Disease Control in Age Structure Population

Kouokam, Etienne; Zucker, Jean-Daniel; Fondjo, Franklin; Choisy, Marc

doi:10.5402/2013/703230

Cited by 5 publications

(11 citation statements)

References 28 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Table 2 we give the parameter values and the source from which the parameter values are taken. With these parameter values, we will numerically show the asymptotic stability of E 0 and E 1 based on the values of basic reproduction number in similar lines to [33].…”

Section: Parameters Valuesmentioning

confidence: 99%

“…Taking parameter values from Table 3, the system of Eqs. (2.1)-(2.6) was numerically [34] m 0.000182 [33] solved in math-lab. The solutions of the system (2.1)-(2.6) are depicted in Fig.…”

Section: Stability Of Infection Free Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Chhetri

Vamsi

Sanjeevi

2022

Differ Equ Dyn Syst

View full text Add to dashboard Cite

COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable when R 0 < 1 , and when R 0 is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.

show abstract

Section: Parameters Valuesmentioning

confidence: 99%

“…Taking parameter values from Table 3, the system of Eqs. (2.1)-(2.6) was numerically [34] m 0.000182 [33] solved in math-lab. The solutions of the system (2.1)-(2.6) are depicted in Fig.…”

Section: Stability Of Infection Free Equilibriummentioning

confidence: 99%

See 1 more Smart Citation

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Chhetri

Vamsi

Sanjeevi

2022

Differ Equ Dyn Syst

View full text Add to dashboard Cite

show abstract

“…The classical approach consists of dividing the population into different groups, one for each age bracket under consideration, and establishing an age-dependent transmission rate. This transmission rate can be arranged in a matrix in which each element encodes the transmission probability between groups i and j (this matrix is also known as the Who Acquired Infection from Whom matrix [36,37]). It is also possible to separate the effect of the transmission itself in a common parameter and encode the number of contacts between each group in the matrix [38].…”

Section: Introductionmentioning

confidence: 99%

Data-driven contact structures: From homogeneous mixing to multilayer networks

2020

View full text Add to dashboard Cite

The modeling of the spreading of communicable diseases has experienced significant advances in the last two decades or so. This has been possible due to the proliferation of data and the development of new methods to gather, mine and analyze it. A key role has also been played by the latest advances in new disciplines like network science. Nonetheless, current models still lack a faithful representation of all possible heterogeneities and features that can be extracted from data. Here, we bridge a current gap in the mathematical modeling of infectious diseases and develop a framework that allows to account simultaneously for both the connectivity of individuals and the age-structure of the population. We compare different scenarios, namely, i) the homogeneous mixing setting, ii) one in which only the social mixing is taken into account, iii) a setting that considers the connectivity of individuals alone, and finally, iv) a multilayer representation in which both the social mixing and the number of contacts are included in the model. We analytically show that the thresholds obtained for these four scenarios are different. In addition, we conduct extensive numerical simulations and conclude that heterogeneities in the contact network are important for a proper determination of the epidemic threshold, whereas the age-structure plays a bigger role beyond the onset of the outbreak. Altogether, when it comes to evaluate interventions such as vaccination, both sources of individual heterogeneity are important and should be concurrently considered. Our results also provide an indication of the errors incurred in situations in which one cannot access all needed information in terms of connectivity and age of the population.

show abstract

“…However, there is no enough epidemiological evidence to classify the age groups in transmission. Age structure modelling studies for diseases such as influenza and Dengue can be found in ( [16], [11]). Motivated by the above, in this study, we have proposed a non-linear age structured compartmental model in which the population is divided into two age groups.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Studies on Age Structural Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Chhetri,

Vamsi,

Sanjeevi

2020

Preprint

View full text Add to dashboard Cite

COVID pandemic has catalysed the development of novel coronavirus vaccines across pharmaceutical companies and research organizations. In a situation where the vaccine is still unavailable and the disease is spreading exponentially, an effective control measures seems to be the need of an hour to at least contain the size of the disease. In this context, age related transmissibility of COVID-19 has become a public health concern. This disease has caused the most severe health issues for adults over the age of 60 with particularly fatal results for those 80 years and old. In this situation an age structured modelling could be helpful in understanding the spread of the disease across different age groups. In this study initially, we propose an age structured model and calculate the equilibrium points and basic reproduction number. Later we propose an optimal control problem to understand the roles of treatment in controlling the epidemic.From the Stability analysis we see that the infection free equilibrium remains asymptotically stable whenever R0 < 1 and as R0 crosses unity we have the infected equilibrium to be stable. From the sensitivity analysis parameters u11, b1, β1, d1 and µ were found to be sensitive. Findings from the Optimal Control studies suggests that the infection among the adult population(age ≥ 30) is least considering the second control u12 whereas, when both the controls u11 and u12 are considered together the infectives is minimum in case of young populations(age ≤ 30). The cumulative infected population reduced the maximum when the second control was considered followed by considering both the controls together. The control u12 was effective for mild epidemic (R0 ∈ (1, 2)) whereas control u11 was found to be highly effective when epidemic was severe (R0 ∈ (2, 7)) for the population of age group (≤ 30). Whereas for age group (≥ 30) the control u12 was highly effective for the entire range of basic reproduction number. The effect of saturation level in treatment is also explored numerically.

show abstract

Disease Control in Age Structure Population

Cited by 5 publications

References 28 publications

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Data-driven contact structures: From homogeneous mixing to multilayer networks

Optimal Control Studies on Age Structural Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Contact Info

Product

Resources

About