2024年美赛MCM/ICM报名正式开启！（附23年美赛O奖B篇优秀论文）

2024年美赛MCM/ICM报名正式开启！

（附23年美赛O奖B篇优秀论文）

3 Assumptions
In order to construct our model, we made various simplifying assumptions for the Maasai Mara itself, and for the interactions between each of the processes we modelled in the preservation, as follows:
3.1 Maasai Mara
M-I. Dynamical unifomity: We treat the Maasai Mara in its entirety as one dynamical system, rather than multiple systems interacting with each other. In reality, areas like the Mara Triangle (which is even administered by a different entity to the rest of the preserve) may present different dynamic patterns.
M-2. Mara conservancies The Mara conservancies were all created in the 21st century as alternatives to the natural preserve. Our model does not consider the effect of these conservancies on poaching,tourism, and environmental degradation, though it is likely they do have some effect, by diluting activity beyond just the preserve.
3.2 Fauna
F-1. Classifying fauna: Fauna will fit into two categories – predators and prey.
F-2. Prey growth rate: The population of prey grows in a logistic fashion, limited by a baseline carrying capacity that is negatively affected by the incidence of environmental degradation. That is. greater degradation decreases the carrying capacity for prey.
F-3. Predator growth rate: The predator growth rate is proportional to the population of prey. That is,an increase in the amount of prey will lead to predator population growth, as there is more food availability
F-4. Negative extemal infiuences on prey population: The prey population is hindered by predators and poaching, both of which are proportional to the current prey population
F-5. Migration rate: The outward migratory rate of prey is proportional to the environmental degradation Inherent inward migratory rate is taken to be a positive constant Because environmental degradation is assumed to be periodic, this makes migratory patterns periodic too. Predators are assumed not to follow migratory patterns. so their population is not affected by migration.
F-6. Human influence on predators: The predator population is hindered by both retaliatory killings by the Maasai people and tourism, which are both proportional to the current predator population. More predators means a greater likelihood of attacks on farmers’ cattle, while greater tourist populations hinders normal activity of predators.
3.3 Tourism

T-1. Eristence: Tourism is an intrinsic phenomenon. Regardless of the status of the preservation, there will be a non-zero level of tourism.
T-2. Tourists do not like crowding: There is an inherent propensity for tourists to prefer less crowded and better maintained destinations, regulated by some ” attractiveness” factor. So, few tourists in a destination will attract a proportionally larger amount of new tourists than a large amount.
T-3. Environmental Degradation: The only factors that affect tourism are itself (more tourism makes a growth in tourism hard due to the aforementioned crowding) and environmental degradation, which has a negative effect. That is, the presence of poaching or retaliatory killings, and the relative health of fauna populations does not affect tourism.
T-4. Uniform behavior: Variation in tourist background and behavior is not modelled: that is, all tourists are assumed to fall under the same bucket, instead of splitting them into luxury travellers, adventure travellers. etc. Their effects are thus also all identical at the individual level