Final Edited Sheikh Kura.docx

Mathematical model of the Population Dynamics of a of Staphylococcus aureus with dual-transmission pathways in the presence of Antibiotic-based Therapy 1. Introduction: Staphylococcus aureus (staph) is a member of the staphylococcaceae family that contains more than 50 species (Jawetz et. al, 2010, Ochei and Kolhatkar, 2008). The staph is a leading opportunistic Gram-positive pathogen in human and animal medicine, causing a wide array of hard-to-treat infections ranging from superficial skin and soft tissue infections (SSTIs) to life-threating invasive diseases such as brain abscess, pneumonia, endophthalmitis and sepsis (bloodstream) infection (Leonard and Markey, 2007). Besides this, infertility, sexual dysfunction, impotency (Esmail Khani et al. 2018) and staphylococcal food poisoning remain some of the immediate consequences of staph in humans, accounting for 68.2% of seminal fluid infection in male and female alike (Gupta and Probha, 2012). Meanwhile, staph primary exists as a human commensal, mostly in the anterior nares, from whence it’s able to seed infection, colonizing about a third of the world’s population (Col et.al 2001). The individuals most vulnerable to staphylococcal infections are children and adults of all age who are immune compromised or who have invasive medical devices. (Cunnion, 2003). Transmission of infection can however be spread from skin-to-skin by having direct contact with individuals who are appropriate carriers (Straskova et. al, 2009). Sexual transfer of Saureus is evidently a new trend of transmission which has not been widely explored. Nevertheless, S-aureus still ranks second as the major cause of nosocomial blood stream infection that leads to increased mortality, morbidity, hospital stay and lost (Gravel et. al, 2009; Klevens et. al, 2007). The adaptability of S-aureus to antibiotics is a significant characteristics that led to the emergence of methicillin –Resistant staphylococcus aureus (MRSA) in 1961 in the UK (Patrick et. al 2013). The ability of S-aureus to acquire mecA gene offers then resistance to all -lactam antibiotics. Patients infected with a methicillin-Resistant strains are twice likely to die compared with to those infected with a methicillin-susceptible strains. Nevertheless, antibiotics remain the only available option for treating staphylococcus aureus infection till date (Francois et al., 2017). The dynamics of the staphylococcal infections are complicated by the multiple interactions between the human hosts, pathogens (bacteria) and the environment (Strastkova et. al, 2009); which contribute to both 76direct human –to-human and indirect environment –to-human pathways. Mathematical modelling, simulation and analysis will offer a promising way to look into the nature of the staphylococcal infection dynamics. Beanparlant and Smith (2016) developed a metapopulation model for the spread of MRSA in correctional facilities. They consider a population within two patches with infections modelled standard insistence function in hotspots. Hogea et al. (2014) presented a basic dynamic transmission model of staphylococcus aureus in the US population. The model is dynamic and accounts for the US population growth with MRSA and MSSA strains and illustrated the population-level impact of indirect using an assumed S-aureus vaccination. 1

Wang and Ruan (2017) proposed a models that explicitly accounted for the environmental component (bacteria concentration) in a hospital setting between patients and health care workers (HCW). Batina et al. (2016) provide conditions for elimination and epidemic potential of MRSA in nursing homes. They formulated the deterministic model on a single strain of S-aurus using density dependent transmission approach with decolonization as a control strategy. All these models have their own strategy and weakness; some models only track the human population dynamics directly with nosocomial infection process. Whereas, others focus on environment components while neglecting direct human to human transmission. Meanwhile, most of the models formulated on S-aureus are purely based on hospital and nosocomial transmission. Therefore, the present study intend to propose a unified S-aureus model that allows a general non-linear incidence factors for both sexually human to human and bacteria transmission pathways with antibiotic therapy without concentrating on hospital setting.

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Statement of the problem Antimicrobial drugs resistance over the decades has been a major public health challenge on a global scale in the fight against staph. This problem originated from antibiotic pressure and drugs misuse. Staphylococcal infections were curable with the introduction of Penicillin, but decades of misuse and frequent blind prescription of antibiotics offered resistance to Penicillin. This is similarly experienced in the treatment cases using Methicillin and Vancomycin drugs. Culturing and sensitivity testing has been imperative in order to aid medical prescription process of antibiotics, for the users, since antibiotics remain the treatment option for staph infection till date. Unfortunately, mathematical models as tools for suggesting treatment regimens for staphylococcal infections in nonhospital based setting are very few and not widely explored. To this end, we intend to formulate a generalized mathematical model of staphylococcal infection with dualtransmission pathways in the presence of culture and Antibiotics Susceptibility Testing (AST).

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Aim and objectives of the study The aim of the study is to formulate a mathematical model of staphylococcus aureus with dual-transmission pathways in the presence of antibiotic-based therapy. The specific objectives of the study are to: • • • •

Develop a mathematical model for the population dynamics of a staphylococcal infection with dual-transmission pathways in the presence of Antibiotics Susceptibility Testing. Analyze for the stability otherwise the equilibrium states of the proposed model Compute and analyze the basic reproduction number Carry out the sensitivity analysis of the parameters of the proposed model

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•

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Conduct the numerical simulation of the proposed model using Matlab package Significance of the study The study will shade more light on the population dynamics of the staphylococcus aureus with dual transmission pathways in the presence of antibiotics base therapy.

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Justification of the Study: Staphylococcus aureus (S. Aureus) is one of the most common etiological agents of community – acquired and nosocomial bacteria infections (Mohammed 2005). S. Aureus has emerged as one of the most important human pathogens and has over the past decades been a leading cause of community acquired infections (Lowy, 2003). The spread of methicillin resistant strain of staphylococcus aureus (MRSA) in healthcare settings has become increasingly difficult to control and has since been able to spread in the general community which cause outbreaks (Bean Parlant and Robert Smith 2016). The characterization of S. aureus and monitoring of antimicrobial susceptibility patterns are important for clinicians in selecting empiric antimicrobial therapy will provide useful information on the surveillance of this important pathogen. The mathematical model of a population dynamics of staphylococcus aureus with dual transmission pathways in the presence of antibiotics base therapy will serve as a powerful tool for better understating of epidemiology of the pathogen and for establishing appropriate and effective control measures.

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The model formulation We construct the staphylococcal infection dynamics based on the combination of a regular SIR model and an environmental component using the Beanparlant and Smith (2016) model as a motivation. It helps us in developing a generalized S-aureus transmission model without special reference to hotspots areas and hospital setting.

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The proposed model The following assumptions on the state variables are taken into consideration with the definition of parameters given in table 1; i.

Infected individuals become susceptible at the rate through decolonization

ii.

Transmission can occur through contact with infected individuals using standard incidence function

iii.

Uncolonized (susceptible) can also acquire infection through dirty environment using saturated incidence function The figure below shows the interaction between the components

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The figure below shows the interaction between the components’

Figure 1: Schematic description of the Model

Table 1: State variables and parameters of the proposed model Variable

S (t ) C( t) I ( t) B (t) T A (t) R(t) βs βh K ω α ρ γ r1 r2 d1 d2 μ

Description Number of uncolonized (susceptible) individuals at time t Number of colonized (susceptible) individuals at time t Number of infectious individuals at time t S-aureus bacteria concentration in the dirty environment at time Number of treated individuals at time t Number of recovered individuals at time t Infection rate from environment to humans Rate of infection due to sexual transmissions Saturated concentration of the bacteria Rate of decolonization Progression rate from C to I Treatment rate due to antibiotic based therapy Rate of recovery for those treated Treatment failure resulting to persistently infected individuals Reactivation of the bacteria after recovery Diseased induced death rate Rate of disinfection of the bacteria concentration Natural death rate

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t

dS = Λ−( f B+ λh ) S+ωC−μS dt

}

dC =( f B + λh ) S−( α+ω + μ ) C−μS +r 1 T A dt dI =αC + r 2 R−( ρ+ μ+d 1 ) I ,(1) dt d TA =ρI −( r 1 +γ + μ ) T A dt dR =γ T A−( r 2+ μ ) R dt where

}

( KB+B ) (2) I + ηC λ =β ( N )

f B (C , I , B )=β s h

h

References  Boughton, C., Egan, J., Kelly, G., Markey, B. and Leonard, N. (2007) Rapid Infection of Pigs Following Exposure to Environments Contaminated with Different Levels of Salmonella Typhimurium. Foodborne Pathogens and Disease, 4, 33-40  Cole Am, Tahk S, Oren A, Yoshioka D, Kim YH, Park A, Ganz T (November 2001). “Determinant of Staphylococcus aureus nasal carriage” Clinical and Diogostic Laboaraotry Immunoogy. 8 (6) PMC 96227 PMID 11687441  Cole AM, Tahk S, Oren A, Yoshioka D, Kim YH, Park A, Ganz T (November 2001). "Determinants of Staphylococcus aureus nasal carriage". Clinical and Diagnostic Laboratory Immunology. 8 (6): 1064–9. PMC 96227. PMID 11687441.  Cunnion, K. M., Frank, M. M., 2003. Complement Activation Influences Staphylococcus aureus Adherence to Endothelial Cells. Infection and Immunity. 71 1321-1327.  Francois P, Schrenzel J (2008). "Rapid Diagnosis and typing of Staphylococcus aureus". Staphylococcus: Molecular Genetics. Caister Academic Press. ISBN 978-1-90445529-5.  Gupta R, Khasa YP, Kuhad RC: Evaluation of pretreatment methods in improving the enzymatic saccharification of cellulosic materials. Carbohydr Polym 2011, 84: 1103-1109.  Jawetz, Melnick, & Adelbergs Medical Microbiology 25TH EDITION by Geo. F. Brooks. McGraw-Hill Publishing Company, 2010.  Lowy, F. D., 1998. Staphylococcus aureus Infections. N Engl J Med. 339(8) 520-532.  Lowy, F.D. (2003). Antimicrobial resistance: the example of Staphylococcus aureus. J. Clin. Invest., 111:1265-1273.  Marc Beauparlant, Robert Smith (2016) “A metapopulation model for the spread of MRSA in correctional facilities. KeAi Publishing, Infectious Disease Modelling 1 (11- 27).  Mohamed, N., Jones, S. M., Casey, L. S., Pincus, S. E., Spitalny, G. L., 2005.

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 Ochei, J. and Kolhatkar A., (2008), Medical Laboratory Science, Theory and Practices, Tata McGraw-Hill, Page 311-347.  Patrick, M.K.N., Stefania, D., Christophe, J., John, W., Christophe, L. and Leo, M. (2013). Phenotypic and genotypic antibiotic resistance patterns of Staphylococcus aureus from raw and spontaneously fermented milk camel milk. British Journal of Science and Technology, 3(3):87-98.  Strastkova, Z., Karpiskova, S. and Karpiskova, R. (2009). Occurrence of methicillin-resistant strains of Staphylococcus aureus at a goat-breeding farm. Veterinary Medicine, 54(9):419442.

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