accuracy_rel": 1E-6,
+        "forbidden_names": ["oo", "zoo", "nan", "NaN", "__h"]
     }
 
     def __getitem__(self, key):
diff --git a/odetoolbox/shapes.py b/odetoolbox/shapes.py
index ba9fc0c1..507ab979 100644
--- a/odetoolbox/shapes.py
+++ b/odetoolbox/shapes.py
@@ -21,7 +21,7 @@
 
 from __future__ import annotations
 
-from typing import List, Mapping, Tuple
+from typing import List, Tuple
 
 import functools
 import logging
@@ -30,11 +30,9 @@
 import sympy.parsing.sympy_parser
 
 from sympy.core.expr import Expr as SympyExpr   # works for both sympy 1.4 and 1.8
-from sympy.core.numbers import One as SympyOne
-from sympy.core.numbers import Zero as SympyZero
 
 from .config import Config
-from .sympy_helpers import _custom_simplify_expr, _is_sympy_type, _is_zero
+from .sympy_helpers import _check_numerical_issue, _check_forbidden_name, _custom_simplify_expr, _is_constant_term, _is_sympy_type, _is_zero
 
 
 class MalformedInputException(Exception):
@@ -44,17 +42,6 @@ class MalformedInputException(Exception):
     pass
 
 
-def is_constant_term(term, parameters: Mapping[sympy.Symbol, str] = None):
-    r"""
-    :return: :python:`True` if and only if this term contains only numerical values and parameters; :python:`False` otherwise.
-    """
-    if parameters is None:
-        parameters = {}
-    assert all([type(k) is sympy.Symbol for k in parameters.keys()])
-    return type(term) in [sympy.Float, sympy.Integer, SympyZero, SympyOne] \
-        or all([sym in parameters.keys() for sym in term.free_symbols])
-
-
 class Shape:
     r"""
     This class provides a canonical representation of a shape function independently of the way in which the user specified the shape. It assumes a differential equation of the general form (where bracketed superscript :math:`{}^{(n)}` indicates the :math:`n`-th derivative with respect to time):
@@ -79,6 +66,7 @@ class Shape:
                       "Integer": sympy.Integer,
                       "Float": sympy.Float,
                       "Function": sympy.Function,
+                      "Mul": sympy.Mul,
                       "Pow": sympy.Pow,
                       "power": sympy.Pow,
                       "exp": sympy.exp,
@@ -326,6 +314,9 @@ def from_json(cls, indict, all_variable_symbols=None, parameters=None, _debug=Fa
                     raise MalformedInputException("In defintion of initial value for variable \"" + iv_symbol + "\": differential order (" + str(iv_order) + ") exceeds that of overall equation order (" + str(order) + ")")
                 if initial_val_specified[iv_order]:
                     raise MalformedInputException("Initial value for order " + str(iv_order) + " specified more than once")
+
+                _check_forbidden_name(iv_symbol)
+
                 initial_val_specified[iv_order] = True
                 initial_values[iv_symbol + iv_order * "'"] = iv_rhs
 
@@ -392,13 +383,13 @@ def split_lin_inhom_nonlin(expr, x, parameters=None):
             terms = [expr]
 
         for term in terms:
-            if is_constant_term(term, parameters=parameters):
+            if _is_constant_term(term, parameters=parameters):
                 inhom_term += term
             else:
                 # check if the term is linear in any of the symbols in `x`
                 is_lin = False
                 for j, sym in enumerate(x):
-                    if is_constant_term(term / sym, parameters=parameters):
+                    if _is_constant_term(term / sym, parameters=parameters):
                         lin_factors[j] += term / sym
                         is_lin = True
                         break
@@ -584,8 +575,21 @@ def from_ode(cls, symbol: str, definition: str, initial_values: dict, all_variab
         order: int = len(initial_values)
         all_variable_symbols_dict = {str(el): el for el in all_variable_symbols}
         definition = sympy.parsing.sympy_parser.parse_expr(definition.replace("'", Config().differential_order_symbol), global_dict=Shape._sympy_globals, local_dict=all_variable_symbols_dict)  # minimal global_dict to make no assumptions (e.g. "beta" could otherwise be recognised as a function instead of as a parameter symbol)
+
+        # validate input for forbidden names
+        _initial_values = {k: sympy.parsing.sympy_parser.parse_expr(v, evaluate=False, global_dict=Shape._sympy_globals, local_dict=all_variable_symbols_dict) for k, v in initial_values.items()}
+        for iv_expr in _initial_values.values():
+            for var in iv_expr.atoms():
+                _check_forbidden_name(var)
+
+        # parse input
         initial_values = {k: sympy.parsing.sympy_parser.parse_expr(v, global_dict=Shape._sympy_globals, local_dict=all_variable_symbols_dict) for k, v in initial_values.items()}
 
+        # validate input for numerical issues
+        for iv_expr in initial_values.values():
+            for var in iv_expr.atoms():
+                _check_numerical_issue(var)
+
         local_symbols = [symbol + Config().differential_order_symbol * i for i in range(order)]
         local_symbols_sympy = [sympy.Symbol(sym_name) for sym_name in local_symbols]
         if not symbol in all_variable_symbols:
diff --git a/odetoolbox/sympy_helpers.py b/odetoolbox/sympy_helpers.py
index 0d59f588..ba45457c 100644
--- a/odetoolbox/sympy_helpers.py
+++ b/odetoolbox/sympy_helpers.py
@@ -1,5 +1,5 @@
 #
-# sympy_printer.py
+# sympy_helpers.py
 #
 # This file is part of the NEST ODE toolbox.
 #
@@ -19,6 +19,8 @@
 # along with NEST.  If not, see <http://www.gnu.org/licenses/>.
 #
 
+from typing import Mapping
+
 import logging
 import sympy
 import sys
@@ -26,6 +28,37 @@
 from .config import Config
 
 
+class NumericalIssueException(Exception):
+    r"""Thrown in case of numerical issues, like division by zero."""
+    pass
+
+
+def _is_constant_term(term, parameters: Mapping[sympy.Symbol, str] = None) -> bool:
+    r"""
+    :return: :python:`True` if and only if this term contains only numerical values and parameters; :python:`False` otherwise.
+    """
+    if parameters is None:
+        parameters = {}
+    assert all([type(k) is sympy.Symbol for k in parameters.keys()])
+    return type(term) in [sympy.Float, sympy.Integer, sympy.core.numbers.Zero, sympy.core.numbers.One] \
+        or all([sym in parameters.keys() for sym in term.free_symbols])
+
+
+def _check_numerical_issue(var: str) -> None:
+    forbidden_vars = ["zoo", "oo", "nan", "NaN"]
+    stripped_var_name = str(var).strip("'")
+    if stripped_var_name in forbidden_vars:
+        raise NumericalIssueException("The variable \"" + stripped_var_name + "\" was found. This indicates a numerical problem while solving the system of ODEs. Please check the input for correctness (such as the presence of divisions by zero).")
+
+
+def _check_forbidden_name(var: str) -> None:
+    from .shapes import MalformedInputException
+
+    stripped_var_name = str(var).strip("'")
+    if stripped_var_name in Config().forbidden_names + dir(sympy.core.numbers):
+        raise MalformedInputException("Variable by name \"" + stripped_var_name + "\" not allowed; this is a reserved name.")
+
+
 def _is_zero(x):
     r"""
     Check if a sympy expression is equal to zero.
diff --git a/tests/test_malformed_input.py b/tests/test_malformed_input.py
new file mode 100644
index 00000000..12b9dcf3
--- /dev/null
+++ b/tests/test_malformed_input.py
@@ -0,0 +1,67 @@
+#
+# test_malformed_input.py
+#
+# This file is part of the NEST ODE toolbox.
+#
+# Copyright (C) 2017 The NEST Initiative
+#
+# The NEST ODE toolbox is free software: you can redistribute it
+# and/or modify it under the terms of the GNU General Public License
+# as published by the Free Software Foundation, either version 2 of
+# the License, or (at your option) any later version.
+#
+# The NEST ODE toolbox is distributed in the hope that it will be
+# useful, but WITHOUT ANY WARRANTY; without even the implied warranty
+# of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+# General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with NEST.  If not, see <http://www.gnu.org/licenses/>.
+#
+
+import pytest
+
+from .context import odetoolbox
+from odetoolbox.shapes import MalformedInputException
+from odetoolbox.sympy_helpers import NumericalIssueException
+
+
+class TestMalformedInput:
+    r"""Test for failure when forbidden names are used in the input."""
+
+    @pytest.mark.xfail(strict=True, raises=MalformedInputException)
+    def test_malformed_input_iv(self):
+        indict = {"dynamics": [{"expression": "x' = 0",
+                                "initial_value": "zoo"}]}
+        result = odetoolbox.analysis(indict, disable_stiffness_check=True)
+
+    @pytest.mark.xfail(strict=True, raises=MalformedInputException)
+    def test_malformed_input_expr(self):
+        indict = {"dynamics": [{"expression": "x' = 42 * NaN",
+                                "initial_value": "0."}]}
+        result = odetoolbox.analysis(indict, disable_stiffness_check=True)
+
+    @pytest.mark.xfail(strict=True, raises=MalformedInputException)
+    def test_malformed_input_sym(self):
+        indict = {"dynamics": [{"expression": "oo' = 0",
+                                "initial_value": "0."}]}
+        result = odetoolbox.analysis(indict, disable_stiffness_check=True)
+
+    def test_correct_input(self):
+        indict = {"dynamics": [{"expression": "foo' = 0",
+                                "initial_value": "0."}]}
+        result = odetoolbox.analysis(indict, disable_stiffness_check=True)
+
+    @pytest.mark.xfail(strict=True, raises=NumericalIssueException)
+    def test_malformed_input_numerical_iv(self):
+        indict = {"dynamics": [{"expression": "foo' = 0",
+                                "initial_value": "1/0"}]}
+        result = odetoolbox.analysis(indict, disable_stiffness_check=True)
+        import pdb;pdb.set_trace()
+
+    @pytest.mark.xfail(strict=True, raises=NumericalIssueException)
+    def test_malformed_input_numerical_parameter(self):
+        indict = {"dynamics": [{"expression": "foo' = bar",
+                                "initial_value": "1"}],
+                  "parameters": {"bar": "1/0"}}
+        result = odetoolbox.analysis(indict, disable_stiffness_check=True)