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Epidemic Modelling [12+1] An epidemic can be modeled either from human perspective (HP) – how people get infected, react, and heal/die; or from pathogen’s success perspective (PP) – its ability to find more and more hosts before dying out. Consider a city with population of n (say, for Delhi n = 2,00,00,000) where its people are living: 15% in extreme congestion zone (ECZ) 30% in high congestion zone (HCZ) 35% in moderate congestion zone (MOCZ) 10% in mild congestion zone (MICZ) 7% in moderately spaced zone (MSZ) 2% in safe space zone (SSZ) 0.8% in ideal space zone (ISZ) 0.1% in sparse zone (SPZ) 0.1% in dispersed zone (DZ) Zones have the following description Zone Average inter-person space (radial) in Dwelling Units (DU) ECZ <=0.5 meters HCZ More than 0.5 but < 1 meter MOCZ 1 to 1.5 meters MICZ 1.5 to 2 meters MSZ 2 to 2.5 meters SSZ 2.5 to 3 meters ISZ 3 to 5 meters SPZ 5 to 8 meters DZ >8 meters A pathogen infects by spread of respiratory droplets. Such a droplet stays in air for 30 minutes as aerosol, and is then completely destroyed. Assuming a random distribution of initial carriers (i.e. carrier exists in a set of people with a very small probability, but uniformly – say there is one carrier per r persons (e.g. r = 1 million). The transmission of infection is possible with probability 0.7 if carrier is within 2 meter radius on another person for 5 seconds or more. Assume daily Mobility of Population (MOP) at three levels: Static (S) – eveyone stays at home Dynamic (D) – normal movement for work etc. Sensitive (SN) – only sick (possibly infected) stay at home/quarantine The dwelling area is 25% of the total city area. (Rest is roads, parks, offices, and so on...). The average number of persons per DU is linearly inversely proportional to Average interperson radial distance. When population moves, smaller spaces (say, a bus) get 3 times more persons for relatively shorter duration than larger spaces (say an office) fewer persons for relatively longer duration in the ratio. (a) Choose a model – HP or PP giving agruments in support of your choice for modeling the epidemic. (b) With values for n, and r, assumed as per your choice, construct a suitable inference model (program) that can answer questions as following: (i) How much time is needed for x% population to be infected (say x = 1, 5, 10, ...) (ii) Effect on answers to (i) above if MOP is S, D, or SN (iii) Identify the most important change that could be done to the city to handle a future similar epidemic better, illustrating with infection progression data after the change (as in (i) above) Answer to (a) and (b) should be well reasoned. An implementation of the inference model you construct (say in Prolog) should support your computed data. You are free to restrict the variables, without distorting the fundamental description (for example, MOP could be taken as 2 instead or 3, or fewer no of Zones), similarly, you could introduce more variables as you deem fit, but the design should be rational. A suggestive hint for Q.2: <You have full freedom to not follow the suggestion> You could think of a graph where nodes are people, pathogens the tiny travellers on the connecting arcs whose lengths are Zone distances, and reaching other side a function (of distance, probability, and so on...). View this in terms of sets and their properties to visualize a rule-base system, or a belief-world.