I would also like to thank all other faculty members of the Department of Computer Science & Engineering, Indian Institute of Technology, Hyderabad for their continuous review and feedback of the work and motivation to continue pursuing the research interest. Factors such as social distancing and early detection contribute greatly to controlling the spread and consequences of the epidemic.
Types of Epidemiological Studies
The behavioral adaptations in the midst of an epidemic change social contact networks and influence the epidemic's progress. Epidemiology today is not only about predicting the spread of the pathogen in a network, but more about anticipating the above things and having a model or methodology that can adapt to them.
Evolution of Epidemic Modeling
Classification of Computational Epidemiology Models
Classification based on approach
Mass Compartment Models – These are models based on differential velocity and follow a set of mathematical equations to represent the propagation of an infection in a network. Agent-based models - These are interaction-based models based on a network of people.
Use-time classification of models
Examples include Bernoulli [7], Ross, Kermack and McKendrick models for deterministic ODEs and Bartlett [8], Bailey [9] and Brauer models for stochastic ODEs.
Epidemic Quantities of Interest
SIR Model - Kermack & McKendrick (1927)
The second category of variables represents the fraction of the total population in each compartment. We also assume that a fixed fraction γ of the infected population will recover on a given day.
Evaluation of Mass Action Models
These are usually the parameter values for the total population of N and an initial number of people in the SIR compartments. The values of β and γ are based on the infection and can be adjusted as necessary based on the data. Other similar variants of the Kermack & McKendrick SIR model, such as SIS, SEIR or SEIS, work on similar assumptions and follow the methodology above.
Interaction Based Modeling
Simulation Modeling
Interaction-based modeling is a specific type of simulation modeling technique that can be used to find solutions to real-world problems. A simulation model is a set of rules that define how the system will change its state in the future. Simulation modeling gives us a way to optimize our solutions for the real world before actually implementing them.
The need for simulation modeling arises from the fundamental fact that it is not possible to have an analytical model for all the world's problems. However, unlike in the real world, we can set up a scale model and run the simulations to test our hypothesis before implementing it in the real world. Modeling a real-world problem can be divided into three phases: an abstraction of a real-world problem into a scale model, analysis and optimization of the model, and mapping the solution to the real world.
Agent Based Modeling
Components of an Agent Based Model
Advantages of Agent Based Models
Areas of Applications
Network Flows - A flow network can be represented as a directed graph where each edge has a flow and capacity (maximum flow). A flow network can be used to solve multiple problems, such as maximizing flow, minimizing cost, finding the source of flow, etc. Agents in a flow network typically have a variety of responses that can be captured with an ABM.
It can be used in places like stock exchanges, shopping markets and strategic economic simulations. ABM can be used to estimate the loss in such cases and how it will affect the system. ABM can be created for an application such as spreading fake news on Twitter or in real life.
Modeling Lifecycle of an Agent Based Model
Similarly, organizational design and induction of resources in a particular project or organization and its effect can be modeled using an ABM. Events such as the spread of the virus in a computer network, the spread of infection in an epidemic, viral market or the transmission of fake news on social media. ABM can be used in these cases where people are influenced or affected by their contact network, be it online or offline.
The objective of this phase is to have an idea of what is expected from the model. For the city module, it includes the city ID and the agent ID of the people currently residing in the city. In the case of epidemiological modeling, application-specific information consists of the original location (city of origin), health status (SIR), infection timestamp, scan status, and neighbor list for the current timestamp.
Structure of HStrat
- Network of cities
- Social Contact Network
- Mobility Model
- Transmission Model
- Recovery Model
- Healthcare Model
By default, the tool takes the value of M as 50 and distributes the population in proportion to the population of the top 50 cities in India. Implemented in an application-based component, the mobility model consists of a people movement policy. Implemented in the application-based component, the probability of infection depends on the number of infected neighbors and the total number of neighbors in the person's contact network.
The recovery model follows an exponential rate of increase in the probability of recovery as the number of days increases. This K limit can be entered by the user to represent the capacity of the HCU units. When an HCU heals people, it can stay in the same city for another day or move to a new city.
Implementation Details
Simulation Process
The tool accepts as input a configuration file containing all input parameters such as the number of agents and their attribute values, movement thresholds, infection rate, recovery rate, file paths, etc. After generating the graph structure, the agents are generated based on the input parameters with a shell script (Generate Input.sh). After the infection module, the recovery module is called to find agents that will naturally recover from the disease.
The movement module is called to find the next location of all agents based on movement probabilities. After all simulations, transitions are performed and the simulation starts the next day. All people belong to exactly one of these cities, which can be said to be his hometown.
Strategies for Resource Allocation
Staying Algorithm
We consider a real life environment of people living in multiple cities that are connected to each other. It is assumed that the person will communicate with other people in his contact network. Despite having a hometown, there are chances that people travel outside their city for multiple reasons.
Now when an infected person interacts with other susceptible people in his contact network, there is a probability that he will spread the infection. To control the epidemic, some health resources are deployed with the ability to treat the infected people, which will slow down the spread of the infection. This means that if the proportion of infected people out of the tested sample is less than a certain threshold Thm, then the HCU will infer that the level of infection is not high and move to a new city.
HCU Allocation Strategies
Experiments & Results
Experimental Setup
Results
From Figure 4.2 we can see that a higher value of Thm results in a lower top in the infection curve. The curve with 0 HCU gives us the benchmark correlation for increases in HCU execution. On closer inspection, we can also observe that there is a postponement of the peak time for infections as the number of HCUs increases.
Primary care is often used as a term for health care benefits that take a role in the neighborhood network. That being said, there is a tremendous disparity in the quality and inclusiveness of medical treatment in India. 21], showed that healthcare providers in the private sector were obliged to spend a longer duration of the procedure with their patients and perform physical tests as part of the visit in contrast to those working in public healthcare.
Universal Healthcare Schemes
Patient Protection and Affordable Care Act (ObamaCare)
Aarogyasri
Pradhan Mantri Jan Arogya Yojana (PMJAY)
Problem Statement
Modeling Healthcare Schemes
- Direct Access Scheme (Model 1)
- Referred Care Scheme (Model 2)
- Model design and implementation
- Evaluation Parameters
Delayed repayment after a certain tolerant period will cause private hospitals to withdraw their participation from the scheme and thus burden the public health service more. The HWCs will act as the first point of contact to avail the benefits of the scheme. Based on the initial diagnosis made by the HWC, the person will either be treated at the HWC in case of minor treatments or will be referred to a hospital for secondary or tertiary care.
Since, we are dealing with the secondary - and tertiary level of care; the recovery model is disabled by keeping the probability of self-recovery as 0. However, the difference between the two models lies in the fact that the Referred Care Model has an additional HWC component. The objective of these experiments is to evaluate the effect that HWCs have on the efficiency of a scheme.
Experiments & Results
Experimental Setup
Results for Direct Access Scheme (Model 1)
Experiment 2: In this experiment we analyze the effect of delay in compensation on the time needed to treat the population sample. From Figure 5.4 we can see that with an increase in delay and consequently the number of patients, there is an increase in the time it takes to treat the patients. Experiment 3: In this experiment we analyze the performance in terms of efficiency of the scheme with respect to a delay in reimbursement to the private hospitals.
Observation: Since the efficiency of public hospitals is assumed to be lower than that of private hospitals, coupled with the fact that a delay in reimbursement would result in more people coming to public hospitals, the overall efficiency of the model will decrease . From Figure 5.5, a drop in model efficiency can be observed, which becomes more apparent as the delay increases. This is also indicative of the fact that excessive pressure on a medical institution will lead to lower efficiency.
Results for Referred Care Scheme (Model 2)
Experiment 3: In this experiment we analyze the performance in terms of efficiency of the scheme with respect to an increase in the number of EWKs. The model is designed so that HWCs form a bottleneck for referral, and patients must visit them. However, since these are only the primary health care centers, the efficiency of the EWKs is assumed to be low.
Also, this decrease is not dependent on the number of HWCs as they all have almost similar efficiency, so we see very little change as the number of HWCs increases. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of vaccination to prevent it. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume 4: Contributions to Biology and Health Problems.
