Typhoid Model Research Articles

Stability Analysis and Optimal Control for Spreading Typhoid Fever Model with Direct and Indirect Transmissions

This article discusses a model of spreading typhoid fever with direct and indirect transmissions. There are five compartments included in the model, namely susceptible individuals, infected individuals, chronic carrier individuals, recovered individuals, and salmonella typhi bacteria in the environment. As an effort to control and minimize the numbers of infected individuals and chronic carrier individuals, we introduce simultaneously campaign for the susceptible individuals and treatment for the infected individuals and for chronic carrier individuals. The resulting model is a system of non-linear differential equations and quite challenging to analysis globally. Existence of both disease-free equilibrium point and endemic equilibrium point are analysed analytically. Stability of the equilibrium point is analysed locally by determining the eigenvalues of the associated Jacobian matrix, Routh-Hurwitz stability criteria, and basic reproduction number () via next generation matrix. The minimum Pontryagin principle and Hamiltonian equation are referred to minimize the numbers of infected and chronic carrier individuals. Simulation is carried out using suitable values of parameters. We found that the eigenvalues for endemic equilibrium point are all negative real numbers and . Optimal paths for state and constate variables are plotted using fourth order forward-backward Runge-Kutta method. In case there are no campaign and treatments, we found and endemic occurs. When campaign and treatments are included together in the model, we found optimal paths for all compartments that minimize the number of infected and chronic carrier individuals. Giving campaign and treatments increase significantly the susceptible and recovered individuals. At the same time, it reduces significantly the infected, chronic carrier individuals, and salmonella typhi bacteria in the environment. Involving campaign and treatment in the model of spreading typhoid fever can be considered as an effective strategy to minimize the numbers of infected and chronic carrier individuals.

Numerical approximation of the typhoid disease model via Genocchi wavelet collocation method

AbstractIn this paper, we have considered the fractional typhoid disease model and obtained the numerical approximation of the model via the innovative wavelet scheme called the Genocchi wavelet collocation method (GWCM) with the help of Caputo fractional derivative for the fractional order. The approach under consideration is a powerful tool for obtaining numerical solutions to fractional-order nonlinear differential equations. The GWCM approach yields accurate solutions that are very close to exact solutions for highly nonlinear problems by avoiding data rounding and just computing a few terms. The Genocchi wavelet basis functions possess remarkable properties, including compact support, making them well-suited for approximating solutions to differential equations. The main benefit of this method lies in its capability to reduce the computational complexity associated with solving systems of ODEs, resulting in accurate and efficient solutions. The results of the developed technique, the RK4 method, and the ND solver have been compared. The numerical outcomes demonstrate that the implemented technique is incredibly effective and precise for solving the Typhoid model of fractional order. This paper contributes to numerical analysis by introducing the Genocchi wavelet method as a robust tool for solving biological models.

From intestine to beyond: Salmonella entry factors display distinct transcription pattern upon infection in murine models.

The infectious process of bacteria of the genus Salmonella requires the finely regulated use of various virulence factors. Among them, the type 3 secretion system-1 (T3SS-1) and the Rck and PagN invasins are involved in the internalization of the pathogen within eukaryotic cells, but their precise role in the host and in the pathogenic process is still poorly understood. In this study, we aimed to determine the kinetics of expression of these entry factors in a typhoid fever-like and a gastroenteritis model in mice by in vivo imaging using bioluminescent Salmonella Typhimurium reporter strains carrying chromosomal transcriptional fusions. Only pagN and T3SS-1 transcription has been clearly identified. Independently of the pathological model, the caecum was identified as the main transcription site of both pagN and the T3SS-1-encoding gene both at early and late stages of the infection. An intense transcription of pagN was also observed in deep organs in the typhoid fever-like model, while that of T3SS-1 remained quite sporadic in these organs, and mainly focused on the intestine all along the infection. This work will help to understand the respective role of these entry factors at the cellular level in the pathogenesis of Salmonella in vivo.

Numerical investigation of a typhoid disease model in fuzzy environment

Salmonella Typhi, a bacteria, is responsible for typhoid fever, a potentially dangerous infection. Typhoid fever affects a large number of people each year, estimated to be between 11 and 20 million, resulting in a high mortality rate of 128,000 to 161,000 deaths. This research investigates a robust numerical analytic strategy for typhoid fever that takes infection protection into consideration and incorporates fuzzy parameters. The use of fuzzy parameters acknowledges the variation in parameter values among individuals in the population, which leads to uncertainties. Because of their diverse histories, different age groups within this community may exhibit distinct customs, habits, and levels of resistance. Fuzzy theory appears as the most appropriate instrument for dealing with these uncertainty. With this in mind, a model of typhoid fever featuring fuzzy parameters is thoroughly examined. Two numerical techniques are developed within a fuzzy framework to address this model. We employ the non-standard finite difference (NSFD) scheme, which ensures the preservation of essential properties like dynamic consistency and positivity. Additionally, we conduct numerical simulations to illustrate the practical applicability of the developed technique. In contrast to many classical methods commonly found in the literature, the proposed approach exhibits unconditional convergence, solidifying its status as a dependable tool for investigating the dynamics of typhoid disease.

Typhoid fever dynamical model with cost-effective optimalcontrol

Typhoid fever is a highly communicable and infectious disease that can be fatal and causes severe complications if unattended to timely. The infection, at times, can be more complex, challenging, and impossible to treat as antibiotics become less effective. Hence, the effect of limited clinical efficacy of the antibiotics with corresponding relapse response to treatment on infected humans is considered in this paper by formulating a deterministic model for direct and indirect transmission mode of Typhoid infection. The basic reproduction number is analytically derived and used to implement the global sensitivity analysis. Following the sensitivity analysis result, the optimal control analysis is carried out and simulated numerically with four controls: sanitation and hygiene practice and awareness campaign control, sterilisation and disinfection control, the potency of antibiotics control and screening control. Finally, the cost-effectiveness analysis for infected and susceptible humans with four cases that compared fifteen strategies is analysed. The results indicate that the sanitation and hygiene practice and awareness campaign is good to implement for single control implementation, while for double control implementation, Strategy 6, which is the combination of Strategy 1 and the potency of antibiotics administered to typhoid patients, is the best to consider. Combining Strategy 6 and screening control is the most cost-effective for triple controls. Furthermore, the overall computation of cost-effectiveness among all the most cost-effective with all the controls combined suggests that sanitation and hygiene practice and awareness campaign is the most cost-effective strategy to implement for eradicating typhoid infection in the population and for preventing susceptible populations from contracting the bacteria.

Fractional‐calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers

AbstractTyphoid fever poses a severe hazard to public health and affects at least 27 million people annually around the globe. It is significant to conceptualize the key factors of the transmission phenomena of this bacterial infection. We formulate a novel epidemic model for typhoid fever with vaccination and carriers via Caputo‐Fabrizio operator. The fundamental results of the model are inspected analytically and the basic reproduction value are then assessed. The Jacobian matrix approach has been used to demonstrate the local stability of the infection‐free steady‐state for . We interrogated the uniqueness and existence of the solution of the recommended fractional dynamics of typhoid fever. We illustrated the solution pathways of the recommended system of typhoid fever numerically and demonstrated the dynamics of the infection with variation of different parameters. Our results demonstrated how the dynamical behavior of the typhoid fever infection is influenced by input parameters. The findings highlight the significance and persuasive behavior of fractional order and show that the model's fractional memory effects appear to be a good fit for these kinds of findings. We have shown the most attractive factors of the system for the control and prevention through our study.

Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination

We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number R0. This demonstrates the global stability of the disease-free solution if R0<1. On the contrary, if R0>1, the disease persists and positive periodic solutions exist. Numerical simulations validate our theoretical findings. To accurately fit typhoid fever data in Taiwan from 2008 to 2023, we use the model and estimate its parameters using Latin hypercube sampling and least squares techniques. A sensitivity analysis reveals the significant influence of parameters such as infection rates on the reproduction number. Increasing vaccination coverage, despite challenges in developing countries, reduces typhoid cases. Accessible and highly effective vaccines play a critical role in suppressing the epidemic, outweighing concerns about the efficacy of the vaccine. Investigating possible parameter changes in Taiwan highlights the importance of monitoring and managing transmission rates to prevent recurring annual epidemics.

Salmonella enterica serovar Typhi uses two type 3 secretion systems to replicate in human macrophages and colonize humanized mice.

Salmonella enterica serovar Typhi (S. Typhi) is a human-restricted pathogen that replicates in macrophages. In this study, we investigated the roles of the S. Typhi type 3 secretion systems (T3SSs) encoded on Salmonella pathogenicity islands (SPI)-1 (T3SS-1) and SPI-2 (T3SS-2) during human macrophage infection. We found that mutants of S. Typhi deficient for both T3SSs were defective for intramacrophage replication as measured by flow cytometry, viable bacterial counts, and live time-lapse microscopy. T3SS-secreted proteins PipB2 and SifA contributed to S. Typhi replication and were translocated into the cytosol of human macrophages through both T3SS-1 and T3SS-2, demonstrating functional redundancy for these secretion systems. Importantly, an S. Typhi mutant strain that is deficient for both T3SS-1 and T3SS-2 was severely attenuated in the ability to colonize systemic tissues in a humanized mouse model of typhoid fever. Overall, this study establishes a critical role for S. Typhi T3SSs during its replication within human macrophages and during systemic infection of humanized mice. IMPORTANCE Salmonella enterica serovar Typhi is a human-restricted pathogen that causes typhoid fever. Understanding the key virulence mechanisms that facilitate S. Typhi replication in human phagocytes will enable rational vaccine and antibiotic development to limit the spread of this pathogen. While S. Typhimurium replication in murine models has been studied extensively, there is limited information available about S. Typhi replication in human macrophages, some of which directly conflict with findings from S. Typhimurium murine models. This study establishes that both of S. Typhi's two type 3 secretion systems (T3SS-1 and T3SS-2) contribute to intramacrophage replication and virulence.

Discovery of New States of Immunomodulation for Vaccine Adjuvants via High Throughput Screening: Expanding Innate Responses to PRRs.

Stimulation of the innate immune system is crucial in both effective vaccinations and immunotherapies. This is often achieved through adjuvants, molecules that usually activate pattern recognition receptors (PRRs) and stimulate two innate immune signaling pathways: the nuclear factor kappa-light-chain-enhancer of activated B-cells pathway (NF-κB) and the interferon regulatory factors pathway (IRF). Here, we demonstrate the ability to alter and improve adjuvant activity via the addition of small molecule "immunomodulators". By modulating signaling activity instead of receptor binding, these molecules allow the customization of select innate responses. We demonstrate both inhibition and enhancement of the products of the NF-κB and IRF pathways by several orders of magnitude. Some modulators apply generally across many receptors, while others focus specifically on individual receptors. Modulators boost correlates of a protective immune responses in a commercial flu vaccine model and reduced correlates of reactogenicity in a typhoid vaccine model. These modulators have a range of applications: from adjuvanticity in prophylactics to enhancement of immunotherapy.

Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects

In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co-infection to investigate their distinctive correlation under the impact of preventative techniques considering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive investigation of the model, and the basic reproductive number is defined in terms of the existence and stability of dynamic equilibrium. Then, we obtain the sufficient requirements for the existence of an ergodic stationary distribution by utilizing a novel methodology for constructing stochastic Lyapunov candidates. Besides that, the basic stochastic reproductive R0s as a threshold that will examine the extinction and persistence of the disease. Through a rigorous analysis, this study presents the concept of piecewise derivative with the goal of modelling the co-dynamics of pneumonia and typhoid fever with varying kernels. We viewed various possibilities and described numerical strategies for addressing difficulties. Visual observations, such as chaotic and dynamical behaviour patterns, are provided to demonstrate the efficacy of the proposed notion. Thus, the innovative considerations of fractional calculus include more versatile configurations, allowing us to more effectively acclimate to the dynamic system behaviours of real-world manifestations. Finally, we discovered that treating pneumonia with typhoid fever preventative measures is the least expensive. As a result, for advantageous and cost-effective regulation of both pathogens, legislators must prioritize preventative measures while not overlooking treatment of affected patients.

Continuous Measurement of Reactive Oxygen Species Formation in Bacteria-infected Bone Marrow-derived Macrophages Using a Fluorescence Plate Reader.

Macrophages are at the center of innate immunity and are the main target cells of the intracellular pathogen Salmonella enterica serovar Typhi. The production of reactive oxygen and nitrogen species (ROS/RNS) is the host's early response to invading microbes, as oxidative stress is highly toxic for bacteria. Adequate ROS/RNS production in infected macrophages is critical for the clearance of intracellular pathogens; this is achieved by several enzymes, including inducible NADPH phagocyte oxidase (NOX) and nitric oxide synthase (iNOS), respectively. The pro-inflammatory cytokine interferon gamma (IFNγ), primarily produced by activated natural killer cells and T-helper cells type 1, is a potent inducer of iNOS. Therefore, it is crucial for infection control through oxidative microbicidal activity. To characterize the early oxidative stress response via ROS formation, which is critical for the reduction of Salmonella proliferation within macrophages, we established an in vitro model of murine macrophages infected with Salmonella enterica serovar Typhimurium (S.tm). This serovar induces a systemic infection in mice that is frequently used as a model for typhoid fever, which, in human subjects, is caused by Salmonella Typhi. We generated bone marrow-derived macrophages (BMDM) from C57BL/6N wildtype mice using macrophage colony-stimulating factor (M-CSF) stimulation for six days. Thereafter, we infected BMDM withS. tm for one hour. Shortly before infection, cells were stained with CellROXTM Deep Red reagent. In its reduced form, CellROXTM is non-fluorescent. As a result of oxidation by ROS, this reagent exhibits strong fluorescence and persists within the cells. Subsequently, changes as a result of the oxidative stress response can be measured with a TECAN Spark microplate reader over time. We designed this protocol to measure oxidative stress in macrophages through the course of an infection with an intracellular bacterium. The protocol has several advantages over established techniques. First, it allows to continuously monitor and quantify ROS production in living cells from the very start of the infection to the final clearance of the intracellular pathogen. Second, this protocol enables efficient ROS detection without stressing the cells by detaching or staining procedures. Graphical abstract.

Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review

Explaining all published articles on the typhoid disease transmission model was carried out. It has been conducted to understand how Salmonella is transmitted among humans and vectors with variation interventions to control the spread of the typhoid disease. Specific objectives were to (1) identify the model developed, (2) describe the studies, and (3) identify the interventions of the model. It systemically searched and reviewed Dimension, Scopus, and ScienceDirect databases from 2013 through to 2022 for articles that studied the spread of typhoid fever through a compartmental mathematical model. This study obtained 111 unique articles from three databases, resulting in 23 articles corresponding to the created terms. All the articles were elaborated on to identify their identities for more explanation. Various interventions were considered in the model of each article, are identified, and then summarized to find out the opportunities for model development in future works. The whole article’s content was identified and outlined regarding how mathematics plays a role in model analysis and study of typhoid disease spread with various interventions. The study of mathematical modeling for typhoid disease transmission can be developed on analysis and creating the model with direct and indirect interventions to the human population for further work.

Analysis on a coupled system of two sequential hybrid BVPs with numerical simulations to a model of typhoid treatment

In the present paper, we analyze a coupled system of nonlinear three point boundary value problems (BVPs) consisting of a coupled system of higher order hybrid sequential differential equations formulated by fractional operators. We study several new conditions in the direction of existence theory for solutions of the given hybrid system under the weaker hypotheses based on the method of measure of non-compactness in degree theory. The required conditions confirming the uniqueness and stability are derived in relation to the coupled system of hybrid sequential BVPs. Lastly, we extend our hybrid sequential system to a real mathematical model of typhoid treatment with four compartments and by deriving numerical schemes for this generalized hybrid sequential system, we analyze the variations of different fractional orders and their impact on dynamical behaviors of the mentioned hybrid system of typhoid model.

MATHEMATICAL MODEL OF TIPHOID FEVER SPREAD USING SATURATED INCIDENCE RATE

Typhoid fever is a bacterial infectious disease caused by Salmonella typhi, transmitted through food or water contaminated by feces or urine of people whowas infected by Salmonella typhi. In this research , mathematical model of typhoid fever with satura t ed incidence rate that when infected population increase, people more aware and inhibit the spread of the disease. According to model analysis, there was two equilibrium point, free disease and endemic. The basic reproduction number has been computed using next-generation matrix method . We have shown that the disease free equilibrium point of the model is globally asymptotic stable when basic reproduction number is less than unity and endemic equilibrium point is locally asymptotic stable when basic reproduction number is greater than unity. Numerical simulation was shown around e q uilibrium point. The addition of the saturated incidence rate inhibits the spread of typh oid . When the basic reproduction number is less than 1, typh oid will disappear and if the basic reproduction number is greater than 1, typh oid will remain.

Fractional order mathematical modeling of typhoid fever disease

This manuscript is devoted to focusing on the modeling and numerical solution of the dynamical model of Typhoid Fever. We use the Atangana–Baleanu operator with the Mittag–Leffler function in Caputo sense to study the behavior of the model. Both local and global stability analysis are studied. Further, for global stability, we use the Lyapunov function at both disease-free and endemic equilibrium points. As a result, the model of Typhoid fever is locally and globally stable around disease-free and endemic equilibrium points and also possesses a unique solution. The strong numerical Adams–Bashforth method is used for the numerical solution and graphical representation to justify the results. It is observed that increasing the interaction rate among the susceptible and infected population increases basic reproduction number which means that the spread of disease increases by increasing interaction rate and disease transmission can be controlled by decreasing the interaction.

A dynamic model of typhoid fever with optimal control analysis

A dynamic model of typhoid fever with optimal control analysis

Systematic reconstruction of an effector-gene network reveals determinants of Salmonella cellular and tissue tropism

The minimal genetic requirements for microbes to survive within multiorganism communities, including host-pathogen interactions, remain poorly understood. Here, we combined targeted gene mutagenesis with phenotype-guided genetic reassembly to identify a cooperative network of SPI-2 T3SS effector genes that are sufficient for Salmonella Typhimurium (STm) to cause disease in a natural host organism. Five SPI-2 effector genes support pathogen survival within the host cell cytoplasm by coordinating bacterial replication with Salmonella-containing vacuole (SCV) division. Unexpectedly, this minimal genetic repertoire does not support STm systemic infection of mice. Invivo screening revealed a second effector-gene network, encoded by the spv operon, that expands the life cycle of STm from growth in cells to deep-tissue colonization in a murine model of typhoid fever. Comparison between Salmonella infection models suggests how cooperation between effector genes drives tissue tropism in a pathogen group.

A Salmonella Typhi Controlled Human Infection Study for Assessing Correlation between Bactericidal Antibodies and Protection against Infection Induced by Typhoid Vaccination.

Vi-polysaccharide conjugate vaccines are efficacious against typhoid fever in children living in endemic settings, their recent deployment is a promising step in the control of typhoid fever. However, there is currently no accepted correlate of protection. IgG and IgA antibodies generated in response to Vi conjugate or Vi plain polysaccharide vaccination are important but there are no definitive protective titre thresholds. We adapted a luminescence-based serum bactericidal activity (SBA) for use with S. Typhi and assessed whether bactericidal antibodies induced by either Vi tetanus toxoid conjugate (Vi-TT) or Vi plain polysaccharide (Vi-PS) were associated with protection in a controlled human infection model of typhoid fever. Both Vi-PS and Vi-TT induced significant increase in SBA titre after 28 days (Vi-PS; p < 0.0001, Vi-TT; p = 0.003), however higher SBA titre at the point of challenge did not correlate with protection from infection or reduced symptom severity. We cannot eliminate the role of SBA as part of a multifactorial immune response which protects against infection, however, our results do not support a strong role for SBA as a mechanism of Vi vaccine mediated protection in the CHIM setting.

Direct and indirect transmission of typhoid fever model with optimal control

In this paper, a model for direct and indirect transmission dynamics of typhoid fever with three control interventions is analyzed. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We proved the existence and uniqueness of optimal control paths and obtained these optimal paths analytically using Pontryagin’s Maximum Principle. We analyzed our results numerically to compare various strategies of proposed controls. It is observed that the implementation of the three controls among all strategies is most successful. Thus, we conclude that in order to reduce typhoid fever threat, all the three controls must be taken into consideration concurrently.

Multi-epitope DnaK peptide vaccine accords protection against lethal S. typhimurium challenge: Elicits both cell mediated immunity and long-lasting serum-neutralizing antibody titers

Typhoid vaccine development has been impeded by inability of currently available vaccines to induce cellular immunity along with neutralizing antibodies against all serovars of S. Typhi and S. Paratyphi. Unfortunately, antibiotic treatment has shown to be an ineffective therapy due to development of resistance against multiple antibiotics. In the present study, we have explored the immunogenicity and protective efficacy of in-silico designed multi-epitope DnaK peptides as candidate vaccine molecules against Salmonella. Immunization studies in mouse typhoid model revealed three of these peptides (DP1, DP5 and DP7) are highly efficacious, stimulating both humoral and cell mediated immunity along with long lasting antibody memory response. There was significant increase in antibody titers (IgG, IgG1, IgG2a, IgA and IgM), lymphocyte proliferative responses and cytokine levels. Immunized groups showed marked reduction in organ bacterial load, fecal shedding and pronounced protection (upto 80%) as compared to unimmunized controls after challenge with S. typhimurium. Our results demonstrate the huge potential of DnaK peptide vaccine candidates (DP1, DP5 and DP7) to accord protective immunity with significant increase in survivability against Salmonella infection in mice, thus commending these molecules as promising agents to tackle typhoid.