Table 1 The Model’s variables, parameters, biological meaning and values
Variable/Parameter | Biological Meaning | Initial condition/Value used in the simulations |
|---|---|---|
Antibiotic Resistance Modela | ||
X(t) | Individuals susceptible to the hospital infection | 100 |
Y(t) | Individuals infected with a sensitive strain | 1 |
Z(t) | Individuals infected with a resistant strain | 0.41 |
 Λ | Internment rate | 3.33 × 10− 2 days− 1 |
μ | Discharging rate | 3.33 × 10− 2 days− 1 |
β1 | Rate of infection with the sensitive strain | 6.45 × 10− 3 days− 1 |
β2 | Rate of infection with the resistant strain | 6.00 × 10− 3 days− 1 |
p | Fraction treated with the antibiotic | 0.7 |
γ | Recovered from infection with the sensitive strain | 2.50 × 10− 1 days− 1 |
α | Mortality rate induced by the infection | 1.15 × 10− 1 days− 1 |
θ | Rate of mutation from sensitive to resistant strains | 1.00 × 10− 7 days− 1 |
ξ | Treatment induced mutation rate | 1.00 × 10− 6 days− 1 |
ω | Rate of spontaneous plasmids transfer | 1.15 × 10− 5 days− 1 |
δ | Rate of treatment induced plasmids transfer | 1.15 × 10− 4 days− 1 |
σ | Rate of back mutation from resistant to sensitive strains | 1.00 × 10− 8 days− 1 |
Dengue Modelb | ||
SH(t) | Individuals susceptible to dengue | 1.00 × 105 |
\( {I}_H^G(t) \) | Non-hospitalized individuals infected with dengue | 1.0 |
IH(t) | Hospitalized individuals infected with dengue | 0.0 |
RH(t) | Individuals recovered from dengue | 0.0 |
VH(t) | Individuals vaccinated against dengue | 0.0 |
SM(t) | Mosquitoes susceptible to dengue | 1.50 × 105 |
LM(t) | Mosquitoes latent with dengue | 1 |
IM(t) | Mosquitoes infective with dengue | 0 |
μH | Birth/Mortality rate | 3.92 × 10− 5 days− 1 |
Ï…H | Vaccination rate | Variable |
a | Mosquitoes’ biting rate | 10 days− 1 |
b | Probability of infection from mosquitoes to humans | 0.6 |
c | Probability of infection from humans to mosquitoes | 0.6 |
γH | Recovered from infection with the sensitive strain | 5.0 × 10− 1 days− 1 |
αH | Dengue-induced mortality rate | 1.00 × 10−5 days− 1 |
p' | Fraction of dengue-infected individuals mistreated with antibiotics. | Variable |
h | Fraction of dengue-infected individuals that are hospitalized | 0.3 |
κ | Fraction of non-hospitalized dengue-infected individuals that recover from infection | 0.7 |
d | Rate of hospital discharge of dengue patients | 1.00 × 10−2 days−1 |