Advanced analysis in epidemiological modeling: Detection of wave

Atangana, Abdon; Araz, Seda İğret

doi:10.1101/2021.09.02.21263016

Cited by 10 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The disease-free equilibrium (DFE) of this model is therefore N, 0, 0 . Authors such as [17,19,20] have also studied these types of models.…”

Section: Which Would Be An Extension Of the S H I H S H -S V I V S Vmentioning

confidence: 99%

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Drabo,

Bere,

Nitiema

2024

Journal of Applied Mathematics

View full text Add to dashboard Cite

This work presents a stochastic model of malaria spread. We first calculated the basic reproduction number R0 of the models ShIhRhSh‐SvIv and ShLhIhRhSh‐SvLvIv in order to show that the malaria-free equilibrium is asymptotically stable; then, we used a finite Markov chain model to describe the interactions between the different compartments of the model SeLeIeReSe‐SaLaIaRaSa‐SvIv. We carried out numerical simulations of our results for two types of transmission zones: a zone with low malaria transmission and an endemic zone. Through these simulations, we first determined the invariant stationary distribution π∗ of the model, and then, we found that the use of the indoor residual spraying (IRS) method by regular application of insecticides is more effective for the elimination of malaria than the use of long-acting impregnated mosquito nets (LLINs).

show abstract

“…The disease-free equilibrium (DFE) of this model is therefore N, 0, 0 . Authors such as [17,19,20] have also studied these types of models.…”

Section: Which Would Be An Extension Of the S H I H S H -S V I V S Vmentioning

confidence: 99%

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Drabo,

Bere,

Nitiema

2024

Journal of Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…An endemic equilibrium point is the solution to the system of equations (1) in which HBV infection is present in the population. The solution starts in the given interval and stay in the interval for all time.…”

Section: Existence Of Hbv Endemic Equilibrium Pointmentioning

confidence: 99%

Analyzing hepatitis B transmission dynamics: Insights into clinical control and passive immunity strategies through mathematical modeling and simulation

Mirgichan,

Ngari,

Karanja

et al. 2024

J. Math. Prob. Equations Stat.

View full text Add to dashboard Cite

Hepatitis B virus (HBV) infection remains a pressing global public health concern, particularly in underserved rural regions of low and middle-income countries. Despite the availability of therapies, the prevalence of HBV infection persists, often due to neglect in these areas. This paper addresses the complex dynamics of HBV transmission by incorporating passive immunity and clinical control interventions into a deterministic mathematical model. The model, expressed as a system of non-linear differential equations with time-dependent infection rates, reveals the intricate interplay between passive immunity and infection susceptibility among infants born to HBV-infected mothers. Through comprehensive stability analysis and numerical simulations, we illuminate the dynamics of HBV infection within populations. Sensitivity analysis identifies critical parameters that significantly influence disease transmission, including the reproduction number and strength number. By exploring the effects of these key parameters and control measures, we provide insights into potential strategies for mitigating HBV spread. The study underscores the necessity of acknowledging passive immunity and its temporal nature in HBV transmission modeling. Moreover, it highlights the importance of addressing maternal antibody protection and the implications of control measures for public health policy. Ultimately, this research contributes to our understanding of HBV transmission dynamics and offers valuable guidance for effective interventions in combating Hepatitis B, particularly in resource-constrained regions.

show abstract

“…As explained in the paper by Atangana and Araz [6], the detection of waves can be obtained following steps. we solve equations ( S * I * R *) are obtained, then The conditions under which the above are satisfied can be obtained.…”

Section: Existing Theoriesmentioning

confidence: 99%

“…As explained in the paper by Atangana and Araz [6], the detection of waves can be obtained following steps.…”

Section: Existing Theoriesmentioning

confidence: 99%

Step forward in epidemiological modeling: Introducing the indicator function to capture waves

Atangana

Araz

2022

Preprint

Self Cite

View full text Add to dashboard Cite

In the last century mathematical modelled have been used to depict the dynamic spread of infectious. The aim is to determine the total numbers of infectious, recovered and susceptible classes, however the classes only represent accumulative. Having these classes one will be unable to predict waves, to determine a day to day numbers of newly infected cases some additional calculations are required. Collected data from real world situations are represented as day to day newly infections, from these data help to determine numbers of waves. The current existing mathematical models cannot be used to predict waves, while having known the predicted numbers of waves one can take several measures to control the situation. To solve this problem, we questioned the fact that the rates of infection and recovery are constant and suggested an indicator function, the function is obtained using experimental data. The indicator function is used as rate and introduced into the mathematical model. We considered a simple SIR model with different types of differential operators including classical and fractional derivatives. The models were solved numerically using well-known numerical schemes. The numerical solutions were plotted for different theoretical parameters, the obtained results depict real-world behaviours. To test the efficiency of this new approach, we collected data from South Africa and compared with experimental data. Not only our model waves but also it fit experimental data very accurately. This new approach will open new doors of investigation toward revolution to epidemiological modelling.

show abstract

Advanced analysis in epidemiological modeling: Detection of wave

Cited by 10 publications

References 14 publications

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Analyzing hepatitis B transmission dynamics: Insights into clinical control and passive immunity strategies through mathematical modeling and simulation

Step forward in epidemiological modeling: Introducing the indicator function to capture waves

Contact Info

Product

Resources

About