Predicting Disease Dynamics

Predicting Disease Dynamics

Identifying and Predicting the Dynamics of an Infectious Disease

In its broadest sense, public health research may be divided into two main categories: epidemiology and clinical trials. It is a systematic research that uses observational data obtained from a study population that is not subjected to experimental conditions in order to learn about the cause and genesis of diseases (ethology). It is an interdisciplinary science that is found in nature. Clinical epidemiology, behavioral epidemiology, occupational epidemiology, chronic disease epidemiology, infectious disease epidemiology, and environmental epidemiology are some of the fields that fall under this umbrella term. In their opinion, such a study could be carried out, for example, to learn the casual relationship between smoking and lung cancer, air pollution and respiratory illness, heart disease and diet, childhood leukemia and water contamination, as well as investigating the prevalence and incidence of HIV infection and AIDS, among other things [14] [18]. A major part of its mission is to improve the general well-being of the population.

Clinical Trials, on the other hand, are experiments that are particularly designed to examine a certain type of medical therapy or intervention in a controlled experimental environment. Among the many examples of clinical trial studies are comparing the effect of using an HIV drug versus a placebo on the length of time that patients who have contracted AIDS live, learning the effectiveness of a new drug on the development of athletes foot fungus, evaluating hormonal therapy on the reduction of breast cancer, and so forth.

A scientific inquiry that allows for precise, rigorous analysis and quantitative prediction without claiming total assurance is known as modelling. It is about articulating concepts quantitatively in order to make them more understandable. A number of authors, including Cliff and Murray and Spicer, have discussed how modeling the dynamics of infectious disease can have a direct impact on decisions such as whether or not to use curious measures, how to allocate resources efficiently, and how to deploy the most effective medical intervention techniques. [10] [20] [10] [20] The scientific area of epidemiology has reached the end of its useful life. This is not just happening by happenstance. As a result of the increased demand for competence in epidemiology and new methodologies in public health research, this is taking place at an alarming rate. According to Black’s argument in [3], epidemiologic approaches are capable of handling complex ways of evaluating public health risk indicators that come from a wide range of exposures and environmental contaminants that are prevalent in our contemporary culture. Factors and facilitators for epidemiologic techniques are emerging that are more potent than anything previously seen. The advancements in information technology in the twenty-first century, including supercharged microcomputers, the Internet, software innovations, and the exciting potential, cleared the way for a broader range of research to be carried out. When it comes to the delivery of health care today, in particular the emergence and growth of organized health care systems in a digital world, there are numerous opportunities for epidemiology and epidemiologists to shine and become involved in evidence-based public health, as well as the evaluation of health care operation and excellence. In the field of public health exploration, decisions are taken and policies are established based on good epidemiologic data analysis and reasoning, which are becoming a thing of the past. When evidence-based epidemiologic studies are conducted on significant diseases, the general public and medical professionals will benefit from the increased awareness that will be generated. [9] [17] [9] [17] [9] [17] Understanding a disease’s incidence and prevalence rates, as well as its morbidity and mortality rates, its importance (e.g., population-attributable risk fraction or global burden of disease), time (trends – whether the incidence is rising or falling), place (whether there are areas where the disease is particularly common or rare), person (the type of person who is most at risk, taking into account demographics, lifestyle, health status, and workplace), and prevention (primary and secondary prevention) are all important.

It was in the early 18th century that Daniel Bernoulli devised a model to examine the efficiency of immunizing healthy individuals against the smallpox virus in 1760 [26] that the field of epidemiological modeling was born. In addition, Hamer investigated the recurrence of measles epidemics in 1906 and conducted analyses using a discrete time model that he developed [7]. Ronald Ross [22] created differential equation models for malaria in 1911 [22], which was the beginning of the mathematical epidemiologic model that was nearly universally accepted (Ronald Ross, 1857-1932). It has been over a century since mathematical models, an extension of Ross’s model established by Kermack and Mckendrick in 1927, were constructed and epidemic threshold findings were determined [26]. A research conducted by Ross was intended to demonstrate that a disease may be eradicated by meeting specific criteria, which included not just removing all pathogen carrier insects, but also eliminating all pathogens themselves. Hethcote, 1976 and Fred, 2008 have provided in-depth treatment of such a model, which is referred to as the SIR model [25] [27]. A model lacking vital dynamics is referred to as a SIR model.

Traditional epidemiology studies that focus solely on methods of determining disease etiology, such as study design, source of bias, and casual reasoning, have demonstrated the need for a stronger link between these studies and applied epidemiology, which synthesizes and applies the results of etiologic studies to set priorities for intervention, evaluate public health interventions and policies, measures the quality and outcome of medical care, and effectively communicates the findings.

In accordance with the World Health Organization’s standard guidelines [4, the primary premise in conducting an epidemiological study is based on the observation of three fundamental values. These include the identification of significant illnesses, the rise in public health disease knowledge, and the discovery of new cases.

Identifying people or groups who are suspected of being at higher risk of contracting a disease is referred to as case discovery in medical terminology. It entails actively seeking for and methodically identifying high-risk individuals rather than waiting for them to submit themselves to medical attention after symptoms or indications of active disease have manifested in order to get treatment. Take note of the parallels between case finding and screening: both attempt to risk stratify the population using a straightforward and inexpensive method, and both believe that better results may be obtained by recognizing disease in its early stages and providing timely treatment to patients. Using a communicable illness epidemic (e.g., syphilis) as an example, case finding may be done as part of the investigation into the outbreak in order to discover potential origins of the disease. Additionally, it may be used during food-borne epidemics to identify as many potentially at-risk persons as feasible. Case finding has several advantages, including the fact that it is inexpensive and requires less people. Case finding also increases the positive predictive value of a diagnostic test by targeting high-risk individuals who have a greater underlying prevalence. Case-finding tools can aid in the improvement of treatment for people while also lowering expenses for the state by focusing on preventative care. The most significant drawback may be the possibility of increasing health disparities as a result of the difficulty in reaching some high-risk populations (homeless, refugees, etc.)

Evidence-based knowledge in epidemiologic studies refers to the definition of clinical features and distributions of diseases that currently have a significant impact on the health of local populations, with particular reference to diseases that are potentially preventable, require planned provision of health services at individual, community, and structural levels, or are otherwise of particular public concern (e.g. mental health), and the determinants of these features and distributions. Using data from the World Health Organization’s global burden of illness project, researchers can assess the relative importance of all communicable and noncommunicable diseases, as well as deliberate harms, in the worldwide population (e.g. suicide and war). In addition, while the global burden of disease does not take into consideration the extent to which diseases may be prevented or cured, it does serve as a valuable guide to which illnesses have the biggest worldwide effect – and so are of public health relevance [24].

Disease caused by an infectious agent Characterization
It is possible to qualitatively describe the pace and development of an infectious illness based on the factors that contribute to the disease’s development. Infectious diseases are caused by microorganisms that are either microscopic or macroscopic in size and are capable of reproducing themselves and invading human body tissues, as well as generating toxins that poison the cells. To assess the progression of an infectious illness, it is critical to examine the interaction of various pathogens, as well as their growth rates within the human body, as well as the body’s immunological response. The study by [6] and [16] came to the conclusion that knowing the whole process is the fundamental concept of infectious disease epidemiology, as is developing a knowledge of how specific treatments at different phases could prevent or restrict the spread of the illness.

A disease develops when an infectious pathogen makes its way into the human body through a channel of entrance, which is referred to as the route of entry. The respiratory tract, the gastrointestinal tract, and the skin are all potential entrance points for disease transmission. Infectious pathogens such as Mycobacterium tuberculosis enter the human body through the lungs, which are filled with air. Those pathogens that cause diarrhea, for example, enter the human body through contaminated food and drink that is consumed or through the use of unsanitary hands. Naturally, human skin is capable of functioning as a barrier against a wide range of infectious diseases. However, in rare circumstances, such as with malaria parasites, infectious pathogens can enter the human body when an infected mosquito bites the skin in order to suck blood from the victim.


At the beginning of the infection process, the host becomes vulnerable to infection. Here, there is no pathogen present in anyone’s system at all, but there is a low-level, unidentified, and mysterious host immunity that exists in the system. A person entering this stage may be, for example, someone who shakes hands with someone who has a common cold, or a kid who lives in the same room as an adult who has TB, among other things.

The host is then exposed to the possibility of infection. A parasite replicates and develops over time in order to infect the host, but the host may not show any obvious signs of infection and the number of pathogens present may be insufficient to enable additional transmission to occur. Individuals are placed in the exposed stage at this stage. After an infectious disease has entered and begun to multiply, the stage known as exposure is defined as follows: For example, when a person consumes food that has been contaminated with the bacterium that causes typhoid fever (Salmonella typhii), that person is said to have been exposed. In contrast, after the bacterium has penetrated the intestinal lining and begun to proliferate, the individual is considered to have reached the infected stage. There may, however, be no clinical manifestations of the disease at this time, depending on the circumstances. This occurs when the illness symptoms (complaints of a person such as headache, vomiting, dizziness, and so on) and disease signs (features like as high temperature, rapid heart rate, swelling of organs within the body) match, which can only be identified by a qualified health expert. As soon as the pathogens reach this stage, they will become plentiful enough to disseminate themselves and have the possibility of transmitting the disease to another vulnerable individual, and the sickness will have progressed to the infectious stage. Infected individuals can act as carriers, although they are not contagious themselves. They are referred to be active cases if they are contagious or contagious. Individuals reach the recovered stage when the pathogens have been removed from the ill individuals and the host has been cleansed of its infectious stage. The phrase “recovered stage” refers to a stage in which a person has completely recovered from an illness, is handicapped, or has died.

When it comes to infectious diseases, the ultimate categorization (as susceptible, exposed, infectious, or recovered) is based only on the disease’s capacity (in this case, the ability of the host to convey or transmit the pathogen). One of the main takeaways from this study is that the host’s status with respect to the disease is irrelevant, meaning that an individual who appears to be perfectly healthy and has no symptoms can be secreting a significant amount of pathogen; that the boundaries between exposed and infectious (and infectious and recovered) are somewhat blurred, and that the tendency to transmit is not as simple as turning on and off buttons. The complexity of infectious illness is heightened by the need to understand the diversity in response to disease across people and the amount of pathogens during the course of the infection period. In particular, it is important to highlight that the sick time, during which symptoms are observed, is not always associated with any single infection stage.

2. The method of obtaining information

The study from [11] [13] [19] [23] demonstrates that in order to achieve an iconic aim of an epidemiologic study, a properly constructed public health study technique must have the following elements:

In order to offer a scientific foundation for the prevention of illness and damage, as well as the promotion of health, it is necessary to first identify the cause, the genesis of the disease, and environmental variables that have an influence on health.

b. Assesses the relative relevance of various causes of disease, disability, and mortality in order to define research and intervention priorities in these areas.

Identification of those parts of the population that are most at risk from certain causes of ill health in order for the suggested action to be directed in the most effective manner

In addition, it assesses the efficacy of health-care programs and services in improving the general public’s health.

The professionals who work in epidemiological research are primarily concerned with identifying the characteristics that are significant in defining the pattern of a disease and the mode of transmission or dissemination.

According to this hypothesis, there is a constant population, N, which is separated into three states: susceptible S, infected I, and recovered or immune R. The assumption is that the population is divided into three states. To be more explicit, the model encompasses the most basic form of the epidemic SIR model.

The first group consists of persons who have the potential to get infected with a certain disease or virus. Individuals who are afflicted and have the potential to infect others make up the second category. Occasionally, these models contain a class of exposed individuals, designated as E, who are diseased but are unable to transmit the disease. In the end, the class R reflects people who have recovered from the sickness and have developed immunity against infection. Immune responses are triggered by the majority of viral infections, including measles and chickenpox [5]. Once the body has become familiar with a specific sickness, it is very improbable that it would contract it again. When a host is afflicted with a disease, they develop a lifelong immunity to that illness, according to R.

2.1 Factors to consider when modeling

When modeling an epidemic, it is important to take into account aspects such as population structure and demography (age stratification, gender stratification, geographic location, and so on), the natural history of the illness (latency, infectious period, immunity, and so on), and intervention (at what stage of disease transmission).

2.1.1 The rate of transmission

Consider the following example of a person who is sensitive to disease:

The rate of contracting another individual (c) is the rate of contact that applies to all individuals, regardless of whether or not they are infected.

It is necessary to come into touch with infected persons for transmission to occur, and the rate of encountering infectious individuals is expressed as cI/N, where I/N is the proportion of infectious population, I is the number of infected, and N is the entire population.

The rate of transmission from infected people is provided by the ratio ‘pcI/N,’ which is also known as the force of infection, where p is the probability of transmission when an infectious individual comes into touch with a vulnerable one.

If we take into account all susceptible people, the total transmission rate in a population is pcSI/N, where S is the total number of susceptible persons in the community. Most of the time, the letters ‘pc’ are transcribed as ‘b’.

The Simulation of the Epidemic Model (2.2) (SIR)

It is necessary to apply a derivative method in order to determine the time derivatives of S, I, and R. The derivative, given a value of S, I, and R at a given time t, determines the time derivatives of S, I, and R, as well as model parameters such as the recovery duration and transmission rate.

It is always possible to have a population size of N equal to S+I+R since in the model there are no births or deaths.

In this equation, dS/dt = (-bSI/N + gR),

When dI/dt = bSI/N – aI, the equation is

dR/dt = aI – gR = aI – gR

Differential equations may be used to quantitatively describe the transmission of a disease caused by a microbe across a population, as they can be used to simulate many other processes connected with live creatures. There have been numerous models developed to describe the dynamics of disease spread in a population, but the SIR model presented here combines relative simplicity with good modeling of diseases that are spread from person to person and that the general public is familiar with, such as measles, smallpox, and influenza, to name a few examples.

According to the SIR model, members of a population are divided into three categories: those who are susceptible to infection, those who have been infected and are able to spread the disease to susceptible individuals, and those who have recovered from the disease and are immune to subsequent re-infection. The SIR model is based on the assumption that a population is homogeneous. It is possible for an individual to go in only one direction at a time. The two essential parameters of the model, a (the daily infection rate) and b (the daily recovery rate), function as rate constants, controlling how quickly members proceed into the I and R groups, respectively. A composite parameter, g = a/b, is frequently employed, and it is referred to as the contact number in some circles. The differential equations that characterize the SIR model are as follows:

Because solving such an equation algebraically is difficult, the integration approach is employed. As a result, it is possible to see changes in the different rates at each stage of the model over the course of time. When differentiating an equation, the derivatives show how the slopes (changes in rate) relate to the model at any given moment in time, which is known as the inverse relationship.

Initially, S(0) equals one.

It is equal to (bs/a -1)ai, I= I/N, and S= S/N. It is equal to (bs/a -1)ai, I= I/N, and S = S/N.

An epidemic now happens when the number of sick people grows significantly.

dI/dt is greater than zero.

When b/a > 1, this is the case.

On the contrary, if the number of sick people diminishes, the illness will eventually die out.

dI/dt 0 dI/dt

This is true when b/a is less than one.

The base reproduction number is represented by b/a = R0. It is the average number of secondary infections caused by a single infected case in a population that is fully susceptible to the virus.

When the beginning criteria for these groups are provided, the change in the size of these groups may be displayed over time to show how they have changed.

Results of the Simulation
The question of whether an epidemic will occur under certain initial conditions can now be discussed in terms of the contact number, and it is reasonable to expect that we will be able to empirically determine that the transition between epidemic and non-epidemic states occurs when the initial fraction of the population in the susceptible group equals the reciprocal of the number of infected individuals occurs. The recovery rate,b may also be introduced indirectly by introducing the more accessible length of the disease,1/b, as the more accessible duration of the disease

By explaining epidemic dynamics in terms of these more readily comprehensible parameters and enabling R to convert these more easily understandable parameters to the real model parameters behind the scenes, it is feasible to adapt talks of a critical issue to the general public. A benefit of this model’s dynamic output is that it allows for discussions of the influence of changing parameters on the type of disease transmission in a population without having to resort to mathematical formulae that control the model. In particular, by manipulating the appropriate rates of the model, it is possible to investigate the significance of the infected number and the effect of artificially moving members of the population directly from the susceptible group to the recovered (and therefore immune) group through immunization.


A close examination of the SIR model will yield valuable insights into the dynamics of the illness in a community setting. An epidemic is said to have begun if the proportion of the population infected with the disease is initially rising (i.e., dI/dt > 0 at t = 0), which indicates that the disease has begun spreading. It is at this moment that the change from epidemic to non-epidemic transmission of a disease happens, and an examination of the differential equations will soon indicate that this transition point occurs when so= b/a = 0. Additionally, the peak of an epidemic occurs when s=b/a and the rate of change of the infected group ceases to increase and begins to decrease, respectively. In addition, the contact number has a readily recognized “real-world” interpretation: it represents the average number of vulnerable individuals of the general population. While an infected individual is present in the infected group, the illness is disseminated by that individual. The anatomy of an epidemic is such that the number of infections will not be severe and will be minimal at first, as a result of the stochastic character of the epidemic. The illness then begins to spread more widely and more quickly as a result of the increasing prevalence. As illness reduces the number of vulnerable individuals, the rate of infection spreads at a slower pace over time.

4.1 Disappointments

It is assumed in the basic SIR models described here that the overall population size remains constant and that the population is mixing uniformly and homogeneously throughout. Age, gender, and geographical location are only a few of the characteristics that influence mixing. Individuals from diverse geographical and socio-economic backgrounds have varying rates of contact. Furthermore, the models do not take into account random effects, which can be quite relevant when s or I are tiny.

In our attempts to prevent the spread of the disease, we must choose the most effective approach that will provide the most public health advantages. Mathematical models can assist us in better understanding the transmission of an infectious illness and in testing the effectiveness of various control measures. In this work, the epidemic problem is handled by the use of the SIR model and the R statistical package software, as well as through simulation of the epidemic problem. It is possible to create several deterministic models by selecting a different number and kind of epidemic models. The analysis is based on the theory of dynamical systems, which is the approach taken. It is reasonable enough to support the modeling method, and it clarifies the assumptions that underpin the approach to modeling. Model analysis and simulation predictions indicate critical data that should be obtained as well as control techniques that might be applied in order to get the best possible results. Obtaining estimates of R0for different illnesses is important for comparing different diseases. When R0 > 1, an outbreak is averted. When R0S(0) 1, an epidemic is prevented. As a result, if the original susceptible percentage has been decreased to less than 1/R0, for example by vaccination, an epidemic can be avoided.



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