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Parameters estimation and uncertainty assessment in the transmission dynamics of rabies in humans and dogs

Mfano Charles, Sayoki G. Mfinanga, G. A. Lyakurwa, Delfim F. M. Torres, Verdiana G. Masanja

Abstract

Rabies remains a pressing global public health issue, demanding effective modeling and control strategies. This study focused on developing a mathematical model using ordinary differential equations (ODEs) to estimate parameters and assess uncertainties related to the transmission dynamics of rabies in humans and dogs. To determine model parameters and address uncertainties, next-generation matrices were utilized to calculate the basic reproduction number ${\cal R}_{0}$. Furthermore, the Partial Rank Correlation Coefficient was used to identify parameters that significantly influence model outputs. The analysis of equilibrium states revealed that the rabies-free equilibrium is globally asymptotically stable when $R_0<1$, whereas the endemic equilibrium is globally asymptotically stable when ${\cal R}_{0}\geq 1$. To reduce the severity of rabies and align with the Global Rabies Control (GRC) initiative by 2030, the study recommends implementing control strategies targeting indoor domestic dogs.

Parameters estimation and uncertainty assessment in the transmission dynamics of rabies in humans and dogs

Abstract

Rabies remains a pressing global public health issue, demanding effective modeling and control strategies. This study focused on developing a mathematical model using ordinary differential equations (ODEs) to estimate parameters and assess uncertainties related to the transmission dynamics of rabies in humans and dogs. To determine model parameters and address uncertainties, next-generation matrices were utilized to calculate the basic reproduction number . Furthermore, the Partial Rank Correlation Coefficient was used to identify parameters that significantly influence model outputs. The analysis of equilibrium states revealed that the rabies-free equilibrium is globally asymptotically stable when , whereas the endemic equilibrium is globally asymptotically stable when . To reduce the severity of rabies and align with the Global Rabies Control (GRC) initiative by 2030, the study recommends implementing control strategies targeting indoor domestic dogs.

Paper Structure

This paper contains 14 sections, 4 theorems, 52 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Model Formulation
  3. Qualitative analysis
  4. Positivity of the solution
  5. Boundedness of the model solution
  6. Rabies free equilibrium ($\mathbb{E}_0$) and the basic reproduction number ${\cal R}_0$
  7. Global stability of the Rabies free equilibrium
  8. Rabies Persistence Equilibrium Point (RPEP)
  9. Quantitative analysis
  10. Parameter estimation and model fitting
  11. Parameter sensitivity analysis
  12. Numerical simulation
  13. Discussion
  14. Conclusion

Key Result

Lemma 1

All solution of the system in the region eqn1 that start in $\Omega \subset{\mathbb R }^{12}_{+}$ remain positive all the time.

Figures (13)

  • Figure 1: Schematic diagram for the flow of transmission dynamics of rabies.
  • Figure 2: The sensitivity analysis of Rabies model dynamics involved 1000 simulations employing Latin Hypercube Sampling (LHS). The analysis evaluated Partial Rank Correlation Coefficients (PRCCs) concerning (a) domestic dogs, (b) Environment, (c) Free-range dogs, and (d) Human population, respectively.
  • Figure 3: A visual representation showcasing the evolution of parameter sensitivity throughout the progression of the system dynamics. PRRC values over time span of 100 years with respect to (a) domestic dogs, (b) Environment, (c) Free-range dogs, and (d) Human population.
  • Figure 4: Model fitting and scatter plot with corresponding parameter estimation with standard deviation $\sigma$=0.05 and Confidence interval (C.I.)=95% for human population.
  • Figure 5: The sample autocorrelation of the residuals in relation to environment indicating the lack of significance at the 5% level.
  • ...and 8 more figures

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Lemma 3: See kamgang2008computation
  • Theorem 4