## Model and Resilience Analysis

To introduce the concept we will start with a simple model. The premise of the model is that climate change effects may results in deterioration of water quality throughout a region of the world and this would eventually affect the public health of populations. The relationship between the three parameters considered in this model, namely the water quality, public health and the climate change effects parameter can be represented in terms of a box model characterized by the following simultaneous ordinary differential equation:

dt dP

dt H

In the model discussed here, Eq. 1.1 is a nonlinear ordinary differential equation which will be calibrated using data on regional water quality and public health. The non dimensional climate change parameter CC is a variable that would represent the climate change forcing function. In this case it is varied in between 0.05 and 0.45 indicating and increase in temperature. The nonlinear ordinary differential equation system has two stable points, one is at high public health level with low contamination and the other one is at low public health level with high contamination. In this case high contamination implies low water quality. There is the possibility of the system to converge to either of these two stability points depending on the initial conditions of the problem. The low water quality (high contamination) and low public health level is not a desired stability point for this system. On the other hand the stability point of high public health and high water quality (low contamination) is a desired stability point. The resilience of the system is defined as the return time required to any of these stable points given an initial starting point [5] and a disturbance. Obviously, after a disturbance, smaller return time to a stability point indicates the system is more resilient for that stability point even though one of the stability points may not be desired. Notice that the stability points are also a function of the parameter CC , the climate change parameter. The model selected indicates that the domain of attraction of the desired stable point shrinks as the climate change parameter is increased, implying the overall system behavior

Fig. 1.1 Resilience landscape for CC = 0.05 and 0.45

Fig. 1.2 Return time pathways on the phase diagram

Fig. 1.2 Return time pathways on the phase diagram

is dominated more and more by the undesired state (Fig. 1.1). In the phase space, the domain of attraction of these two stability points can be observed as shown in Fig. 1.1 for the climate change parameter range CC=0.05-0.45. All starting points on either side of the dividing surface will converge to the respective stability regions ending up in one of the desired or undesired conditions for the system. In Fig. 1.2 some of these paths are shown for several different starting points for CC=0.05 and CC=0.45.

The analysis of Fig. 1.2 indicates that some of the initial conditions which represent the current state of the public health and water quality conditions of a population that would be in the basin of attraction of a desired stability state may find itself in the basin of attraction of an undesired stability state as the climate change parameter is increased from 0.05 to 0.45 indicating deteriorating climate conditions. Thus, the policy decision that needs to be made for the populations is not uniform across the regions of the world. There are some populations and regions of the world which are in a more vulnerable state than others. These are those regions of the world which are currently at low public health level. In these regions, although the water quality may be at an acceptable level the vulnerability state to climate change of these regions is high. If the public health level is low and the water quality is also low than those populations will immediately feel the adverse effects of deteriorating climate and they will end in very low water quality levels and unsustainable public health conditions.

As a policy decision less vulnerable populations may manage to stay in the basin of attraction of the desirable stability point if they are able to improve their public health state and the local water quality standards. This can only be achieved if the rate of improvement implemented as a policy is higher than the rate of deterioration due to climate change effects. These rates are a function of the rate of movement of the public health factors along the trajectory and also the rate of deterioration effects. These two rates are also not the same for all populations and all regions of the world. These rates are also not constant for a given region and it varies as a function of time. Every starting point shown in Fig. 1.2 has to implement a different rate of improvement at every time step since the constant rate climate deterioration manifests itself at different rates of deterioration depending on these starting points and where the population is along the trajectory when the climate change effects are observed. That is, not only the initial conditions of the population and the region are important but also it is important to know where the region and population is on the phase space at each time when an adverse climate change effect occurs. Thus, uniform policy decisions across the board may not solve the problem in certain cases. The least vulnerable populations are those which are currently at high public health levels with low water quality problems. Seemingly those will survive the easiest according to the model implemented here which ignores the systemic risk. However, that is not the case as will be discussed below. This outcome only reflects the limitations of the model selected for this analysis. More realistic complex system models are necessary to address those conditions.

The outcome observed above may also be reversed. If the climate quality is improved than the basin of attraction of the desired stability point will enlarge and most populations of the world will have good chance of survival. According to the model used here some populations of the world may be already under stress under current climate conditions. The outcome maybe improved significantly, especially for most vulnerable populations, if all regions of the world and both industrialized and developing nations of the world not only collectively contribute to reduce the adverse effects of climate change but also help improve the current water quality conditions and public health levels of most vulnerable countries. Under these conditions it may be possible to control the adverse effects of deteriorating condition of climate change.

0 0