Question

I want detailed step by step research proposal in this format:

Introduction
Literature Survey
Motivation
Research Statement
Objective
Probable Methodology
Expected outcome
Plan of research
Reference

Topic:
Using mathematical models to study the impact of infectious diseases on public health

Answer 1

MATHEMATICAL MODELS TO STUDY THE IMPACT OF INFECTIOUS DISEASES ON PUBLIC HEALTH

INTRODUCTION

Infectious diseases pose a constant threat to human beings. Every individual on the earth can be affected by a disease. The emergence and re-emergence of infectious diseases have become a significant worldwide problem. Proper understanding of transmission mechanisms of diseases caused by existing and new pathogens may facilitate devising prevention tools. Prevention tools against transmissions, including vaccines and drugs, need to be developed at a similar pace to that of the microbes. Implementation and proper use of these sophisticated tools against the microbes is another challenge. This thesis addresses this multi-faceted issue and explores some theoretical frameworks. The current chapter intends to provide some basic information about the infection mechanisms of microbes, their orientation, control mechanism and the role of mathematical models in the epidemiology.

Infectious diseases

An infectious disease is caused by various microbes or pathogen. Most of them are usually microorganisms. Few of them are visible by naked eyes. The most common pathogens are different types of viruses and bacteria. Fungi and Protozoa are also known as pathogens and are responsible for various diseases. Diseases caused by these pathogens are termed as ‘infectious’ as these pathogens can be easily transmitted from one infected person to another non-infected person. The most common and well-known example of such diseases could be influenza or flu that is caused by some kinds of viruses. HIV, mumps, measles, rubella, smallpox, malaria have also caused millions of infections and deaths. Many of these diseases are still prevalent at local or global scales and threaten public health.

Pathogens

As mentioned above, pathogens are solely responsible for causing an infectious disease. In this sub-section we briefly review some common pathogens that cause diseases. We highlight the life cycles and infection mechanisms of the pathogens that are useful and important information in modelling their spread.

Bacteria: Bacteria, single-celled organisms, are well known microbes that cause various diseases. However, most of the bacteria are harmless and some are even beneficial to human. Bacteria are useful in producing cheese, yogurt, and chemicals and medicines. They also play some critical role to synthesize food particles in our intestine to produce energy. Insulin that saves millions of diabetic patients is also produced from genetically modified bacteria. Some bacteria, however, are harmful and life threatening. Gastritis, pneumonia, meningitis, gonorrhoea are some examples caused by various bacteria .Most of the bacterial diseases can be treated by antibiotics.

Viruses: Viruses are the most common and harmful microorganisms that cause severe diseases to human and other species. Influenza or flu which probably no one can avoid, is caused by viruses. Other examples of viral diseases include chickenpox, herpes, human papillomavirus (HPV), mumps, measles, rubella, viral hepatitis, viral meningitis, and viral pneumonia. Human immunodeficiency virus (HIV) is another deadly virus that spreads mainly through sexual contacts and causes AIDS.

Viruses cannot live by themselves, and they need other living cells for their reproduction. Unlike bacterial diseases, viral diseases cannot be treated by antibiotics. Since viruses use host’s cells for reproduction, an antiviral drug could be highly toxic and life-threatening for the host. Thus, instead of killing the target cells, antiviral drugs are used to inhibit viral replication processes. Antiviral drugs act to limit the viral loads and helps keep the infected individual healthy until host’s immune system controls the infection and eliminates the pathogen. In terms of the well-known characterization of HIV replication process, several antiretroviral drugs can be combined to hinder major steps of the viral replication such as fusion, reverse transcriptase, protease, and integrase. The positive side of viral infections, however, is that it develops immunity for the infected hosts which helps prevent them from a successive infection.

Fungi: Fungi are microorganisms that widely vary in sizes from uni-cellular, such as yeast, to multicellular, such as mushrooms and toadstools which can easily be seen with naked eyes. Fungi play a critical role in decomposing dead materials which in turn provide nutrients to the land. The lifesaving antibiotic penicillin is also produced from the fungus Penicillium chrysogenum. Some fungi are harmful by causing infections to plants and animals. Candidiasis, histoplasmosis, mucorycosis, ringworm are common examples of diseases caused by fungi. Vaginal yeast and thrush are fungal diseases that can cause infection to the immunocompromised individuals relatively easily.

Protozoa: Protozoa are comparatively large single-celled organisms. Some protozoa are useful. For example, in the sewage treatment systems, protozoa are used for decomposing organic matters. Some others are human parasites that cause diseases, such as malaria, toxoplasmosis, cryptosporidiosis, trichomoniasis, leishmaniasis, amoebiasis, amoebic dysentery, and acanthamoeba keratitis. Protozoa can be spread through contaminated food, water or through a vector or carrier like arthropod mosquito. The well-known protozoa species Plasmodium vibax that causes malaria spread through female anopheles mosquitoes. When a female mosquito bites an infected person it receives the parasite plasmodium. The parasite grows and reproduces inside the mosquito. When this mosquito bites another person the parasite can be transmitted through its saliva to that person. Malaria is one of the leading death causing diseases that is responsible for about 700,000 deaths each year worldwide.

LITERATURE SURVEY

The very first publication addressing the mathematical modeling of epidemics dates back in 1766. In this seminal paper, Essai d’une nouvelle analyze de la mortalité causée par la petite vérole, Daniel Bernoulli developed a mathematical model to analyze the mortality due to smallpox in England, which at that time was one in of the total mortality. Bernoulli used his model to show that inoculation against the virus would increase the life expectancy at birth by about three years. A translation in English and review of this work can be found in Sally Blower (2004), while a revi-sion of the main findings and a presentation of the criticism by D’Alembert appears in Dietz and Heesterbeek (2002). Lambert, in 1772, followed up the work of Bernoulli extending the model by incorporating age-dependent parameters. Laplace has also worked on the same concept. However this line of research has not been developed systematically until the benchmark paper of Ross in 1911, which actually establishes modern mathematical epidemiology. In this work, Ross addressed the mechanistic a priori modeling approach using a set of equations to approximate the discrete-time dynamics of malaria through the mosquito-borne pathogen transmission (for a discussion and a review of this model see also Smith et al. [2012]

Following up the work of Ross, Kermack and McKendrick published three seminal papers which founded the determin-istic compartmental epidemic modeling. In these papers, they addressed the mass–action incident in disease transmission cycle, suggesting that the probability of infection of a susceptible (virgin from illness) is analogous to the number of its contacts with infected individuals. Hence, the rate at which susceptibles become infected is given by kSI where S and I represent population densities of susceptible and infected people, respectively. In this context, the rate at which infected individuals become recovered is given by λI, while the rate at which recovered individuals become again susceptible is given by μR; k, λ and μ are analogy constants. This mechanistic-deterministic representation holds strong analogy to the Law of Mass Action introduced by Guldberg and Waage in 1864 and is called the SIR model, implying homogeneous mixing of the contacts and conservation of the total mass (population) as well as relatively low rates of interaction. Forty years after the paper of Ross, MacDonald extended Ross’s model to explain in depth the transmission pro-cess of malaria and propose methods for eradicating the disease on an operational level. Due to the importance of MacDonald’s contribution to the field by exploiting the use of computers, mathematical models for the dynamics and the control of mosquito-transmitted pathogens are known as Ross–MacDonald models. At this point it would be remiss of us not to mention the work infection spreads from an infected to a susceptible individual through discrete time Markov chain events. This representation set the basis of contemporary stochastic epidemic modeling.

At this point it would be remiss of us not to mention the work of Enko,who in 1889 published a remarkable probabilistic model for describing the epidemic of measles in discrete time. With the use of the model, Enko evaluated the number of contacts between infective and susceptible in the population. The model of Enko is the precursor of the famous Reed-Frost chain binomial model introduced by W.H. Frost in 1928 in biostatistics lectures at Johns Hopkins University (not published then in a journal, but published in 1979). This model assumes that the infection spreads from an infected to a susceptible individual through discrete time Markov chain events. This representation set the basis of contemporary stochastic epidemic modeling.

MOTIVATION

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals.

RESEARCH STATEMENT

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.

OBJECTIVE

• Current role and potential opportunities for modelling in public health decision-making.
• Modelling infectious diseases for policy: the example of a rapid TB diagnostic.
• Building useful models.
• Linking model results to public health policy around infectious diseases.
• The challenges of using models and approaches to addressing them.
• Recommendations for a future framework.

PROBABLE METHODOLOGY

Mathematical modeling and simulation allows for rapid assessment. Simulation is also used when the cost of collecting data is prohibitively expensive, or there are a large number of experimental conditions to test. Over the years, a vast number of approaches have been proposed looking at the problem from different perspectives. These encompass three general categories:

1. statistical methods for surveillance of outbreaks and identification of spatial patterns in real epidemics,
2. mathematical models within the context of dynamical systems (also called state-space models) used to forecast the evolution of a “hypothetical” or on-going epidemic spread, and
3. machine learning/ expert methods for the forecasting of the evolution of an ongoing epidemic.

EXPECTED OUTCOME

The primary outcomes were the description of the characteristics of the mathematical models incorporated, and the description of the design part considered in the process of planning studies or surveillance systems. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6).

PLAN OF RESEARCH

The characteristics of mathematical models used in planning studies were summarised stratified by study type, i.e. observational and surveillance studies, and clinical trials. We described the infections and populations studied, the main characteristics of the mathematical model used, the main outcome of the study, and the design outcomes investigated by the authors. If there were multiple publications using the same model for the same setting to investigate the same study design, the earliest publication was considered to be the original. We also documented model reporting items (e.g. diagram of the model or parameters values) and how the infection transmission was modelled.

Follow-up	The model was used to determine/inform the follow-up time of the study.
Timing of sampling	The model was used to determine/inform at which time point(s) sampling should be performed.
Frequency	The model was used to determine/inform the frequency at which sampling has to be collected (over time) during the study.
Number	The model was used to determine/inform the number of sampling to collect over time during the study.
Monitoring	The model was used to identify parameters or indicators that should be monitored during the study.
Sample size	The model was used to determine/inform the sample size.
Whom	The model was used to determine/inform which subgroups of the population studied should be sampled.
Power	The model was used to perform statistical power calculations.

REFERENCE

• Keeling MJ, Bjørnstad ON, Grenfell BT. Metapopulation dynamics of infectious diseases. In: Hanski IA, Gaggiotti OE, eds. Ecology, Genetics and Evolution of Metapopulations. Standard Methods for Inventory and Monitoring. Elsevier, 2004.
• World Health Organization. Research for universal health coverage. Geneva, Switzerland: World Health Organization; 2013.

• Agur Z, Cojocaru L, Anderson RM, Danon YL. Pulse mass measles vaccination across age cohorts. Proc Natl Acad Sci USA 1993;
• A.L. Grosso, K.H. Tram, O. Ryan, and S. Baral, 2012. Countries where HIV is concentrated among most-at-risk populations get disproportionally lower funding from PEPFAR, Health Affairs.

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