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Hypothetical Situation with No Disease Transmission
The final scenario considers a hypothetical situation where there is no disease transmission, and hence the term XS becomes zero in the cattle growth equations 4.2 and 4.3. This may be the case if buffalo are effectively prevented from entering the adjacent areas of the conservation area; that is, no fences are destroyed, etc, or cattle vaccination is totally preventing the cattle stock from being infected. When also assuming that no cattle are infected initially, or that is it is possible to stamp out all infected cattle, the livestock equations 4.2 and 4.3 collapse into: dZ dt GZ
The benefit function of the cattle farmers changes accordingly, since farmers only slaughter healthy animals such that the slaughter price is S p . As there are no externalities in this model, there is no interaction among the agents. Therefore, when the conservation agency optimises its situation, the buffalo stock under a no-disease scenario will be identical to what was found under the conservation perspective, n * X X (superscript ‘n’ denotes the no disease transmission scenario). The steady state profit for the conservation agency will also be similar under these two scenarios.
The equation of motion is given by equation (4.22). The steady state for cattle population with singular control (golden rule) is then determined by:
The steady state singular optimal slaughter policy n follows through Z G(Z) . This solution n Z and n indicates the optimal size of the cattle stock and slaughtering when there are no resource conflicts due to disease transmission between the conservation agency and cattle farmers. In addition, assuming that there is no discounting, the steady state benefit under this scenario exceeds the previous cases, n p * U U U .
Data and specification of functional forms
The standard logistic forms were used for the natural growth functions of the buffalo as well as the healthy and infected cattle populations, as specified in Chapter 4. The disease transmission mechanisms are as given in the analytical model specifications of chapter 4. The culling cost function for the conservation agency is assumed to be linear in the harvest and does not include any stock effect. With the exception of the stock cost function to control the herd size of buffalo in the park, all other cost and benefit functions are assumed to be linear. Thus, the maintenance cost function for farmers is specified as A(Z) aZ a (S I ) with a 0 and the cattle stock value function as W(Z) wZ w (S I )with w 0 . The tourist value function for the conservation agency is measured by B(X) bX with b 0, while the cost function for buffalo stock is specified as strictly convex and represented by 2 V(X) (v / 2)X with v 0 .
The values of the biological and economic parameters are taken either from previous studies, from South African National Parks and the Directorate of Veterinary Services in the KZN, or based on qualified guess work and calibration (Table 5.1). The carrying capacity for the cattle population in the open grazing area is L 32 5000 (animals) while the carrying capacity for the buffalo population is K 50 000 (animals). The baseline value proportion of buffalo escaping the park is assumed to be 0.003, indicating that about 150 buffalo escape the park if the buffalo stock is close to its carrying capacity. The associated disease interaction coefficient between buffalo and livestock is 0.0001. With a healthy cattle population of, say, 200 000 animals, the number of healthy cattle that becomes instantaneously infected because of the 150 buffalo mingling with the cattle population is then XS 3000 animals.
The disease transmission coefficient within the cattle populations, , is assumed to be far lower than the disease transmission coefficient between wildlife and healthy cattle. This assumption is based on the rapid response by the local Veterinary Services Department when an FMD outbreak is reported. Immediately after an outbreak has been reported, infected animals are kept in quarantine areas in order to avoid further transmission within the cattle populations (Personal communication with the local animal health technician). The disease coefficient within cattle populations was set at 0.000001. Based on the values of the disease interaction coefficient terms as well as stock levels, one finds that with a healthy cattle stock of 200 000 animals and an infected stock of 3 000 animals, the instantaneous loss of healthy cattle due to interaction with infected cattle is IS 600 animals. The mortality rate (m) of infected cattle is rather small, and its baseline value is fixed at 5% (0.05). As indicated in the steady state analysis of chapter 4, it will be beneficial for the cattle farmer to slaughter as many of the infected animals as possible to reduce disease transmission and extract benefits from sales. Thus, the slaughter fraction of infected cattle is arbitrarily set at max 0.90 I under the conservation as well as the social planner scenarios.
It is, however, difficult to assess the conservation cost and benefit values of the buffalo, because buffalo is just one of the many species present in the park. Based on the entrance fee of R196 ($1=ZAR7.562) and the annual number of tourists, 1.4 million people (SanParks, 2011), the total (gross) tourist value of the park is known. In addition to assessing the number of the other key species in the park and adding some intrinsic, or existence, value of the buffalo, one ends up with the arbitrary assumption of a baseline value of 175 (rand/animal). The culling cost per animal is assumed to be 1000 (rand/animal). This estimate is based on the contraceptive method that is currently used to manage the elephant population in the Greater Makalali Private Game Reserve in Limpopo Province, using a contraceptive vaccine derived from Pig Zona Pellucida (Delsink et al., 2007). The maintenance cost for the buffalo stock is calculated taking into consideration that South Africa has a complicated system of fencing along its national park borders, which are regularly supervised and maintained. Some estimates of these costs do not include the capital investment in constructing fences (Perry et al., 2003). Based on these considerations, the cost to keep the buffalo in the park v is then calibrated to ensure that the net stock buffalo value [B(X) V(X)] reaches a peak value below that of the carrying capacity.
The slaughter market price for healthy cattle and infected cattle is based on survey, where the healthy animal price is 4030 S p (rand/animal). The infected animal price is assumed to be 25% lower. The maintenance cost of the cattle is based on survey information where the farmers have assessed the average monthly cost of holding, or herding cattle. Based on a monthly cost of R300 per flock and assuming an average herd size of nine, one arrives at a yearly cost of about 500 (rand/animal). The non-market benefit for livestock (eg draught power) is estimated through the weighting proportion of male and female cattle (the herd size) as well as the market prices of male and female cattle; male cattle are more valuable. Finally, the baseline discount rate is assumed to be zero, indicating that the steady states, or target populations, are similar to what is found when the current benefit in biological, or ecological, equilibrium is maximised (see Clark, 1990). The analysis has also studied the consequences of other values for some of the key parameters.
CHAPTER 1: INTRODUCTION
1.0 Background
1.1 Statement of the Problem
1.2 Objectives of the Study
1.3 Hypotheses of the Study
1.4 Approaches and Methods of the Study
1.5 Organisation of the Thesis
CHAPTER 2: REVIEW OF RELEVANT LITERATURE
2.1 Partial Equilibrium Models
2.2 Multi-sector models
2.3 Studies on the Economics of Animal Disease within Wildlife-livestock Interface
2.4. Conclusion
CHAPTER 3 : DETERMINANTS OF LIVESTOCK OWNERSHIP AMONG SMALL-SCALE FARMERS LIVING ADJACENT TO THE KNP IN LIMPOPO PROVINCE
3.0 Introduction
3.1 Economic Significance of the Livestock Sector in South Africa
3.2 Materials and Methods
3.3 Results
3.4. Conclusions and implications of the study
CHAPTER 4: ANALYTICAL FRAMEWORK FOR OPTIMAL CONTROL OF FMD TRANSMISSION FROM WILDLIFE TO LIVESTOCK POPULATIONS IN THE STUDY AREA
4.0 Introduction
4.1 FMD problem in the KNP area
4.2. The FMD transmission mechanism between buffalo and cattle populations
4.3. The Basic Mode
4.4. Cost and Benefit Functions
4.5. Solving the Model Theoretically
4.6. Conclusions
CHAPTER 5: EMPIRICAL RESULTS AND DISCUSSIONS
5.0 Introduction
5.1 Data and specification of functional forms
5.2 Results
5.3 Conclusions
CHAPTER 6: SUMMARY, CONCLUSIONS AND IMPLICATIONS FOR POLICY AND FUTURE RESEARCH
6.0 Summary and Conclusions
6.2 Implications of the study
6.3 Contributions and limitations of the study
APPENDICES
REFERENCES
